WorldWideScience

Sample records for next-to-leading order perturbative

  1. Production of transverse energy from minijets in next-to-leading order perturbative QCD

    CERN Document Server

    Eskola, Kari J

    2000-01-01

    We compute in next-to-leading order (NLO) perturbative QCD the transverse energy carried into the central rapidity unit of hadron or nuclear collisions by the partons freed in the few-GeV subcollisions. The formulation is based on a rapidity window and a measurement function of a new type. The behaviour of the NLO results as a function of the minimum transverse momentum and as a function of the scale choice is studied. The NLO results are found to be stable relative to the leading-order ones even in the few-GeV domain.

  2. The Matrix Element Method at Next-to-Leading Order

    OpenAIRE

    Campbell, John M.; Giele, Walter T.; Williams, Ciaran

    2012-01-01

    This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...

  3. Some higher moments of deep inelastic structure functions at next-to-next-to-leading order of perturbative QCD

    International Nuclear Information System (INIS)

    Retey, A.; Vermaseren, J.A.M.

    2001-01-01

    We present the analytic next-to-next-to-leading QCD calculation of some higher moments of deep inelastic structure functions in the leading twist approximation. We give results for the moments N=1,3,5,7,9,11,13 of the structure function F 3 . Similarly we present the moments N=10,12 for the flavour singlet and N=12,14 for the non-singlet structure functions F 2 and F L . We have calculated both the three-loop anomalous dimensions of the corresponding operators and the three-loop coefficient functions of the moments of these structure functions

  4. Higgs production at next-to-next-to-leading order

    Indian Academy of Sciences (India)

    Instituut-Lorentz, University of Leiden, Leiden, The Netherlands. Abstract. We describe the calculation of inclusive Higgs boson production at hadronic colliders at next-to-next-to-leading order (NNLO) in perturbative quantum chromody- namics. We have used the technique developed in ref. [4]. Our results agree with those.

  5. Fourth generation CP violation effects on B-->Kpi, phiK, and rhoK in next-to-leading-order perturbative QCD.

    Science.gov (United States)

    Hou, Wei-Shu; Li, Hsiang-nan; Mishima, Satoshi; Nagashima, Makiko

    2007-03-30

    We study the effect from a sequential fourth generation quark on penguin-dominated two-body nonleptonic B meson decays in the next-to-leading order perturbative QCD formalism. With an enhancement of the color-suppressed tree amplitude and possibility of a new CP phase in the electroweak penguin amplitude, we can account better for A(CP)(B(0)-->K+ pi-)-A(CP)(B+-->K+ pi0). Taking |V(t's)V(t'b)| approximately 0.02 with a phase just below 90 degrees, which is consistent with the b-->sl+ l- rate and the B(s) mixing parameter Deltam(B)(s), we find a downward shift in the mixing-induced CP asymmetries of B(0)-->K(S)(pi 0) and phi(K)(S). The predicted behavior for B(0)-->rho(0)(K)(S) is opposite.

  6. Anatomy of Bs → PV decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach

    Science.gov (United States)

    Yan, Da-Cheng; Yang, Ping; Liu, Xin; Xiao, Zhen-Jun

    2018-06-01

    In this paper, we will make systematic calculations for the branching ratios and the CP-violating asymmetries of the twenty one Bbars0 → PV decays by employing the perturbative QCD (PQCD) factorization approach. Besides the full leading-order (LO) contributions, all currently known next-to-leading order (NLO) contributions are taken into account. We found numerically that: (a) the NLO contributions can provide ∼ 40% enhancement to the LO PQCD predictions for B (Bbars0 →K0K bar * 0) and B (Bbars0 →K±K*∓), or a ∼ 37% reduction to B (Bbars0 →π-K*+); and we confirmed that the inclusion of the known NLO contributions can improve significantly the agreement between the theory and those currently available experimental measurements; (b) the total effects on the PQCD predictions for the relevant Bs0 → P transition form factors after the inclusion of the NLO twist-2 and twist-3 contributions is generally small in magnitude: less than 10% enhancement respect to the leading order result; (c) for the "tree" dominated decay Bbars0 →K+ρ- and the "color-suppressed-tree" decay Bbars0 →π0K*0, the big difference between the PQCD predictions for their branching ratios are induced by different topological structure and by interference effects among the decay amplitude AT,C and AP: constructive for the first decay but destructive for the second one; and (d) for Bbars0 → V (η ,η‧) decays, the complex pattern of the PQCD predictions for their branching ratios can be understood by rather different topological structures and the interference effects between the decay amplitude A (Vηq) and A (Vηs) due to the η-η‧ mixing.

  7. Next to leading order three jet production at hadron colliders

    International Nuclear Information System (INIS)

    Kilgore, W.

    1997-01-01

    Results from a next-to-leading order event generator of purely gluonic jet production are presented. This calculation is the first step in the construction of a full next-to-leading order calculation of three jet production at hadron colliders. Several jet algorithms commonly used in experiments are implemented and their numerical stability is investigated. A numerical instability is found in the iterative cone algorithm which makes it inappropriate for use in fixed order calculations beyond leading order. (author)

  8. Next-To-Leading Order Determination of Fragmentation Functions

    CERN Document Server

    Bourhis, L; Guillet, J P; Werlen, M

    2001-01-01

    We analyse LEP and PETRA data on single inclusive charged hadron cross-sections to establish new sets of Next-to-Leading order Fragmentation Functions. Data on hadro-production of large-$p_{\\bot}$ hadrons are also used to constrain the gluon Fragmentation Function. We carry out a critical comparison with other NLO parametrizations.

  9. Next-to-leading order corrections to the valon model

    Indian Academy of Sciences (India)

    Next-to-leading order corrections to the valon model. G R BOROUN. ∗ and E ESFANDYARI. Physics Department, Razi University, Kermanshah 67149, Iran. ∗. Corresponding author. E-mail: grboroun@gmail.com; boroun@razi.ac.ir. MS received 17 January 2014; revised 31 October 2014; accepted 21 November 2014.

  10. Next-to-leading order corrections to the valon model

    Indian Academy of Sciences (India)

    A seminumerical solution to the valon model at next-to-leading order (NLO) in the Laguerre polynomials is presented. We used the valon model to generate the structure of proton with respect to the Laguerre polynomials method. The results are compared with H1 data and other parametrizations.

  11. Next to leading order semi-inclusive spin asymmetries

    International Nuclear Information System (INIS)

    Florian, D. de; Epele, L.N.; Fanchiotti, H.; Garcia C, C.A.; Sassot, R.

    1996-04-01

    We have computed semi-inclusive spin asymmetries for proton and deuteron targets including next to leading order (NLO) QCD corrections and contributions coming from the target fragmentation region. These corrections have been estimated using NLO fragmentation functions, parton distributions and also a model for spin dependent fracture functions which is proposed here. We have found that NLO corrections are small but non-negligible in a scheme where gluons are polarised and that our estimate for target fragmentation effects, which is in agreement with the available semi-inclusive data, does not modify significantly charged asymmetries but is non-negligible for the so called difference asymmetries. (author). 18 refs., 7 figs

  12. Double collinear splitting amplitudes at next-to-leading order

    Energy Technology Data Exchange (ETDEWEB)

    Sborlini, Germán F.R. [Departamento de Física and IFIBA, FCEyN, Universidad de Buenos Aires (1428) Pabellón 1 Ciudad Universitaria, Capital Federal (Argentina); Instituto de Física Corpuscular, Universitat de València -Consejo Superior de Investigaciones Científicas,Parc Científic, E-46980 Paterna (Valencia) (Spain); Florian, Daniel de [Departamento de Física and IFIBA, FCEyN, Universidad de Buenos Aires (1428) Pabellón 1 Ciudad Universitaria, Capital Federal (Argentina); Rodrigo, Germán [Instituto de Física Corpuscular, Universitat de València -Consejo Superior de Investigaciones Científicas,Parc Científic, E-46980 Paterna (Valencia) (Spain)

    2014-01-07

    We compute the next-to-leading order (NLO) QCD corrections to the 1→2 splitting amplitudes in different dimensional regularization (DREG) schemes. Besides recovering previously known results, we explore new DREG schemes and analyze their consistency by comparing the divergent structure with the expected behavior predicted by Catani’s formula. Through the introduction of scalar-gluons, we show the relation among splittings matrices computed using different schemes. Also, we extended this analysis to cover the double collinear limit of scattering amplitudes in the context of QCD+QED.

  13. Comparison of three jet events to predictions from a next-to-leading order calculation

    Energy Technology Data Exchange (ETDEWEB)

    Brandl, Alexander [Univ. of New Mexico, Albuquerque, NM (United States)

    2002-01-01

    The properties of three-jet events in data of integrated luminosity 86±4 pb-1 from CDF Run 1b and with total transverse energy greater than 175 GeV have been analyzed and compared to predictions from a next-to-leading order perturbative QCD calculation.

  14. Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD.

    Science.gov (United States)

    Dixon, Lance J; Luo, Ming-Xing; Shtabovenko, Vladyslav; Yang, Tong-Zhi; Zhu, Hua Xing

    2018-03-09

    The energy-energy correlation (EEC) between two detectors in e^{+}e^{-} annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

  15. Top-quark decay at next-to-next-to-leading order in QCD.

    Science.gov (United States)

    Gao, Jun; Li, Chong Sheng; Zhu, Hua Xing

    2013-01-25

    We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and W boson width effects. In particular, we also show the first results of the fully differential decay rates for the top-quark semileptonic decay t → W(+)(l(+)ν)b at next-to-next-to-leading order in QCD. Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory. Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.

  16. High temperature color conductivity at next-to-leading log order

    International Nuclear Information System (INIS)

    Arnold, Peter; Yaffe, Laurence G.

    2000-01-01

    The non-Abelian analogue of electrical conductivity at high temperature has previously been known only at leading logarithmic order -- that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling. We calculate the first sub-leading correction. This has immediate application to improving, to next-to-leading log order, both effective theories of non-perturbative color dynamics, and calculations of the hot electroweak baryon number violation rate

  17. QCD with two colors at finite baryon density at next-to-leading order

    International Nuclear Information System (INIS)

    Splittorff, K.; Toublan, D.; Verbaarschot, J.J.M.

    2002-01-01

    We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau-Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order

  18. Heavy-quark fragmentation functions at next-to-leading perturbative QCD

    Energy Technology Data Exchange (ETDEWEB)

    Moosavi Nejad, S.M. [Yazd University, Faculty of Physics, Yazd (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of); Sartipi Yarahmadi, P. [Yazd University, Faculty of Physics, Yazd (Iran, Islamic Republic of)

    2016-10-15

    It is well known that the dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. This mechanism is described by the fragmentation functions (FFs) which are the universal and process-independent functions. Here, we review the perturbative FFs formalism as an appropriate tool for studying these hadronization processes and detail the extension of this formalism at next-to-leading order (NLO). Using Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to fragment into a S-wave heavy meson at NLO. As an example, we study the LO and NLO FFs for a charm quark to split into the S-wave D-meson and compare our analytic results both with experimental data and well-known phenomenological models. (orig.)

  19. Mueller-Navelet jets in next-to-leading order BFKL. Theory versus experiment

    Energy Technology Data Exchange (ETDEWEB)

    Caporale, F.; Murdaca, B.; Papa, A. [Universita della Calabria, Dipartimento di Fisica, Cosenza (Italy); Gruppo collegato di Cosenza, Istituto Nazionale di Fisica Nucleare, Cosenza (Italy); Ivanov, D.Yu. [Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk (Russian Federation)

    2014-10-15

    We study, within QCD collinear factorization and including BFKL resummation at the next-to-leading order, the production of Mueller-Navelet jets at LHC with center-of-mass energy of 7 TeV. The adopted jet vertices are calculated in the approximation of a small aperture of the jet cone in the pseudorapidity-azimuthal angle plane. We consider several representations of the dijet cross section, differing only beyond the next-to-leading order, to calculate a few observables related with this process. We use various methods of optimization to fix the energy scales entering the perturbative calculation and compare our results with the experimental data from the CMS collaboration. (orig.)

  20. Charm-Quark Production in Deep-Inelastic Neutrino Scattering at Next-to-Next-to-Leading Order in QCD.

    Science.gov (United States)

    Berger, Edmond L; Gao, Jun; Li, Chong Sheng; Liu, Ze Long; Zhu, Hua Xing

    2016-05-27

    We present a fully differential next-to-next-to-leading order calculation of charm-quark production in charged-current deep-inelastic scattering, with full charm-quark mass dependence. The next-to-next-to-leading order corrections in perturbative quantum chromodynamics are found to be comparable in size to the next-to-leading order corrections in certain kinematic regions. We compare our predictions with data on dimuon production in (anti)neutrino scattering from a heavy nucleus. Our results can be used to improve the extraction of the parton distribution function of a strange quark in the nucleon.

  1. Detailed comparison of next-to-leading order predictions for jet photoproduction at HERA.

    Energy Technology Data Exchange (ETDEWEB)

    Harris, B. W.; Klassen, M.; Vossebeld, J.

    1999-06-02

    The precision of new HERA data on jet photoproduction opens up the possibility to discriminate between different models of the photon structure. This requires equally precise theoretical predictions from perturbative QCD calculations. In the past years, next-to-leading order calculations for the photoproduction of jets at HERA have become available. Using the kinematic cuts of recent ZEUS analyses, we compare the predictions of three calculations for different dijet and three-jet distributions. We find that in general all three calculations agree within the statistical accuracy of the Monte Carlo integration yielding reliable theoretical predictions. In certain restricted regions of phase space, the calculations differ by up to 5%.

  2. Differential Higgs boson pair production at next-to-next-to-leading order in QCD

    International Nuclear Information System (INIS)

    Florian, Daniel de; Mazzitelli, Javier; Grazzini, Massimiliano; Hanga, Catalin; Lindert, Jonas M.; Kallweit, Stefan; Maierhoefer, Philipp; Rathlev, Dirk

    2016-06-01

    We report on the first fully differential calculation for double Higgs boson production through gluon fusion in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation is performed in the heavy-top limit of the Standard Model, and in the phenomenological results we focus on pp collisions at √(s)=14 TeV. We present differential distributions through NNLO for various observables including the transverse-momentum and rapidity distributions of the two Higgs bosons. NNLO corrections are at the level of 10%-25% with respect to the next-to-leading order (NLO) prediction with a residual scale uncertainty of 5%-15% and an overall mild phase-space dependence. Only at NNLO the perturbative expansion starts to converge yielding overlapping scale uncertainty bands between NNLO and NLO in most of the phase-space. The calculation includes NLO predictions for pp→HH+jet+X. Corrections to the corresponding distributions exceed 50% with a residual scale dependence of 20%-30%.

  3. Next-to-next-to-leading order evolution of non-singlet fragmentation functions

    International Nuclear Information System (INIS)

    Mitov, A.; Moch, S.; Vogt, A.

    2006-04-01

    We have investigated the next-to-next-to-leading order (NNLO) corrections to inclusive hadron production in e + e - annihilation and the related parton fragmentation distributions, the 'time-like' counterparts of the 'space-like' deep-inelastic structure functions and parton densities. We have re-derived the corresponding second-order coefficient functions in massless perturbative QCD, which so far had been calculated only by one group. Moreover we present, for the first time, the third-order splitting functions governing the NNLO evolution of flavour non-singlet fragmentation distributions. These results have been obtained by two independent methods relating time-like quantities to calculations performed in deep-inelastic scattering. We briefly illustrate the numerical size of the NNLO corrections, and make a prediction for the difference of the yet unknown time-like and space-like splitting functions at the fourth order in the strong coupling constant. (Orig.)

  4. Direct Photon Production at Next-to–Next-to-Leading Order

    Energy Technology Data Exchange (ETDEWEB)

    Campbell, John M.; Ellis, R. Keith; Williams, Ciaran

    2017-05-01

    We present the first calculation of direct photon production at next-to-next-to leading order (NNLO) accuracy in QCD. For this process, although the final state cuts mandate only the presence of a single electroweak boson, the underlying kinematics resembles that of a generic vector boson plus jet topology. In order to regulate the infrared singularities present at this order we use the $N$-jettiness slicing procedure, applied for the first time to a final state that at Born level includes colored partons but no required jet. We compare our predictions to ATLAS 8 TeV data and find that the inclusion of the NNLO terms in the perturbative expansion, supplemented by electroweak corrections, provides an excellent description of the data with greatly reduced theoretical uncertainties.

  5. Higgs boson production in association with a jet at next-to-next-to-leading order

    CERN Document Server

    Boughezal, Radja; Melnikov, Kirill; Petriello, Frank; Schulze, Markus

    2015-01-01

    We present precise predictions for Higgs boson production in association with a jet. Our calculation is accurate to next-to-next-to-leading order (NNLO) QCD in the Higgs Effective Field Theory and constitutes the first complete NNLO computation for Higgs production with a final-state jet in hadronic collisions. We include all relevant phenomenological channels and present fully-differential results as well as total cross sections for the LHC. Our NNLO predictions reduce the unphysical scale dependence by more than a factor of two and enhance the total rate by about twenty percent compared to NLO QCD predictions. Our results demonstrate for the first time satisfactory convergence of the perturbative series.

  6. Chiral effective field theory on the lattice at next-to-leading order

    International Nuclear Information System (INIS)

    Borasoy, B.; Epelbaum, E.; Krebs, H.; Meissner, U.G.; Lee, D.

    2008-01-01

    We study nucleon-nucleon scattering on the lattice at next-to-leading order in chiral effective field theory. We determine phase shifts and mixing angles from the properties of two-nucleon standing waves induced by a hard spherical wall in the center-of-mass frame. At fixed lattice spacing we test model independence of the low-energy effective theory by computing next-to-leading-order corrections for two different leading-order lattice actions. The first leading-order action includes instantaneous one-pion exchange and same-site contact interactions. The second leading-order action includes instantaneous one-pion exchange and Gaussian-smeared interactions. We find that in each case the results at next-to-leading order are accurate up to corrections expected at higher order. (orig.)

  7. Resummed B→Xulν decay distributions to next-to-leading order

    International Nuclear Information System (INIS)

    Aglietti, U.

    2001-01-01

    We perform factorization of the most general distribution in semileptonic B→X u decays and we resum the threshold logarithms to next-to-leading order. From this (triple-differential) distribution, any other distribution is obtained by integration. As an application of our method, we derive simple analytical expressions for a few distributions, resummed to leading approximation. It is shown that the shape function can be directly determined by measuring the distribution in m X 2 /E X 2 , not in m X 2 /m B 2 . We compute the resummed hadron energy spectrum, which has a 'Sudakov shoulder', and we show how the distribution in the singular region is related to the shape function. We also present an improved formula for the photon spectrum in B→X s γ, which includes soft-gluon resummation and non-leading operators in the effective Hamiltonian. We explicitly show that the same non-perturbative function -- namely, the shape function -- controls the non-perturbative effects in all the distributions in the semileptonic and in the rare decay

  8. Resonance saturation of the chiral couplings at next-to-leading order in 1/NC

    International Nuclear Information System (INIS)

    Rosell, Ignasi; Ruiz-Femenia, Pedro; Sanz-Cillero, Juan Jose

    2009-01-01

    The precision obtainable in phenomenological applications of chiral perturbation theory is currently limited by our lack of knowledge on the low-energy constants (LECs). The assumption that the most important contributions to the LECs come from the dynamics of the low-lying resonances, often referred to as the resonance saturation hypothesis, has stimulated the use of large-N C resonance Lagrangians in order to obtain explicit values for the LECs. We study the validity of the resonance saturation assumption at the next-to-leading order in the 1/N C expansion within the framework of resonance chiral theory. We find that, by imposing QCD short-distance constraints, the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly on the coefficients of the chiral operators in the Goldstone boson sector of resonance chiral theory. As we argue, this is the counterpart formulation of the resonance saturation statement in the context of the resonance Lagrangian. Going beyond leading order in the 1/N C counting allows us to keep full control of the renormalization scale dependence of the LEC estimates.

  9. A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction

    International Nuclear Information System (INIS)

    Frixione, Stefano; Ridolfi, Giovanni; Nason, Paolo

    2007-01-01

    We present a next-to-leading order calculation of heavy flavour production in hadronic collisions that can be interfaced to shower Monte Carlo programs. The calculation is performed in the context of the POWHEG method. It is suitable for the computation of charm, bottom and top hadroproduction. In the case of top production, spin correlations in the decay products are taken into account

  10. Production of heavy flavours at the next-to-leading order

    International Nuclear Information System (INIS)

    Nason, P.; Ridolfi, G.; Frixione, S.; Mangano, M.L.

    1993-01-01

    The status of next-to-leading calculations of heavy quark production is reviewed. In particular, results on the doubly-differential cross section for the photoproduction of heavy flavours are discussed. The possibility of using heavy flavour production in order to determine the gluon density in the proton at HERA is also discussed. 3 figs., 22 refs

  11. Conformally symmetric contributions to BFKL evolution at next to leading order

    International Nuclear Information System (INIS)

    Coriano, C.; White, A.R.

    1995-01-01

    Unitarity corrections to the BFKL evolution at next to leading order determine a new component of the evolution kernel which is shown to possess conformal invariance properties. Expressions for the complete spectrum of the new component and the correction to the intercept of the pomeron trajectory are presented

  12. Single jet photoproduction at HERA in next-to-leading order QCD

    International Nuclear Information System (INIS)

    Kramer, G.; Salesch, S.G.

    1993-01-01

    We present results for next- to-leading order calculations of single jet inclusive cross sections by resolved photons in ep-collisions at HERA. The dependence on the jet recombination cut and on the choice of the renormalization and factorization scales is studied in detail. (orig.). 5 figs

  13. Transverse momentum dependent fragmentation function at next-to-next-to-leading order

    NARCIS (Netherlands)

    Garcia, M.; Scimemi, I.; Vladimirov, A.

    2016-01-01

    We calculate the unpolarized transverse momentum dependent fragmentation function at next-to-next-to-leading order, evaluating separately the transverse momentum dependent (TMD) soft factor and the TMD collinear correlator. For the first time, the cancellation of spurious rapidity divergences in a

  14. On some aspects of optimisation of factorisation scheme dependence at the next-to-leading order in QCD

    International Nuclear Information System (INIS)

    Chyla, J.

    1989-01-01

    Several recent papers attempting to apply the optimised QCD perturbation theory to reactions involving real or virtual photons are discussed with particular attention paid to the ambiguity appearing in the definition of parton distribution and fragmentation functions at the next-to-leading order (NLO). The necessity to use NLO parametrisations of quark densities is stressed and the problem with respect to the factorisation mass M for the 'physical' definition of parton densities is pointed out. (orig.)

  15. Quarkonium spectral function in medium at next-to-leading order for any quark mass

    International Nuclear Information System (INIS)

    Burnier, Yannis

    2015-01-01

    The vector channel spectral function at zero spatial momentum is calculated at next-to-leading order in thermal QCD for any quark mass. It corresponds to the imaginary part of the massive quark contribution to the photon polarisation tensor. The spectrum shows a well-defined transport peak in contrast to both the heavy quark limit studied previously, where the low frequency domain is exponentially suppressed at this order, and the naive massless case where it vanishes at leading order and diverges at next-to-leading order. From our general expressions, the massless limit can be taken and we show that no divergences occur if done carefully. Finally, we compare the massless limit to results from lattice simulations. (orig.)

  16. Multi-parton loop amplitudes and next-to-leading order jet cross-sections

    International Nuclear Information System (INIS)

    Bern, Z.; Dixon, L.; Kosower, D.A.; Signer, A.

    1998-02-01

    The authors review recent developments in the calculation of QCD loop amplitudes with several external legs, and their application to next-to-leading order jet production cross-sections. When a number of calculational tools are combined together--helicity, color and supersymmetry decompositions, plus unitarity and factorization properties--it becomes possible to compute multi-parton one-loop QCD amplitudes without ever evaluating analytically standard one-loop Feynman diagrams. One-loop helicity amplitudes are now available for processes with five external partons (ggggg, q anti qggg and q anti qq anti q' g), and for an intermediate vector boson V ≡ γ * , Z, W plus four external partons (V q anti q and V q anti qq'anti q'). Using these amplitudes, numerical programs have been constructed for the next-to-leading order corrections to the processes p anti p → 3 jets (ignoring quark contributions so far) and e + e - → 4 jets

  17. The Gluon-Induced Mueller-Tang Jet Impact Factor at Next-to-Leading Order

    CERN Document Server

    Hentschinski, Martin; Murdaca, Beatrice; Vera, Agustín Sabio

    2014-01-01

    We complete the computation of the Mueller-Tang jet impact factor at next-to-leading order (NLO) initiated in arXiv:1406.5625 and presented in arXiv:1404.2937 by computing the real corrections associated to gluons in the initial state making use of Lipatov's effective action. NLO corrections for this effective vertex are an important ingredient for a reliable description of large rapidity gap phenomenology within the BFKL approach.

  18. A next-to-leading order QCD analysis of the spin structure function $g_1$

    CERN Document Server

    AUTHOR|(CDS)2067425; Arik, E; Badelek, B; Bardin, G; Baum, G; Berglund, P; Betev, L; Birsa, R; De Botton, N R; Bradamante, Franco; Bravar, A; Bressan, A; Bültmann, S; Burtin, E; Crabb, D; Cranshaw, J; Çuhadar-Dönszelmann, T; Dalla Torre, S; Van Dantzig, R; Derro, B R; Deshpande, A A; Dhawan, S K; Dulya, C M; Eichblatt, S; Fasching, D; Feinstein, F; Fernández, C; Forthmann, S; Frois, Bernard; Gallas, A; Garzón, J A; Gilly, H; Giorgi, M A; von Goeler, E; Görtz, S; Gracia, G; De Groot, N; Grosse-Perdekamp, M; Haft, K; Von Harrach, D; Hasegawa, T; Hautle, P; Hayashi, N; Heusch, C A; Horikawa, N; Hughes, V W; Igo, G; Ishimoto, S; Iwata, T; Kabuss, E M; Kageya, T; Karev, A G; Kessler, H J; Ketel, T; Kiryluk, J; Kiselev, Yu F; Krämer, Dietrich; Krivokhizhin, V G; Kröger, W; Kukhtin, V V; Kurek, K; Kyynäräinen, J; Lamanna, M; Landgraf, U; Le Goff, J M; Lehár, F; de Lesquen, A; Lichtenstadt, J; Litmaath, M; Magnon, A; Mallot, G K; Marie, F; Martin, A; Martino, J; Matsuda, T; Mayes, B W; McCarthy, J S; Medved, K S; Meyer, W T; Van Middelkoop, G; Miller, D; Miyachi, Y; Mori, K; Moromisato, J H; Nassalski, J P; Naumann, Lutz; Niinikoski, T O; Oberski, J; Ogawa, A; Ozben, C; Pereira, H; Perrot-Kunne, F; Peshekhonov, V D; Piegia, R; Pinsky, L; Platchkov, S K; Pló, M; Pose, D; Postma, H; Pretz, J; Puntaferro, R; Rädel, G; Rijllart, A; Reicherz, G; Roberts, J; Rodríguez, M; Rondio, Ewa; Sabo, I; Saborido, J; Sandacz, A; Savin, I A; Schiavon, R P; Schiller, A; Sichtermann, E P; Simeoni, F; Smirnov, G I; Staude, A; Steinmetz, A; Stiegler, U; Stuhrmann, H B; Szleper, M; Tessarotto, F; Thers, D; Tlaczala, W; Tripet, A; Ünel, G; Velasco, M; Vogt, J; Voss, Rüdiger; Whitten, C; Windmolders, R; Willumeit, R; Wislicki, W; Witzmann, A; Ylöstalo, J; Zanetti, A M; Zaremba, K; Zhao, J

    1998-01-01

    We present a next-to-leading order QCD analysis of the presently available data on the spin structure function $g_1$ including the final data from the Spin Muon Collaboration (SMC). We present resu lts for the first moments of the proton, deuteron and neutron structure functions, and determine singlet and non-singlet parton distributions in two factorization schemes. We also test the Bjor ken sum rule and find agreement with the theoretical prediction at the level of 10\\%.

  19. A positive-weight next-to-leading-order Monte Carlo for Z pair hadroproduction

    International Nuclear Information System (INIS)

    Nason, Paolo; Ridolfi, Giovanni

    2006-01-01

    We present a first application of a previously published method for the computation of QCD processes that is accurate at next-to-leading order, and that can be interfaced consistently to standard shower Monte Carlo programs. We have considered Z pair production in hadron-hadron collisions, a process whose complexity is sufficient to test the general applicability of the method. We have interfaced our result to the HERWIG and PYTHIA shower Monte Carlo programs. Previous work on next-to-leading order corrections in a shower Monte Carlo (the MC-NLO program) may involve the generation of events with negative weights, that are avoided with the present method. We have compared our results with those obtained with MC-NLO, and found remarkable consistency. Our method can also be used as a standalone, alternative implementation of QCD corrections, with the advantage of positivity, improved convergence, and next-to-leading logarithmic accuracy in the region of small transverse momentum of the radiated parton

  20. QCD event generators with next-to-leading order matrix-elements and parton showers

    International Nuclear Information System (INIS)

    Kurihara, Y.; Fujimoto, J.; Ishikawa, T.; Kato, K.; Kawabata, S.; Munehisa, T.; Tanaka, H.

    2003-01-01

    A new method to construct event-generators based on next-to-leading order QCD matrix-elements and leading-logarithmic parton showers is proposed. Matrix elements of loop diagram as well as those of a tree level can be generated using an automatic system. A soft/collinear singularity is treated using a leading-log subtraction method. Higher order resummation of the soft/collinear correction by the parton shower method is combined with the NLO matrix-element without any double-counting in this method. An example of the event generator for Drell-Yan process is given for demonstrating a validity of this method

  1. Next-to leading order analysis of target mass corrections to structure functions and asymmetries

    International Nuclear Information System (INIS)

    Brady, L.T.; Accardi, A.; Hobbs, T.J.; Melnitchouk, W.

    2011-01-01

    We perform a comprehensive analysis of target mass corrections (TMCs) to spin-averaged structure functions and asymmetries at next-to-leading order. Several different prescriptions for TMCs are considered, including the operator product expansion, and various approximations to it, collinear factorization, and xi-scaling. We assess the impact of each of these on a number of observables, such as the neutron to proton F 2 structure function ratio, and parity-violating electron scattering asymmetries for protons and deuterons which are sensitive to gamma-Z interference effects. The corrections from higher order radiative and nuclear effects on the parity-violating deuteron asymmetry are also quantified.

  2. Matching next-to-leading order predictions to parton showers in supersymmetric QCD

    CERN Document Server

    Degrande, Celine; Hirschi, Valentin; Proudom, Josselin; Shao, Hua-Sheng

    2016-04-10

    We present a fully automated framework based on the FeynRules and MadGraph5 aMC@NLO programs that allows for accurate simulations of supersymmetric QCD processes at the LHC. Starting directly from a model Lagrangian that features squark and gluino interactions, event generation is achieved at the next-to-leading order in QCD, matching short-distance events to parton showers and including the subsequent decay of the produced supersymmetric particles. As an application, we study the impact of higher-order corrections in gluino pair-production in a simplified benchmark scenario inspired by current gluino LHC searches.

  3. Matching the Nagy-Soper parton shower at next-to-leading order

    Energy Technology Data Exchange (ETDEWEB)

    Kraus, Manfred [Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen University (Germany)

    2015-07-01

    We give a short review of the shower concept, first introduced by Nagy and Soper, that includes full quantum correlations in the shower evolution. We also state the current status of implementation of the publicly available shower program Deductor. However, the main focus of the talk is the matching of the shower at next-to-leading order within the MC rate at NLO formalism. Matching is necessary in order to increase the accuracy of theoretical predictions and to employ a hadronization model. We show first results using Deductor in conjunction with the Helac-NLO framework for top quark pair production in association with one hard jet.

  4. Event generation for next to leading order chargino production at the international linear collider

    Energy Technology Data Exchange (ETDEWEB)

    Robens, T.

    2006-10-15

    At the International Linear Collider (ILC), parameters of supersymmetry (SUSY) can be determined with an experimental accuracy matching the precision of next-to-leading order (NLO) and higher-order theoretical predictions. Therefore, these contributions need to be included in the analysis of the parameters. We present a Monte-Carlo event generator for simulating chargino pair production at the ILC at next-to-leading order in the electroweak couplings. We consider two approaches of including photon radiation. A strict fixed-order approach allows for comparison and consistency checks with published semianalytic results in the literature. A version with soft- and hard-collinear resummation of photon radiation, which combines photon resummation with the inclusion of the NLO matrix element for the production process, avoids negative event weights, so the program can simulate physical (unweighted) event samples. Photons are explicitly generated throughout the range where they can be experimentally resolved. In addition, it includes further higher-order corrections unaccounted for by the fixed-order method. Inspecting the dependence on the cutoffs separating the soft and collinear regions, we evaluate the systematic errors due to soft and collinear approximations for NLO and higher-order contributions. In the resummation approach, the residual uncertainty can be brought down to the per-mil level, coinciding with the expected statistical uncertainty at the ILC. We closely investigate the two-photon phase space for the resummation method. We present results for cross sections and event generation for both approaches. (orig.)

  5. Next to Leading Order QCD Corrections to Polarized $\\Lambda$ Production in DIS

    CERN Document Server

    de Florian, D

    1997-01-01

    We calculate next to leading order QCD corrections to semi-inclusive polarized deep inelastic scattering and $e^+e^-$ annihilation cross sections for processes where the polarization of the identified final-state hadron can also be determined. Using dimensional regularization and the HVBM prescription for the $\\gamma_5$ matrix, we compute corrections for different spin-dependent observables, both in the $\\overline{MS}$ and $\\overline{MS_p}$ factorization schemes, and analyse their structure. In addition to the well known corrections to polarized parton distributions, we also present those for final-state polarized fracture functions and polarized fragmentation functions, in a consistent factorization scheme.

  6. Automized squark-neutralino production to next-to-leading order

    International Nuclear Information System (INIS)

    Binoth, Thomas; Wigmore, Ioan; Netto, Dorival Goncalves; Lopez-Val, David; Plehn, Tilman; Mawatari, Kentarou

    2011-01-01

    The production of one hard jet in association with missing transverse energy is a major LHC search channel motivated by many scenarios for physics beyond the standard model. In scenarios with a weakly interacting dark matter candidate, like supersymmetry, it arises from the associated production of a quark partner with the dark matter agent. We present the next-to-leading-order cross section calculation as the first application of the fully automized MadGolem package. We find moderate corrections to the production rate with a strongly reduced theory uncertainty.

  7. Towards next-to-leading order transport coefficients from the four-particle irreducible effective action

    International Nuclear Information System (INIS)

    Carrington, M. E.; Kovalchuk, E.

    2010-01-01

    Transport coefficients can be obtained from two-point correlators using the Kubo formulas. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the resummed two-point function that is obtained from the three-loop three-particle irreducible resummed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the four-loop four-particle irreducible effective action for a scalar theory with cubic and quartic interactions, with a nonvanishing field expectation value. We obtain a set of integral equations that determine the resummed two-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.

  8. Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Alarcon, Jose Manuel [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Thomas Jefferson National Accelerator Facility, Theory Center, Newport News, VA (United States); Du, Dechuan; Laehde, Timo A.; Li, Ning; Lu, Bing-Nan; Luu, Thomas [Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Forschungszentrum Juelich, Juelich (Germany); Klein, Nico [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Lee, Dean [North Carolina State University, Department of Physics, Raleigh, NC (United States); Meissner, Ulf G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Forschungszentrum Juelich, Juelich (Germany); Forschungszentrum Juelich, JARA - High Performance Computing, Juelich (Germany)

    2017-05-15

    We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing. (orig.)

  9. Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

    Energy Technology Data Exchange (ETDEWEB)

    Kamiński, Wojciech, E-mail: wkaminsk@fuw.edu.pl [Wydział Fizyki, Uniwersytet Warszawski, Hoża 69, 00-681, Warsaw (Poland); Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany); Steinhaus, Sebastian, E-mail: steinhaus.sebastian@gmail.com [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany)

    2013-12-15

    We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.

  10. Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

    International Nuclear Information System (INIS)

    Kamiński, Wojciech; Steinhaus, Sebastian

    2013-01-01

    We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol

  11. Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

    Science.gov (United States)

    Kamiński, Wojciech; Steinhaus, Sebastian

    2013-12-01

    We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.

  12. Study of beauty quark production and next-to-leading order at HERA

    Energy Technology Data Exchange (ETDEWEB)

    Nuncio Quiroz, Adriana Elizabeth

    2008-08-15

    In this thesis a study on the production and evolution of beauty quarks in ep collisions at HERA is presented. The emphasis is put on the corresponding Quantum Chromodynamics predictions including next-to-leading order corrections. In the context of this work the FMNR x Pythia interface was developed, which calculates next-to-leading order Quantum Chromodynamics predictions at visible level for heavy-flavour processes in the photoproduction regime. This is achieved using the RedStat routines which transform the FMNR program into a Monte Carlo-like event generator. The parton-level events obtained are interfaced to Pythia using the Le Houches accord routines. All branching ratios and decay channels of the heavy quarks implemented in the Pythia framework are used, and therefore complex cuts on the nal state can be applied. The FMNR x Pythia interface is applied in this thesis to obtain next-to-leading order predictions for the recently finished heavy flavour ZEUS analyses: the ep {yields} b anti bX {yields} D{sup *}{mu}X' and ep {yields} b anti bX {yields} {mu}{sup +}{mu}{sup -}X' channels. A comparison with the H1 D{sup *}{mu} measurement is also performed. Since the use of such double tagging techniques to identify events where heavy flavours are present proved to be very convenient when the nal state is a pair of leptons, another part of this thesis work deals with the implementation of an electron finder, the {sup G}Elec finder. This finder is tested on the reconstruction of the J/{psi} {yields} e{sup +}e{sup -} signal. Finally, a heavy-flavour analysis has been started, namely the ep {yields} b anti bX {yields} e{mu}X' dilepton channel, using an integrated luminosity of 114 pb{sup -1} gated by the ZEUS detector in the years 1996-2000. Compared to previous analyses the study of beauty quark production in this channel extends the phase space of the measurement closer to the kinematic threshold, since electrons provide access to lower p{sub T} values

  13. Study of beauty quark production and next-to-leading order effects at HERA

    International Nuclear Information System (INIS)

    Nuncio Quiroz, Adriana Elizabeth

    2008-08-01

    In this thesis a study on the production and evolution of beauty quarks in ep collisions at HERA is presented. The emphasis is put on the corresponding Quantum Chromodynamics predictions including next-to-leading order corrections. In the context of this work the FMNR x Pythia interface was developed, which calculates next-to-leading order Quantum Chromodynamics predictions at visible level for heavy-flavour processes in the photoproduction regime. This is achieved using the RedStat routines which transform the FMNR program into a Monte Carlo-like event generator. The parton-level events obtained are interfaced to Pythia using the Le Houches accord routines. All branching ratios and decay channels of the heavy quarks implemented in the Pythia framework are used, and therefore complex cuts on the nal state can be applied. The FMNR x Pythia interface is applied in this thesis to obtain next-to-leading order predictions for the recently finished heavy flavour ZEUS analyses: the ep → b anti bX → D * μX' and ep → b anti bX → μ + μ - X' channels. A comparison with the H1 D * μ measurement is also performed. Since the use of such double tagging techniques to identify events where heavy flavours are present proved to be very convenient when the nal state is a pair of leptons, another part of this thesis work deals with the implementation of an electron finder, the G Elec finder. This finder is tested on the reconstruction of the J/ψ → e + e - signal. Finally, a heavy-flavour analysis has been started, namely the ep → b anti bX → eμX' dilepton channel, using an integrated luminosity of 114 pb -1 gated by the ZEUS detector in the years 1996-2000. Compared to previous analyses the study of beauty quark production in this channel extends the phase space of the measurement closer to the kinematic threshold, since electrons provide access to lower p T values than muons do. The technical part of this thesis consisted in the calibration, maintenance and data

  14. On top-pair hadro-production at next-to-next-to-leading order

    International Nuclear Information System (INIS)

    Moch, S.; Uwer, P.; Vogt, A.

    2012-03-01

    We study the QCD corrections at next-to-next-to-leading order (NNLO) to the cross section for the hadronic pair-production of top quarks. We present new results in the high-energy limit using the well-known framework of k t -factorization. We combine these findings with the known threshold corrections and present improved approximate NNLO results over the full kinematic range. This approach is employed to quantify the residual theoretical uncertainty of the approximate NNLO results which amounts to about 4% for the Tevatron and 5% for the LHC cross-section predictions. Our analytic results in the high-energy limit will provide an important check on future computations of the complete NNLO cross sections.

  15. Single Top Production at Next-to-Leading Order in the Standard Model Effective Field Theory.

    Science.gov (United States)

    Zhang, Cen

    2016-04-22

    Single top production processes at hadron colliders provide information on the relation between the top quark and the electroweak sector of the standard model. We compute the next-to-leading order QCD corrections to the three main production channels: t-channel, s-channel, and tW associated production, in the standard model including operators up to dimension six. The calculation can be matched to parton shower programs and can therefore be directly used in experimental analyses. The QCD corrections are found to significantly impact the extraction of the current limits on the operators, because both of an improved accuracy and a better precision of the theoretical predictions. In addition, the distributions of some of the key discriminating observables are modified in a nontrivial way, which could change the interpretation of measurements in terms of UV complete models.

  16. Model for next-to-leading order threshold resummed form factors

    International Nuclear Information System (INIS)

    Aglietti, Ugo; Ricciardi, Giulia

    2004-01-01

    We present a model for next-to-leading order resummed threshold form factors based on a timelike coupling recently introduced in the framework of small x physics. Improved expressions for the form factors in N-space are obtained which are not plagued by Landau-pole singularities, as the included absorptive effects - usually neglected - act as regulators. The physical reason is that, because of faster decay of gluon jets, there is not enough resolution time to observe the Landau pole. Our form factors reduce to the standard ones when the absorptive parts related to the coupling are neglected. The inverse transform from N-space to x-space can be done directly without any prescription and we obtain analytical expressions for the form factors, which are well defined in all x-space

  17. Next-to-leading order strong interaction corrections to the ΔF = 2 effective Hamiltonian in the MSSM

    International Nuclear Information System (INIS)

    Ciuchini, Marco; Franco, E.; Guadagnoli, D.; Lubicz, Vittorio; Porretti, V.; Silvestrini, L.

    2006-01-01

    We compute the next-to-leading order strong interaction corrections to gluino-mediated ΔF = 2 box diagrams in the Minimal Supersymmetric Standard Model. These corrections are given by two loop diagrams which we have calculated in three different regularization schemes in the mass insertion approximation. We obtain the next-to-leading order Wilson coefficients of the ΔF = 2 effective Hamiltonian relevant for neutral meson mixings. We find that the matching scale uncertainty is largely reduced at the next-to-leading order, typically from about 10-15% to few percent

  18. Virasoro vacuum block at next-to-leading order in the heavy-light limit

    Energy Technology Data Exchange (ETDEWEB)

    Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido [Dipartimento di Matematica e Fisica Ennio De Giorgi,Università del Salento & INFN, Via Arnesano, 73100 Lecce (Italy)

    2016-02-11

    We consider the semiclassical limit of the vacuum Virasoro block describing the diagonal 4-point correlation functions on the sphere. At large central charge c, after exponentiation, it depends on two fixed ratios h{sub H}/c and h{sub L}/c, where h{sub H,L} are the conformal dimensions of the 4-point function operators. The semiclassical block may be expanded in powers of the light ratio h{sub L}/c and the leading non-trivial (linear) order is known in closed form as a function of h{sub H}/c. Recently, this contribution has been matched against AdS{sub 3} gravity calculations where heavy operators build up a classical geometry corresponding to a BTZ black hole, while the light operators are described by a geodesic in this background. Here, we compute for the first time the next-to-leading quadratic correction O((h{sub L}/c){sup 2}), again in closed form for generic heavy operator ratio h{sub H}/c. The result is a highly non-trivial extension of the leading order and may be relevant for further refined AdS{sub 3}/CFT{sub 2} tests. Applications to the two-interval Rényi entropy are also presented.

  19. Next-to-leading order QCD predictions for the hadronic WH+jet production

    International Nuclear Information System (INIS)

    Su Jijuan; Ma Wengan; Zhang Renyou; Guo Lei

    2010-01-01

    We calculate the next-to-leading order (NLO) QCD corrections to the WH 0 production in association with a jet at hadron colliders. We study the impacts of the complete NLO QCD radiative corrections to the integrated cross sections, the scale dependence of the cross sections, and the differential cross sections ((dσ/dcosθ), (dσ/dp T )) of the final W-, Higgs boson and jet. We find that the corrections significantly modify the physical observables, and reduce the scale uncertainty of the leading-order cross section. Our results show that by applying the inclusive scheme with p T,j cut =20 GeV and taking m H =120 GeV, μ=μ 0 ≡(1/2)(m W +m H ), the K-factor is 1.15 for the process pp→W ± H 0 j+X at the Tevatron, while the K-factors for the processes pp→W - H 0 j+X and pp→W + H 0 j+X at the LHC are 1.12 and 1.08, respectively. We conclude that to understand the hadronic associated WH 0 production, it is necessary to study the NLO QCD corrections to the WH 0 j production process which is part of the inclusive WH 0 production.

  20. The radiative decays $B \\to V_{\\gamma}$ at next-to-leading order in QCD

    CERN Document Server

    Bosch, S W; Bosch, Stefan W.; Buchalla, Gerhard

    2002-01-01

    We provide a model-independent framework for the analysis of the radiative B-meson decays B -> K* gamma and B -> rho gamma. In particular, we give a systematic discussion of the various contributions to these exclusive processes based on the heavy-quark limit of QCD. We propose a novel factorization formula for the consistent treatment of B -> V gamma matrix elements involving charm (or up-quark) loops, which contribute at leading power in Lambda_QCD/m_B to the decay amplitude. Annihilation topologies are shown to be power suppressed. In some cases they are nevertheless calculable. The approach is similar to the framework of QCD factorization that has recently been formulated for two-body non-leptonic B decays. These results allow us, for the first time, to compute exclusive b -> s(d) gamma decays systematically beyond the leading logarithmic approximation. We present results for these decays complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Phenomenological implications ...

  1. Percent-level-precision physics at the Tevatron: next-to-next-to-leading order QCD corrections to qq¯→tt¯+X.

    Science.gov (United States)

    Bärnreuther, Peter; Czakon, Michał; Mitov, Alexander

    2012-09-28

    We compute the next-to-next-to-leading order QCD corrections to the partonic reaction that dominates top-pair production at the Tevatron. This is the first ever next-to-next-to-leading order calculation of an observable with more than two colored partons and/or massive fermions at hadron colliders. Augmenting our fixed order calculation with soft-gluon resummation through next-to-next-to-leading logarithmic accuracy, we observe that the predicted total inclusive cross section exhibits a very small perturbative uncertainty, estimated at ±2.7%. We expect that once all subdominant partonic reactions are accounted for, and work in this direction is ongoing, the perturbative theoretical uncertainty for this observable could drop below ±2%. Our calculation demonstrates the power of our computational approach and proves it can be successfully applied to all processes at hadron colliders for which high-precision analyses are needed.

  2. Production of massless bottom jets in p anti p and pp collisions at next-to-leading order of QCD

    Energy Technology Data Exchange (ETDEWEB)

    Bierenbaum, Isabella [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Kramer, Gustav [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2016-03-15

    We present predictions for the inclusive production of bottom jets in proton-antiproton collisions at 1.96 TeV and proton-proton collisions at 7 TeV. The bottom quark is considered massless. In this scheme, we find that at small transverse momentum (p{sub T}) the ratio of the next-to-leading order to the leading-order cross section (K factor) is smaller than one. It increases with increasing p{sub T} and approaches one at larger p{sub T} at a value depending essentially on the choice of the renormalization scale. Adding non-perturbative corrections obtained from PYTHIA Monte Carlo calculations leads to reasonable agreement with experimental b-jet cross sections obtained by the CDF and the CMS collaborations.

  3. Production of massless bottom jets in p anti p and pp collisions at next-to-leading order of QCD

    International Nuclear Information System (INIS)

    Bierenbaum, Isabella; Kramer, Gustav

    2016-03-01

    We present predictions for the inclusive production of bottom jets in proton-antiproton collisions at 1.96 TeV and proton-proton collisions at 7 TeV. The bottom quark is considered massless. In this scheme, we find that at small transverse momentum (p T ) the ratio of the next-to-leading order to the leading-order cross section (K factor) is smaller than one. It increases with increasing p T and approaches one at larger p T at a value depending essentially on the choice of the renormalization scale. Adding non-perturbative corrections obtained from PYTHIA Monte Carlo calculations leads to reasonable agreement with experimental b-jet cross sections obtained by the CDF and the CMS collaborations.

  4. Next-to-leading-order tests of NRQCD factorization with J/{psi} yield and polarization

    Energy Technology Data Exchange (ETDEWEB)

    Butenschoen, Mathias [Wien Univ. (Austria). Fakultaet fuer Physik; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2012-12-15

    We report on recent progress in testing the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) at next-to-leading order (NLO) for J/{psi} yield and polarization. We demonstrate that it is possible to unambiguously determine the leading color-octet long-distance matrix elements (LDMEs) in compliance with the velocity scaling rules through a global fit to experimental data of unpolarized J/{psi} production in pp, p anti p, ep, {gamma}{gamma}, and e{sup +}e{sup -} collisions.Three data sets not included in the fit, from hadroproduction and from photoproduction in the fixed-target and colliding-beam modes, are nicely reproduced. The polarization observables measured in different frames at DESY HERA and CERN LHC reasonably agree with NLO NRQCD predictions obtained using the LDMEs extracted from the global fit, while measurements from the FNAL Tevatron exhibit severe disagreement. We demonstrate that alternative LDME sets recently obtained in two other NLO NRQCD analyses of J/{psi} yield and polarization, with different philosophies, also fail to reconcile the Tevatron polarization data with the other available world data.

  5. Extended Holstein-Primakoff mapping for the next-to-leading order of the 1/N expansion at finite temperature

    International Nuclear Information System (INIS)

    Dzhioev, Alan; Storozhenko, A.; Vdovin, A.; Aouissat, Z.; Wambach, J.

    2004-01-01

    An extended Holstein-Primakoff mapping which incorporates both single- and double-fermion mappings is used in the context of thermofield dynamics to study the next-to-leading order of the 1/N expansion at finite temperature. For the Lipkin-Meshkov-Glick model it is shown that the extended mapping naturally leads to the correct Fermi statistics both in leading and next-to-leading order

  6. Higgs Boson Production at Hadron Colliders: Differential Cross Section Through Next-to-Next-to-Leading Order

    International Nuclear Information System (INIS)

    Anastasiou, C

    2004-01-01

    The authors present a calculation of the fully differential cross section for Higgs boson production in the gluon fusion channel through next-to-next-to-leading order in perturbative QCD. They apply the method introduced in [1] to compute double real emission corrections. The calculation permits arbitrary cuts on the final state in the reaction hh → H + X. it can be easily extended to include decays of the Higgs boson into observable final states. In this Letter, they discuss the most important features of the calculation, and present some examples of physical applications that illustrate the range of observables that can be studied using the result. They compute the NNLO rapidity distribution of the Higgs boson, and also calculate the NNLO rapidity distribution with a veto on jet activity

  7. Regge vertex for quark production in the central rapidity region in the next-to-leading order

    Energy Technology Data Exchange (ETDEWEB)

    Kozlov, M. G., E-mail: M.G.Kozlov@inp.nsk.su; Reznichenko, A. V., E-mail: A.V.Reznichenko@inp.nsk.su [Russian Academy of Sciences, Budker Institute of Nuclear Physics, Siberian Branch (Russian Federation)

    2016-03-15

    The effective vertex for quark production in the interaction of a Reggeized quark and a Reggeized gluon is calculated in the next-to-leading order (NLO). The resulting vertex is the missing component of the NLO multi-Regge amplitude featuring quark and gluon exchanges in the t channels. This calculation will make it possible to develop in future the bootstrap approach to proving quark Reggeization in the next-to-leading logarithmic approximation.

  8. Inclusive hadron production in photon-photon collisions at next-to-leading order

    International Nuclear Information System (INIS)

    Binnewies, J.

    1996-01-01

    We study inclusive charged-hadron production in collisions of quasireal photons at next-to-leading order (NLO) in the QCD-improved parton model, using fragmentation functions recently extracted from PEP and LEP1 data of e + e - annihilation. We consistently superimpose the direct (DD), single-resolved (DR), and double-resolved (RR) γγ channels. We consider photon spectra generated by electromagnetic bremsstrahlung and/or beamstrahlung off colliding e + and e - beams as well as those which result from backscattering of laser light off such beams. First, we revisit existing single-tag data taken by TASSO at PETRA and by MARK II at PEP (with e + e - energy √S∼30 GeV) and confront them with our NLO calculations imposing the respective experimental cuts. We also make comparisons with the neutral-kaon to charged-hadron ratio measured by MARK II. Then, we present NLO predictions for LEP2, a next-generation e + e - linear collider (NLC) in the TESLA design with √S=500 GeV, and a Compton collider obtained by converting a 500-GeV NLC. We analyze transverse-momentum and rapidity spectra with regard to the scale dependence, the interplay of the DD, DR, and RR components, the sensitivity to the gluon density inside the resolved photon, and the influence of gluon fragmentation. It turns out that the inclusive measurement of small-p T hadrons at a Compton collider would greatly constrain the gluon density of the photon and the gluon fragmentation function. (orig.)

  9. Production of heavy neutrino in next-to-leading order QCD at the LHC and beyond

    International Nuclear Information System (INIS)

    Das, Arindam; Konar, Partha; Majhi, Swapan

    2016-01-01

    Majorana and pseudo-Dirac heavy neutrinos are introduced into the type-I and inverse seesaw models, respectively, in explaining the naturally small neutrino mass. TeV scale heavy neutrinos can also be accommodated to have a sizable mixing with the Standard Model light neutrinos, through which they can be produced and detected at the high energy colliders. In this paper we consider the Next-to-Leading Order QCD corrections to the heavy neutrino production, and study the scale variation in cross-sections as well as the kinematic distributions with different final states at 14 TeV LHC and also in the context of 100 TeV hadron collider. The repertoire of the Majorana neutrino is realized through the characteristic signature of the same-sign dilepton pair, whereas, due to a small lepton number violation, the pseudo-Dirac heavy neutrino can manifest the trileptons associated with missing energy in the final state. Using the √s=8 TeV, 20.3 fb"−"1 and 19.7 fb"−"1 data at the ATLAS and CMS respectively, we obtain prospective scale dependent upper bounds of the light-heavy neutrino mixing angles for the Majorana heavy neutrinos at the 14 TeV LHC and 100 TeV collider. Further exploiting a recent study on the anomalous multilepton search by CMS at √s=8 TeV with 19.5 fb"−"1 data, we also obtain the prospective scale dependent upper bounds on the mixing angles for the pseudo-Dirac neutrinos. We thus project a scale dependent prospective reach using the NLO processes at the 14 TeV LHC.

  10. Evolution of spin-dependent structure functions from DGLAP equations in leading order and next to leading order

    International Nuclear Information System (INIS)

    Baishya, R.; Jamil, U.; Sarma, J. K.

    2009-01-01

    In this paper the spin-dependent singlet and nonsinglet structure functions have been obtained by solving Dokshitzer, Gribov, Lipatov, Altarelli, Parisi evolution equations in leading order and next to leading order in the small x limit. Here we have used Taylor series expansion and then the method of characteristics to solve the evolution equations. We have also calculated t and x evolutions of deuteron structure functions, and the results are compared with the SLAC E-143 Collaboration data.

  11. Next-to-Leading-Order QCD Corrections to Higgs Boson Plus Jet Production with Full Top-Quark Mass Dependence

    Science.gov (United States)

    Jones, S. P.; Kerner, M.; Luisoni, G.

    2018-04-01

    We present the next-to-leading-order QCD corrections to the production of a Higgs boson in association with one jet at the LHC including the full top-quark mass dependence. The mass of the bottom quark is neglected. The two-loop integrals appearing in the virtual contribution are calculated numerically using the method of sector decomposition. We study the Higgs boson transverse momentum distribution, focusing on the high pt ,H region, where the top-quark loop is resolved. We find that the next-to-leading-order QCD corrections are large but that the ratio of the next-to-leading-order to leading-order result is similar to that obtained by computing in the limit of large top-quark mass.

  12. On the next-to-next-to-leading order evolution of flavour-singlet fragmentation functions

    International Nuclear Information System (INIS)

    Almasy, A.A.; Moch, S.; Vogt, A.

    2012-01-01

    We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep-inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top limit. A numerically tolerable uncertainty remains for the quark-gluon splitting function, which does not affect the endpoint logarithms for small and large momentum fractions. We briefly discuss these limits and illustrate the numerical impact of the third-order corrections. Compact and accurate parametrizations are provided for all third-order timelike splitting functions.

  13. On the next-to-next-to-leading order evolution of flavour-singlet fragmentation functions

    Energy Technology Data Exchange (ETDEWEB)

    Almasy, A.A.; Vogt, A. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2011-07-15

    We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep-inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top limit. A numerically tolerable uncertainty remains for the quark-gluon splitting function, which does not affect the endpoint logarithms for small and large momentum fractions. We briefly discuss these limits and illustrate the numerical impact of the third-order corrections. Compact and accurate parametrizations are provided for all third-order timelike splitting functions. (orig.)

  14. CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order

    International Nuclear Information System (INIS)

    Iancu, E.; Mueller, A.H.; Triantafyllopoulos, D.N.

    2016-01-01

    Within the Color Glass Condensate effective theory, we reconsider the next-to-leading order (NLO) calculation of the single inclusive particle production at forward rapidities in proton-nucleus collisions at high energy. Focusing on quark production for definiteness, we establish a new factorization scheme, perturbatively correct through NLO, in which there is no ‘rapidity subtraction’. That is, the NLO correction to the impact factor is not explicitly separated from the high-energy evolution. Our construction exploits the skeleton structure of the (NLO) Balitsky-Kovchegov equation, in which the first step of the evolution is explicitly singled out. The NLO impact factor is included by computing this first emission with the exact kinematics for the emitted gluon, rather than by using the eikonal approximation. This particular calculation has already been presented in the literature http://dx.doi.org/10.1103/PhysRevLett.108.122301, http://dx.doi.org/10.1103/PhysRevD.86.054005, but the reorganization of the perturbation theory that we propose is new. As compared to the proposal in http://dx.doi.org/10.1103/PhysRevLett.108.122301, http://dx.doi.org/10.1103/PhysRevD.86.054005, our scheme is free of the fine-tuning inherent in the rapidity subtraction, which might be the origin of the negativity of the NLO cross-section observed in previous studies.

  15. CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order

    Energy Technology Data Exchange (ETDEWEB)

    Iancu, E. [Institut de physique théorique, Université Paris Saclay,CNRS, CEA, F-91191 Gif-sur-Yvette (France); Mueller, A.H. [Department of Physics, Columbia University,New York, NY 10027 (United States); Triantafyllopoulos, D.N. [European Centre for Theoretical Studies in Nuclear Physics and Related Areas - ECT*, Trento (Italy); Fondazione Bruno Kessler, Strada delle Tabarelle 286, I-38123 Villazzano (Italy)

    2016-12-13

    Within the Color Glass Condensate effective theory, we reconsider the next-to-leading order (NLO) calculation of the single inclusive particle production at forward rapidities in proton-nucleus collisions at high energy. Focusing on quark production for definiteness, we establish a new factorization scheme, perturbatively correct through NLO, in which there is no ‘rapidity subtraction’. That is, the NLO correction to the impact factor is not explicitly separated from the high-energy evolution. Our construction exploits the skeleton structure of the (NLO) Balitsky-Kovchegov equation, in which the first step of the evolution is explicitly singled out. The NLO impact factor is included by computing this first emission with the exact kinematics for the emitted gluon, rather than by using the eikonal approximation. This particular calculation has already been presented in the literature http://dx.doi.org/10.1103/PhysRevLett.108.122301, http://dx.doi.org/10.1103/PhysRevD.86.054005, but the reorganization of the perturbation theory that we propose is new. As compared to the proposal in http://dx.doi.org/10.1103/PhysRevLett.108.122301, http://dx.doi.org/10.1103/PhysRevD.86.054005, our scheme is free of the fine-tuning inherent in the rapidity subtraction, which might be the origin of the negativity of the NLO cross-section observed in previous studies.

  16. Top quark forward-backward asymmetry in e+ e- annihilation at next-to-next-to-leading order in QCD.

    Science.gov (United States)

    Gao, Jun; Zhu, Hua Xing

    2014-12-31

    We report on a complete calculation of electroweak production of top-quark pairs in e+ e- annihilation at next-to-next-to-leading order in quantum chromodynamics. Our setup is fully differential in phase space and can be used to calculate any infrared-safe observable. Especially we calculated the next-to-next-to-leading-order corrections to the top-quark forward-backward asymmetry and found sizable effects. Our results show a large reduction of the theoretical uncertainties in predictions of the forward-backward asymmetry, and allow for a precision determination of the top-quark electroweak couplings at future e+ e- colliders.

  17. Next-to-leading order electroweak corrections to off-shell WWW production at the LHC arXiv

    CERN Document Server

    Schönherr, Marek

    Triboson processes allow for a measurement of the triple and quartic couplings of the Standard Model gauge bosons, which can be used to constrain anomalous gauge couplings. In this paper we calculate the next-to-leading order electroweak corrections to fully off-shell $W^-W^+W^+$ production, namely the production of a $\\ell_1^-\\ell_2^+\\ell_3^+\\bar{\

  18. Inclusive particle production at HERA: Resolved and direct quasi-real photon contributions in next-to-leading order QCD

    International Nuclear Information System (INIS)

    Kniehl, B.A.; Kramer, G.

    1994-01-01

    We calculate in next-to-leading order inclusive cross sections of single-particle production via both direct and resolved photons in ep collisions at HERA. Transverse-momentum and rapidity distributions are presented and the dependences on renormalization and factorization scales and subtraction schemes are investigated. (orig.)

  19. Next-to-leading order unitarity fits in Two-Higgs-Doublet models with soft ℤ{sub 2} breaking

    Energy Technology Data Exchange (ETDEWEB)

    Cacchio, Vincenzo; Chowdhury, Debtosh; Eberhardt, Otto [Istituto Nazionale di Fisica Nucleare, Sezione di Roma,Piazzale Aldo Moro 2, I-00185 Roma (Italy); Murphy, Christopher W. [Scuola Normale Superiore,Piazza dei Cavalieri 7, I-56126 Pisa (Italy)

    2016-11-07

    We fit the next-to-leading order unitarity conditions to the Two-Higgs-Doublet model with a softly broken ℤ{sub 2} symmetry. In doing so, we alleviate the existing uncertainty on how to treat higher order corrections to quartic couplings of its Higgs potential. A simplified approach to implementing the next-to-leading order unitarity conditions is presented. These new bounds are then combined with all other relevant constraints, including the complete set of LHC Run I data. The upper 95% bounds we find are 4.2 on the absolute values of the quartic couplings, and 235 GeV (100 GeV) for the mass degeneracies between the heavy Higgs particles in the type I (type II) scenario. In type II, we exclude an unbroken ℤ{sub 2} symmetry with a probability of 95%. All fits are performed using the open-source code HEPfit.

  20. Imaginary part of the next-to-leading-order static gluon self-energy in an anisotropic plasma

    International Nuclear Information System (INIS)

    Carrington, M. E.; Rebhan, A.

    2009-01-01

    Using hard-loop (HL) effective theory for an anisotropic non-Abelian plasma, which even in the static limit involves nonvanishing HL vertices, we calculate the imaginary part of the static next-to-leading-order gluon self-energy in the limit of a small anisotropy and with external momentum parallel to the anisotropy direction. At leading order, the static propagator has spacelike poles corresponding to plasma instabilities. On the basis of a calculation using bare vertices, it has been conjectured that, at next-to-leading order, the static gluon self-energy acquires an imaginary part which regulates these spacelike poles. We find that the one-loop resummed expression taken over naively from the imaginary-time formalism does yield a nonvanishing imaginary part even after including all HL vertices. However, this result is not correct. Starting from the real-time formalism, which is required in a nonequilibrium situation, we construct a resummed retarded HL propagator with correct causality properties and show that the static limit of the retarded one-loop-resummed gluon self-energy is real. This result is also required for the time-ordered propagator to exist at next-to-leading order.

  1. Polarized Di-hadron production in lepton-nucleon collisions at the next-to-leading order of QCD

    International Nuclear Information System (INIS)

    Hendlmeier, Christof

    2008-05-01

    We compute the next-to-leading order QCD corrections to the spin-dependent cross section for hadron-pair photoproduction. In the first part of the Thesis the calculation is performed using largely analytical methods. We present a detailed phenomenological study of our results focussing on the K-factors and scale dependence of the next-to-leading order cross sections. The second part is dedicated to an alternative approach using Monte-Carlo integration techniques. We present a detailed description how this method works in practice and give phenomenological studies for the photoproduction of two hadrons. This process is relevant for the extraction of the gluon polarization in present and future spin-dependent lepton-nucleon scattering experiments. (orig.)

  2. Polarized Di-hadron production in lepton-nucleon collisions at the next-to-leading order of QCD

    Energy Technology Data Exchange (ETDEWEB)

    Hendlmeier, Christof

    2008-05-15

    We compute the next-to-leading order QCD corrections to the spin-dependent cross section for hadron-pair photoproduction. In the first part of the Thesis the calculation is performed using largely analytical methods. We present a detailed phenomenological study of our results focussing on the K-factors and scale dependence of the next-to-leading order cross sections. The second part is dedicated to an alternative approach using Monte-Carlo integration techniques. We present a detailed description how this method works in practice and give phenomenological studies for the photoproduction of two hadrons. This process is relevant for the extraction of the gluon polarization in present and future spin-dependent lepton-nucleon scattering experiments. (orig.)

  3. Survival probability for diffractive dijet production in p anti p collisions from next-to-leading order calculations

    International Nuclear Information System (INIS)

    Klasen, M.; Kramer, G.

    2009-08-01

    We perform next-to-leading order calculations of the single-diffractive and non-diffractive cross sections for dijet production in proton-antiproton collisions at the Tevatron. By comparing their ratio to the data published by the CDF collaboration for two different center-of-mass energies, we deduce the rapidity-gap survival probability as a function of the momentum fraction of the parton in the antiproton. Assuming Regge factorization, this probability can be interpreted as a suppression factor for the diffractive structure function measured in deep-inelastic scattering at HERA. In contrast to the observations for photoproduction, the suppression factor in protonantiproton collisions depends on the momentum fraction of the parton in the Pomeron even at next-to-leading order. (orig.)

  4. Extending the Matrix Element Method beyond the Born approximation: calculating event weights at next-to-leading order accuracy

    Energy Technology Data Exchange (ETDEWEB)

    Martini, Till; Uwer, Peter [Humboldt-Universität zu Berlin, Institut für Physik,Newtonstraße 15, 12489 Berlin (Germany)

    2015-09-14

    In this article we illustrate how event weights for jet events can be calculated efficiently at next-to-leading order (NLO) accuracy in QCD. This is a crucial prerequisite for the application of the Matrix Element Method in NLO. We modify the recombination procedure used in jet algorithms, to allow a factorisation of the phase space for the real corrections into resolved and unresolved regions. Using an appropriate infrared regulator the latter can be integrated numerically. As illustration, we reproduce differential distributions at NLO for two sample processes. As further application and proof of concept, we apply the Matrix Element Method in NLO accuracy to the mass determination of top quarks produced in e{sup +}e{sup −} annihilation. This analysis is relevant for a future Linear Collider. We observe a significant shift in the extracted mass depending on whether the Matrix Element Method is used in leading or next-to-leading order.

  5. Extending the Matrix Element Method beyond the Born approximation: calculating event weights at next-to-leading order accuracy

    International Nuclear Information System (INIS)

    Martini, Till; Uwer, Peter

    2015-01-01

    In this article we illustrate how event weights for jet events can be calculated efficiently at next-to-leading order (NLO) accuracy in QCD. This is a crucial prerequisite for the application of the Matrix Element Method in NLO. We modify the recombination procedure used in jet algorithms, to allow a factorisation of the phase space for the real corrections into resolved and unresolved regions. Using an appropriate infrared regulator the latter can be integrated numerically. As illustration, we reproduce differential distributions at NLO for two sample processes. As further application and proof of concept, we apply the Matrix Element Method in NLO accuracy to the mass determination of top quarks produced in e"+e"− annihilation. This analysis is relevant for a future Linear Collider. We observe a significant shift in the extracted mass depending on whether the Matrix Element Method is used in leading or next-to-leading order.

  6. Dijet production in diffractive deep-inelastic scattering in next-to-next-to-leading order QCD arXiv

    CERN Document Server

    Britzger, D.; Gehrmann, T.; Huss, A.; Niehues, J.; Žlebčík, R.

    Hard processes in diffractive deep-inelastic scattering can be described by a factorisation into parton-level subprocesses and diffractive parton distributions. In this framework, cross sections for inclusive dijet production in diffractive deep-inelastic electron-proton scattering (DIS) are computed to next-to-next-to-leading order (NNLO) QCD accuracy and compared to a comprehensive selection of data. Predictions for the total cross sections, 39 single-differential and four double-differential distributions for six measurements at HERA by the H1 and ZEUS collaborations are calculated. In the studied kinematical range, the NNLO corrections are found to be sizeable and positive. The NNLO predictions typically exceed the data, while the kinematical shape of the data is described better at NNLO than at next-to-leading order (NLO). A significant reduction of the scale uncertainty is achieved in comparison to NLO predictions. Our results use the currently available NLO diffractive parton distributions, and the dis...

  7. Next-to-leading-order electroweak corrections to the production of three charged leptons plus missing energy at the LHC

    Science.gov (United States)

    Biedermann, Benedikt; Denner, Ansgar; Hofer, Lars

    2017-10-01

    The production of a neutral and a charged vector boson with subsequent decays into three charged leptons and a neutrino is a very important process for precision tests of the Standard Model of elementary particles and in searches for anomalous triple-gauge-boson couplings. In this article, the first computation of next-to-leading-order electroweak corrections to the production of the four-lepton final states μ + μ -e+ ν e, {μ}+{μ}-{e}-{\\overline{ν}}e , μ + μ - μ + ν μ , and {μ}+{μ}-{μ}-{\\overline{ν}}_{μ } at the Large Hadron Collider is presented. We use the complete matrix elements at leading and next-to-leading order, including all off-shell effects of intermediate massive vector bosons and virtual photons. The relative electroweak corrections to the fiducial cross sections from quark-induced partonic processes vary between -3% and -6%, depending significantly on the event selection. At the level of differential distributions, we observe large negative corrections of up to -30% in the high-energy tails of distributions originating from electroweak Sudakov logarithms. Photon-induced contributions at next-to-leading order raise the leading-order fiducial cross section by +2%. Interference effects in final states with equal-flavour leptons are at the permille level for the fiducial cross section, but can lead to sizeable effects in off-shell sensitive phase-space regions.

  8. Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy

    Science.gov (United States)

    Del Duca, Vittorio; Duhr, Claude; Kardos, Adam; Somogyi, Gábor; Trócsányi, Zoltán

    2016-10-01

    We introduce a completely local subtraction method for fully differential predictions at next-to-next-to-leading order (NNLO) accuracy for jet cross sections and use it to compute event shapes in three-jet production in electron-positron collisions. We validate our method on two event shapes, thrust and C parameter, which are already known in the literature at NNLO accuracy and compute for the first time oblateness and the energy-energy correlation at the same accuracy.

  9. A Next-to-Leading Order QCD Analysis of Neutrino - Iron Structure Functions at the Tevatron

    Energy Technology Data Exchange (ETDEWEB)

    Seligman, William Glenn [Nevis Labs, Columbia U.

    1997-01-01

    Nucleon structure functions measured in neutrino-iron and antineutrinoiron charged-current interactions are presented. The data were taken in two high-energy high-statistics runs by the LAB-E detector at the Fermilab Tevatron. Structure functions are extracted from a sample of 950,000 neutrino and 170,000 antineutrino events with neutrino energies from 30 to 360 Ge V. The structure functions $F_2$ and $xF_3$ are compared with the the predictions of perturbative Quantum Chromodynamics (PQCD). The combined non-singlet and singlet evolution in the context of PQCD gives NL0(4) . 2 value of $\\Lambda^{NLO,(4)}_{\\overline MS}$ = 337 ± 28 (exp.) MeV, which corresponds to $\\alpha_s$ ($M^2_z$) = 0.119 ± 0.002 (exp.) ± 0.004 (theory), and with a gluon distribution given by $xG(x,Q^2_0 = 5 GeV^2$ ) = (2.22±0.34) x ($1-x)^{4.65 \\pm 0.68}$

  10. Next to leading order evolution of SIDIS processes in the forward region

    International Nuclear Information System (INIS)

    Daleo, A.; Sassot, R.

    2003-01-01

    We compute the order α s 2 quark initiated corrections to semi-inclusive deep inelastic scattering extending the approach developed recently for the gluon contributions. With these corrections we complete the order α s 2 QCD description of these processes, verifying explicitly the factorization of collinear singularities. We also obtain the corresponding NLO evolution kernels, relevant for the scale dependence of fracture functions. We compare the non-homogeneous evolution effects driven by these kernels with those obtained at leading order accuracy and discuss their phenomenological implications

  11. The next-to-leading order (NLO) gluon distribution from DGLAP ...

    Indian Academy of Sciences (India)

    leading order (NLO) is obtained by applying the method of characteristics. Its compatibility with double leading logarithmic approximation (DLLA) asymptotics is discussed and comparison with the exact ones like GRV98NLO is made. The solution ...

  12. Impact of Next-to-Leading Order Contributions to Cosmic Microwave Background Lensing.

    Science.gov (United States)

    Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth

    2017-05-26

    In this Letter we study the impact on cosmological parameter estimation, from present and future surveys, due to lensing corrections on cosmic microwave background temperature and polarization anisotropies beyond leading order. In particular, we show how post-Born corrections, large-scale structure effects, and the correction due to the change in the polarization direction between the emission at the source and the detection at the observer are non-negligible in the determination of the polarization spectra. They have to be taken into account for an accurate estimation of cosmological parameters sensitive to or even based on these spectra. We study in detail the impact of higher order lensing on the determination of the tensor-to-scalar ratio r and on the estimation of the effective number of relativistic species N_{eff}. We find that neglecting higher order lensing terms can lead to misinterpreting these corrections as a primordial tensor-to-scalar ratio of about O(10^{-3}). Furthermore, it leads to a shift of the parameter N_{eff} by nearly 2σ considering the level of accuracy aimed by future S4 surveys.

  13. Next-to-Leading Order Computation of Exclusive Diffractive Light Vector Meson Production in a Saturation Framework.

    Science.gov (United States)

    Boussarie, R; Grabovsky, A V; Ivanov, D Yu; Szymanowski, L; Wallon, S

    2017-08-18

    We perform the first next-to-leading order computation of the γ^{(*)}→V (ρ,ϕ,ω) exclusive impact factor in the QCD shock-wave approach and in the most general kinematics. This paves the way to the very first quantitative study of high-energy nucleon and nucleus saturation beyond the leading order for a whole range of small-x exclusive processes, to be measured in ep, eA, pp, and pA collisions at existing and future colliders.

  14. Towards next-to-leading order corrections to the heavy quark potential in the effective string theory

    Directory of Open Access Journals (Sweden)

    Hwang Sungmin

    2017-01-01

    Full Text Available We present our calculation of the non-relativistic corrections to the heavy quark-antiquark potential up to leading and next-to-leading order (NLO via the effective string theory (EST. Full systematics of effective field theory (EFT are discussed in order for including the NLO contribution that arises in the EST. We also show how the number of dimensionful parameters arising from the EST are reduced by the constraints between the Wilson coeffcients from non-relativistic EFTs for QCD.

  15. Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory.

    Science.gov (United States)

    Tews, I; Krüger, T; Hebeler, K; Schwenk, A

    2013-01-18

    Neutron matter presents a unique system for chiral effective field theory because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N(3)LO). We present the first complete N(3)LO calculation of the neutron matter energy. This includes the subleading three-nucleon forces for the first time and all leading four-nucleon forces. We find relatively large contributions from N(3)LO three-nucleon forces. Our results provide constraints for neutron-rich matter in astrophysics with controlled theoretical uncertainties.

  16. Fully differential Higgs boson pair production in association with a Z boson at next-to-next-to-leading order in QCD

    Science.gov (United States)

    Li, Hai Tao; Li, Chong Sheng; Wang, Jian

    2018-04-01

    We present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a Z boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2-1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

  17. The complete vertical stroke ΔS vertical stroke =2-hamiltonian in the next-to-leading order

    International Nuclear Information System (INIS)

    Herrlich, S.; Nierste, U.

    1996-04-01

    We present the complete next-to-leading order short-distance QCD corrections to the effective vertical stroke ΔS vertical stroke =2-hamiltonian in the Standard Model. The calculation of the coefficient η 3 is described in great detail. It involves the two-loop mixing of bilocal structures composed of two vertical stroke ΔS vertical stroke =1 operators into vertical stroke ΔS vertical stroke =2 operators. The next-to-leading order corrections enhance η 3 by 27% to η 3 =0.47(+0.03-0.04) thereby affecting the phenomenology of ε K sizeably. η 3 depends on the physical input parameters m t , m c and Λsub(anti M anti S) only weakly. The quoted error stems from renormalization scale dependences, which have reduced compared to the old leading log result. The known calculation of η 1 and η 2 is repeated in order to compare the structure of the three QCD coefficients. We further discuss some field theoretical aspects of the calculation such as the renormalization group equation for Green's functions with two operator insertions and the renormalization scheme dependence caused by the presence of evanescent operators. (orig.)

  18. Next-to-leading order QCD corrections to W+W- production via vector-boson fusion

    International Nuclear Information System (INIS)

    Jaeger, Barbara; Oleari, Carlo; Zeppenfeld, Dieter

    2006-01-01

    Vector-boson fusion processes constitute an important class of reactions at hadron colliders, both for signals and backgrounds of new physics in the electroweak interactions. We consider what is commonly referred to as W + W - production via vector-boson fusion (with subsequent leptonic decay of the Ws), or, more precisely, e + ν e μ - ν-bar μ + 2 jets production in proton-proton scattering, with all resonant and non-resonant Feynman diagrams and spin correlations of the final-state leptons included, in the phase-space regions which are dominated by t-channel electroweak-boson exchange. We compute the next-to-leading order QCD corrections to this process, at order α 6 α s . The QCD corrections are modest, changing total cross sections by less than 10%. Remaining scale uncertainties are below 2%. A fully-flexible next-to-leading order partonic Monte Carlo program allows to demonstrate these features for cross sections within typical vector-boson-fusion acceptance cuts. Modest corrections are also found for distributions

  19. Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order

    Energy Technology Data Exchange (ETDEWEB)

    Buras, Andrzej J.; /Munich, Tech. U.; Gorbahn, Martin; /Durham U., IPPP /Karlsruhe U., TTP; Haisch, Ulrich; /Fermilab /Zurich U.; Nierste, Ulrich; /Karlsruhe U., TTP

    2006-03-01

    The authors calculate the complete next-to-next-to-leading order QCD corrections to the charm contribution of the rare decay K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}. They encounter several new features, which were absent in lower orders. They discuss them in detail and present the results for the two-loop matching conditions of the Wilson coefficients, the three-loop anomalous dimensions, and the two-loop matrix elements of the relevant operators that enter the next-to-next-to-leading order renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the next-to-next-to-leading order QCD corrections leads to a significant reduction of the theoretical uncertainty from {+-} 9.8% down to {+-} 2.4% in the relevant parameter P{sub c}(X), implying the leftover scale uncertainties in {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) and in the determination of |V{sub td}|, sin 2{beta}, and {gamma} from the K {yields} {pi}{nu}{bar {nu}} system to be {+-} 1.3%, {+-} 1.0%, {+-} 0.006, and {+-} 1.2{sup o}, respectively. For the charm quark {ovr MS} mass m{sub c}(m{sub c}) = (1.30 {+-} 0.05) GeV and |V{sub us}| = 0.2248 the next-to-leading order value P{sub c}(X) = 0.37 {+-} 0.06 is modified to P{sub c}(X) = 0.38 {+-} 0.04 at the next-to-next-to-leading order level with the latter error fully dominated by the uncertainty in m{sub c}(m{sub c}). They present tables for P{sub c}(X) as a function of m{sub c}(m{sub c}) and {alpha}{sub s}(M{sub z}) and a very accurate analytic formula that summarizes these two dependences as well as the dominant theoretical uncertainties. Adding the recently calculated long-distance contributions they find {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) = (8.0 {+-} 1.1) x 10{sup -11} with the present uncertainties in m{sub c}(m{sub c}) and the Cabibbo-Kobayashi-Maskawa elements being the dominant individual sources in the quoted error. They also emphasize that improved calculations of the long

  20. Top-quark pair production at next-to-next-to-leading order QCD in electron positron collisions

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Long [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University,52056 Aachen (Germany); Dekkers, Oliver [PRISMA Cluster of Excellence and Institut für Physik,Johannes-Gutenberg-Universität Mainz,55099 Mainz (Germany); Heisler, Dennis; Bernreuther, Werner [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University,52056 Aachen (Germany); Si, Zong-Guo [School of Physics, Shandong University,Jinan, Shandong 250100 (China)

    2016-12-19

    We set up a formalism, within the antenna subtraction framework, for computing the production of a massive quark-antiquark pair in electron positron collisions at next-to-next-to-leading order in the coupling α{sub s} of quantum chromodynamics at the differential level. Our formalism applies to the calculation of any infrared-safe observable. We apply this set-up to the production of top-quark top antiquark pairs in the continuum. We compute the production cross section and several distributions. We determine, in particular, the top-quark forward-backward asymmetry at order α{sub s}{sup 2}. Our result agrees with previous computations of this observable.

  1. Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence.

    Science.gov (United States)

    Borowka, S; Greiner, N; Heinrich, G; Jones, S P; Kerner, M; Schlenk, J; Schubert, U; Zirke, T

    2016-07-01

    We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.

  2. Charm production in deep-inelastic e$\\gamma$ scattering to next-to-leading order in QCD

    CERN Document Server

    Laenen, Eric

    1995-01-01

    We discuss the calculation of F_2^{\\gamma}({\\rm charm}) to next-to-leading order (NLO) in QCD, including contributions from both hadronlike and pointlike photons. We show that the former dominates strongly below x\\simeq 0.01, and the latter above this value. This fact makes F_2^{\\gamma}({\\rm charm}) for x \\geq 0.01 calculable, whereas for x \\leq 0.01 it serves to constrain the small-x gluon density in the photon. Both ranges in x are accessible at LEP2. Theoretical uncertainties are well under control. We present rates for single-tag events for the process for e^+e^- \\rightarrow e^+e^- c X for LEP2. Although these event rates are small, we believe a measurement of F_2^{\\gamma}({\\rm charm}) is feasible.

  3. Revisiting the vector form factor at next-to-leading order in 1/N{sub C}

    Energy Technology Data Exchange (ETDEWEB)

    Rosell, Ignasi, E-mail: rosell@uch.ceu.e [Departamento de Ciencias Fisicas, Matematicas y de la Computacion, Universidad CEU Cardenal Herrera, c/ Sant Bartomeu 55, E-46115 Alfara del Patriarca, Valencia (Spain); IFIC, Universitat de Valencia - CSIC, Apt. Correus 22085, E-46071 Valencia (Spain)

    2010-10-15

    Using the Resonance Chiral Theory lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/N{sub C} expansion. Imposing the correct QCD short-distance constraints, one determines it in terms of F, G{sub V}, F{sub A} and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L{sub 9} and C{sub 88} -C{sub 90} at NLO, keeping full control of their renormalization scale dependence. At {mu}{sub 0} = 0.77 GeV, we obtain L{sup r}{sub 9}({mu}{sub 0}) = (7.6 {+-} 0.6) . 10{sup -3} and C{sup r}{sub 88}({mu}{sub 0}) -C{sup r}{sub 90}({mu}{sub 0}) = (-4.5 {+-} 0.5) . 10{sup -5}.

  4. Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC

    Energy Technology Data Exchange (ETDEWEB)

    Biedermann, Benedikt; Denner, Ansgar [Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, 97074 Würzburg (Germany); Dittmaier, Stefan [Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg (Germany); Hofer, Lars [Institut de Ciències del Cosmo (ICCUB), Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona - UB, 08028 Barcelona (Spain); Jäger, Barbara [Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, 72076 Tübingen (Germany)

    2017-01-09

    We present a state-of-the-art calculation of the next-to-leading-order electroweak corrections to ZZ production, including the leptonic decays of the Z bosons into μ{sup +}μ{sup −}e{sup +}e{sup −} or μ{sup +}μ{sup −}μ{sup +}μ{sup −} final states. We use complete leading-order and next-to-leading-order matrix elements for four-lepton production, including contributions of virtual photons and all off-shell effects of Z bosons, where the finite Z-boson width is taken into account using the complex-mass scheme. The matrix elements are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential distributions. We present integrated and differential cross sections for the LHC at 13 TeV both for an inclusive setup where only lepton identification cuts are applied, and for a setup motivated by Higgs-boson analyses in the four-lepton decay channel. The electroweak corrections are divided into photonic and purely weak contributions. The former show the well-known pronounced tails near kinematical thresholds and resonances; the latter are generically at the level of ∼−5% and reach several −10% in the high-energy tails of distributions. Comparing the results for μ{sup +}μ{sup −}e{sup +}e{sup −} and μ{sup +}μ{sup −}μ{sup +}μ{sup −} final states, we find significant differences mainly in distributions that are sensitive to the μ{sup +}μ{sup −} pairing in the μ{sup +}μ{sup −}μ{sup +}μ{sup −} final state. Differences between μ{sup +}μ{sup −}e{sup +}e{sup −} and μ{sup +}μ{sup −}μ{sup +}μ{sup −} channels due to interferences of equal-flavour leptons in the final state can reach up to 10% in off-shell-sensitive regions. Contributions induced by incoming photons, i.e. photon-photon and quark-photon channels, are included, but turn out to be phenomenologically unimportant.

  5. Nuclear forces with Δ excitations up to next-to-next-to-leading order. Part I: Peripheral nucleon-nucleon waves

    International Nuclear Information System (INIS)

    Krebs, H.; Epelbaum, E.; Meissner, U.G.

    2007-01-01

    We study the two-nucleon force at next-to-next-to-leading order in a chiral effective field theory with explicit Δ degrees of freedom. Fixing the appearing low-energy constants from a next-to-leading-order calculation of pion-nucleon threshold parameters, we find an improved convergence of most peripheral nucleon-nucleon phases compared to the theory with pions and nucleons only. In the delta-full theory, the next-to-leading-order corrections are dominant in most partial waves considered. (orig.)

  6. Next-to-leading resummation of cosmological perturbations via the Lagrangian picture: 2-loop correction in real and redshift spaces

    International Nuclear Information System (INIS)

    Okamura, Tomohiro; Taruya, Atsushi; Matsubara, Takahiko

    2011-01-01

    We present an improved prediction of Lagrangian resummation theory (LRT), the nonlinear perturbation theory (PT) via the Lagrangian picture originally proposed by Matsubara (2008). Based on the relations between the power spectrum in standard PT and that in LRT, we derive analytic expressions for the power spectrum in LRT up to 2-loop order in both real and redshift spaces. Comparing the improved prediction of LRT with N-body simulations in real space, we find that the 2-loop corrections can extend the valid range of wave numbers where we can predict the power spectrum within 1% accuracy by a factor of 1.0 (z = 0.5), 1.3 (1), 1.6 (2) and 1.8 (3) vied with 1-loop LRT results. On the other hand, in all redshift ranges, the higher-order corrections are shown to be less significant on the two-point correlation functions around the baryon acoustic peak, because the 1-loop LRT is already accurate enough to explain the nonlinearity on those scales in N-body simulations

  7. Antinucleon-nucleon interaction at next-to-next-to-next-to-leading order in chiral effective field theory

    Science.gov (United States)

    Dai, Ling-Yun; Haidenbauer, Johann; Meißner, Ulf-G.

    2017-07-01

    Results for the antinucleon-nucleon (\\overline{N}N) interaction obtained at next-to-next-to-next-to-leading order in chiral effective field theory (EFT) are reported. A new local regularization scheme is used for the pion-exchange contributions that has been recently suggested and applied in a pertinent study of the N N force within chiral EFT. Furthermore, an alternative strategy for estimating the uncertainty is utilized that no longer depends on a variation of the cutoffs. The low-energy constants associated with the arising contact terms are fixed by a fit to the phase shifts and inelasticities provided by a phase-shift analysis of \\overline{p}p scattering data. An excellent description of the \\overline{N}N amplitudes is achieved at the highest order considered. Moreover, because of the quantitative reproduction of partial waves up to J = 3, there is also a nice agreement on the level of \\overline{p}p observables. Specifically, total and integrated elastic and charge-exchange cross sections agree well with the results from the partial-wave analysis up to laboratory energies of 300 MeV, while differential cross sections and analyzing powers are described quantitatively up to 200-250 MeV. The low-energy structure of the \\overline{N}N amplitudes is also considered and compared to data from antiprotonic hydrogen.

  8. QCD next-to-leading-order predictions matched to parton showers for vector-like quark models.

    Science.gov (United States)

    Fuks, Benjamin; Shao, Hua-Sheng

    2017-01-01

    Vector-like quarks are featured by a wealth of beyond the Standard Model theories and are consequently an important goal of many LHC searches for new physics. Those searches, as well as most related phenomenological studies, however, rely on predictions evaluated at the leading-order accuracy in QCD and consider well-defined simplified benchmark scenarios. Adopting an effective bottom-up approach, we compute next-to-leading-order predictions for vector-like-quark pair production and single production in association with jets, with a weak or with a Higgs boson in a general new physics setup. We additionally compute vector-like-quark contributions to the production of a pair of Standard Model bosons at the same level of accuracy. For all processes under consideration, we focus both on total cross sections and on differential distributions, most these calculations being performed for the first time in our field. As a result, our work paves the way to precise extraction of experimental limits on vector-like quarks thanks to an accurate control of the shapes of the relevant observables and emphasise the extra handles that could be provided by novel vector-like-quark probes never envisaged so far.

  9. QCD next-to-leading order predictions matched to parton showers for vector-like quark models

    CERN Document Server

    Fuks, Benjamin

    2017-02-27

    Vector-like quarks are featured by a wealth of beyond the Standard Model theories and are consequently an important goal of many LHC searches for new physics. Those searches, as well as most related phenomenological studies, however rely on predictions evaluated at the leading-order accuracy in QCD and consider well-defined simplified benchmark scenarios. Adopting an effective bottom-up approach, we compute next-to-leading-order predictions for vector-like-quark pair-production and single production in association with jets, with a weak or with a Higgs boson in a general new physics setup. We additionally compute vector-like-quark contributions to the production of a pair of Standard Model bosons at the same level of accuracy. For all processes under consideration, we focus both on total cross sections and on differential distributions, most these calculations being performed for the first time in our field. As a result, our work paves the way to precise extraction of experimental limits on vector-like quarks...

  10. Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions

    Energy Technology Data Exchange (ETDEWEB)

    Benić, Sanjin [Physics Department, Faculty of Science, University of Zagreb,Zagreb 10000 (Croatia); Department of Physics, The University of Tokyo,7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Fukushima, Kenji [Department of Physics, The University of Tokyo,7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Garcia-Montero, Oscar [Institut für Theoretische Physik, Universität Heidelberg,Philosophenweg 16, 69120 Heidelberg (Germany); Venugopalan, Raju [Physics Department, Brookhaven National Laboratory,Bldg. 510A, Upton, NY 11973 (United States)

    2017-01-26

    We compute the cross section for photons emitted from sea quarks in proton-nucleus collisions at collider energies. The computation is performed within the dilute-dense kinematics of the Color Glass Condensate (CGC) effective field theory. Albeit the result obtained is formally at next-to-leading order in the CGC power counting, it provides the dominant contribution for central rapidities. We observe that the inclusive photon cross section is proportional to all-twist Wilson line correlators in the nucleus. These correlators also appear in quark-pair production; unlike the latter, photon production is insensitive to hadronization uncertainties and therefore more sensitive to multi-parton correlations in the gluon saturation regime of QCD. We demonstrate that k{sub ⊥} and collinear factorized expressions for inclusive photon production are obtained as leading twist approximations to our result. In particular, the collinearly factorized expression is directly sensitive to the nuclear gluon distribution at small x. Other results of interest include the realization of the Low-Burnett-Kroll soft photon theorem in the CGC framework and a comparative study of how the photon amplitude is obtained in Lorenz and light-cone gauges.

  11. Next-to-leading-order QCD and electroweak corrections to WWW production at proton-proton colliders

    Science.gov (United States)

    Dittmaier, Stefan; Huss, Alexander; Knippen, Gernot

    2017-09-01

    Triple-W-boson production in proton-proton collisions allows for a direct access to the triple and quartic gauge couplings and provides a window to the mechanism of electroweak symmetry breaking. It is an important process to test the Standard Model (SM) and might be background to physics beyond the SM. We present a calculation of the next-to-leading order (NLO) electroweak corrections to the production of WWW final states at proton-proton colliders with on-shell W bosons and combine the electroweak with the NLO QCD corrections. We study the impact of the corrections to the integrated cross sections and to kinematic distributions of the W bosons. The electroweak corrections are generically of the size of 5-10% for integrated cross sections and become more pronounced in specific phase-space regions. The real corrections induced by quark-photon scattering turn out to be as important as electroweak loops and photon bremsstrahlung corrections, but can be reduced by phase-space cuts. Considering that prior determinations of the photon parton distribution function (PDF) involve rather large uncertainties, we compare the results obtained with different photon PDFs and discuss the corresponding uncertainties in the NLO predictions. Moreover, we determine the scale and total PDF uncertainties at the LHC and a possible future 100 TeV pp collider.

  12. First determination of D* -meson fragmentation functions and their uncertainties at next-to-next-to-leading order

    Science.gov (United States)

    Soleymaninia, Maryam; Khanpour, Hamzeh; Nejad, S. Mohammad Moosavi

    2018-04-01

    We present, for the first time, a set of next-to-next-to-leading order (NNLO) fragmentation functions (FFs) describing the production of charmed-meson D* from partons. Exploiting the universality and scaling violations of FFs, we extract the NLO and NNLO FFs through a global fit to all relevant data sets from single-inclusive e+e- annihilation. The uncertainties for the resulting FFs as well as the corresponding observables are estimated using the Hessian approach. We evaluate the quality of the SKM18 FFs determined in this analysis by comparing with the recent results in literature and show how they describe the available data for single-inclusive D*±-meson production in electron-positron annihilation. As a practical application, we apply the extracted FFs to make our theoretical predictions for the scaled-energy distributions of D*±-mesons inclusively produced in top quark decays. We explore the implications of SKM18 for LHC phenomenology and show that our findings of this study can be introduced as a channel to indirect search for top-quark properties.

  13. Transverse energy-energy correlations in next-to-leading order in {alpha}{sub s} at the LHC

    Energy Technology Data Exchange (ETDEWEB)

    Ali, Ahmed; Wang, Wei [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Barreiro, Fernando; Llorente, Javier [Universidad Autonoma de Madrid (Spain). Dept. de Fisica

    2012-05-15

    We compute the transverse energy-energy correlation (EEC) and its asymmetry (AEEC) in next-to-leading order (NLO) in {alpha}{sub s} in proton-proton collisions at the LHC with the center-of-mass energy E{sub c.m.}=7 TeV. We show that the transverse EEC and the AEEC distributions are insensitive to the QCD factorization- and the renormalization-scales, structure functions of the proton, and for a judicious choice of the jet-size, also the underlying minimum bias events. Hence they can be used to precisely test QCD in hadron colliders and determine the strong coupling {alpha}{sub s}. We illustrate these features by defining the hadron jets using the anti-k{sub T} jet algorithm and an event selection procedure employed in the analysis of jets at the LHC and show the {alpha}{sub s}(M{sub Z})-dependence of the transverse EEC and the AEEC in the anticipated range 0.11{<=} {alpha}{sub s}(M{sub Z}){<=}0.13.

  14. Next-to-leading-order QCD corrections to e+e−→H+γ

    Directory of Open Access Journals (Sweden)

    Wen-Long Sang

    2017-12-01

    Full Text Available The associated production of Higgs boson with a hard photon at lepton collider, i.e., e+e−→Hγ, is known to bear a rather small cross section in Standard Model, and can serve as a sensitive probe for the potential new physics signals. Similar to the loop-induced Higgs decay channels H→γγ,Zγ, the e+e−→Hγ process also starts at one-loop order provided that the tiny electron mass is neglected. In this work, we calculate the next-to-leading-order (NLO QCD corrections to this associated H+γ production process, which mainly stem from the gluonic dressing to the top quark loop. The QCD corrections are found to be rather modest at lower center-of-mass energy range (s<300 GeV, thus of negligible impact on Higgs factory such as CEPC. Nevertheless, when the energy is boosted to the ILC energy range (s≈400 GeV, QCD corrections may enhance the leading-order cross section by 20%. In any event, the e+e−→Hγ process has a maximal production rate σmax≈0.08 fb around s=250 GeV, thus CEPC turns out to be the best place to look for this rare Higgs production process. In the high energy limit, the effect of NLO QCD corrections become completely negligible, which can be simply attributed to the different asymptotic scaling behaviors of the LO and NLO cross sections, where the former exhibits a milder decrement ∝1/s , but the latter undergoes a much faster decrease ∝1/s2. Keywords: Standard Model, Higgs boson, QCD corrections

  15. On the next-to-next-to leading order QCD corrections to heavy-quark production in deep-inelastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Kawamura, H. [KEK Theory Center, Tsukuba (Japan); Lo Presti, N.A.; Vogt, A. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2012-05-15

    The contribution of quarks with masses m >> {lambda}{sub QCD} is the only part of the structure functions in deep-inelastic scattering (DIS) which is not yet known at the next-to-next-to-leading order (NNLO) of perturbative QCD. We present improved partial NNLO results for the most important structure function F{sub 2}(x,Q{sup 2}) near the partonic threshold, in the high-energy (small-x) limit and at high scales Q{sup 2} >> m{sup 2}; and employ these results to construct approximations for the gluon and quark coefficient functions which cover the full kinematic plane. The approximation uncertainties are carefully investigated, and found to be large only at very small values, x

  16. FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order

    Science.gov (United States)

    Gavin, Ryan; Li, Ye; Petriello, Frank; Quackenbush, Seth

    2011-11-01

    We introduce an improved version of the simulation code FEWZ ( Fully Exclusive W and Z Production) for hadron collider production of lepton pairs through the Drell-Yan process at next-to-next-to-leading order (NNLO) in the strong coupling constant. The program is fully differential in the phase space of leptons and additional hadronic radiation. The new version offers users significantly more options for customization. FEWZ now bins multiple, user-selectable histograms during a single run, and produces parton distribution function (PDF) errors automatically. It also features a significantly improved integration routine, and can take advantage of multiple processor cores locally or on the Condor distributed computing system. We illustrate the new features of FEWZ by presenting numerous phenomenological results for LHC physics. We compare NNLO QCD with initial ATLAS and CMS results, and discuss in detail the effects of detector acceptance on the measurement of angular quantities associated with Z-boson production. We address the issue of technical precision in the presence of severe phase-space cuts. Program summaryProgram title: FEWZ Catalogue identifier: AEJP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6 280 771 No. of bytes in distributed program, including test data, etc.: 173 027 645 Distribution format: tar.gz Programming language: Fortran 77, C++, Python Computer: Mac, PC Operating system: Mac OSX, Unix/Linux Has the code been vectorized or parallelized?: Yes. User-selectable, 1 to 219 RAM: 200 Mbytes for common parton distribution functions Classification: 11.1 External routines: CUBA numerical integration library, numerous parton distribution sets (see text); these are provided with the code

  17. Next-to-next-to-leading order O({alpha}{sup 2}{alpha}{sup 2}{sub s}) results for top quark pair production in photon-photon collisions. The loop-by-loop contribution

    Energy Technology Data Exchange (ETDEWEB)

    Koerner, J.G. [Johannes Gutenberg Univ., Mainz (Germany). Inst. fuer Phys.; Merebashvili, Z. [Tbilisi State Univ. (Georgia). Inst. of High Energy Physics and Informatization; Rogal, M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2006-08-15

    We calculate the so-called loop-by-loop contributions to the next-to-next-to-leading order O({alpha}{sup 2}{alpha}{sup 2}{sub s}) radiative QCD corrections for the production of heavy quark pairs in the collisions of unpolarized on-shell photons. In particular, we present analytical results for the squared matrix elements that correspond to the product of the one-loop amplitudes. All results of the perturbative calculation are given in the dimensional regularization scheme. These results represent the Abelian part of the corresponding gluon-induced next-to-next-to-leading order cross section for heavy quark pair hadroproduction. (orig.)

  18. Next-to-next-to-leading order O(α2α2s) results for top quark pair production in photon-photon collisions. The one-loop squared contribution

    International Nuclear Information System (INIS)

    Koerner, J.G.

    2006-11-01

    We calculate the so-called loop-by-loop contributions to the next-to-next-to-leading order O(α 2 α 2 s ) radiative QCD corrections for the production of heavy quark pairs in the collisions of unpolarized on-shell photons. In particular, we present analytical results for the squared matrix elements that correspond to the product of the one-loop amplitudes. All results of the perturbative calculation are given in the dimensional regularization scheme. These results represent the Abelian part of the corresponding gluon-induced next-to-next-to-leading order cross section for heavy quark pair hadroproduction. (orig.)

  19. Automated next-to-leading order predictions for new physics at the LHC: the case of colored scalar pair production

    CERN Document Server

    Degrande, Céline; Hirschi, Valentin; Proudom, Josselin; Shao, Hua-Sheng

    2015-01-01

    We present for the first time the full automation of collider predictions matched with parton showers at the next-to-leading accuracy in QCD within non-trivial extensions of the Standard Model. The sole inputs required from the user are the model Lagrangian and the process of interest. As an application of the above, we explore scenarios beyond the Standard Model where new colored scalar particles can be pair produced in hadron collisions. Using simplified models to describe the new field interactions with the Standard Model, we present precision predictions for the LHC within the MadGraph5 aMC@NLO framework.

  20. Next-to-next-to-leading order QCD analysis of the revised CCFR data for xF3 structure function

    International Nuclear Information System (INIS)

    Kataev, A.L.; Kotikov, A.V.; Parente, G.; Sidorov, A.V.

    1997-01-01

    The results of the next-to-next-to-leading order QCD analysis of the recently revised experimental data of the CCFR collaboration for the xF 3 structure function using the Jacobi polynomial expansion method are presented. The effects of the higher twist contributions are included into the fits following the infrared renormalon motivated model. It is stressed that at the next-to-next-to-leading order the results for the parameter Λ M -bar S -bar (4) turn out to be almost nonsensitive to the predictions of the infrared renormalon model. The outcomes of our analysis are compared to the ones obtained by the CCFR collaboration itself at the next-to-leading order. (author)

  1. Heavy-quark pair production in gluon fusion at next-to-next-to-leading O({alpha}{sup 4}{sub s}) order. One-loop squared contributions

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, B.A.; Merebashvili, Z. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Koerner, J.G. [Mainz Univ. (Germany). Inst. fuer Physik; Rogal, M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2008-09-15

    We calculate the next-to-next-to-leading order O({alpha}{sup 4}{sub s}) one-loop squared corrections to the production of heavy quark pairs in the gluon-gluon fusion process. Together with the previously derived results on the q anti q production channel the results of this paper complete the calculation of the oneloop squared contributions of the next-to-next-to-leading order O({alpha}{sup 4}{sub s}) radiative QCD corrections to the hadroproduction of heavy flavours. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization. (orig.)

  2. Heavy-quark pair production in gluon fusion at next-to-next-to-leading O(α4s) order. One-loop squared contributions

    International Nuclear Information System (INIS)

    Kniehl, B.A.; Merebashvili, Z.

    2008-09-01

    We calculate the next-to-next-to-leading order O(α 4 s ) one-loop squared corrections to the production of heavy quark pairs in the gluon-gluon fusion process. Together with the previously derived results on the q anti q production channel the results of this paper complete the calculation of the oneloop squared contributions of the next-to-next-to-leading order O(α 4 s ) radiative QCD corrections to the hadroproduction of heavy flavours. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization. (orig.)

  3. Regge behaviour of structure functions and evolution of gluon structure function upto next-to-leading order at low-x

    International Nuclear Information System (INIS)

    Jamil, U.; Sarma, J.K.

    2011-01-01

    Evolution of gluon structure function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations upto next-to-leading order at low-x is presented assuming the Regge behaviour of structure functions. We compare our results of gluon structure function with GRV 98 global parameterization and show the compatibility of Regge behaviour of structure functions with PQCD. (author)

  4. Inclusive two-jet production in photon-photon collisions: Direct and resolved contributions in next-to-leading order QCD

    International Nuclear Information System (INIS)

    Kleinwort, T.; Kramer, G.

    1996-10-01

    We have calculated inclusive two-jet production in photon-photon collisions superimposing direct, single-resolved and double-resolved cross sections for center-of-mass energies of TRISTAN and LEP1.5. All three contributions are calculated up to next-to-leading order. The results are compared with recent experimental data. Three NLO sets of parton distributions of the photon are tested. (orig.)

  5. Next-to-next-to-leading order N-jettiness soft function for one massive colored particle production at hadron colliders

    Energy Technology Data Exchange (ETDEWEB)

    Li, Hai Tao [ARC Centre of Excellence for Particle Physics at the Terascale,School of Physics and Astronomy, Monash University, VIC-3800 (Australia); Wang, Jian [PRISMA Cluster of Excellence Mainz Institute for Theoretical Physics, Johannes Gutenberg University, D-55099 Mainz (Germany); Physik Department T31, Technische Universität München,James-Franck-Straße 1, D-85748 Garching (Germany)

    2017-02-01

    The N-jettiness subtraction has proven to be an efficient method to perform differential QCD next-to-next-to-leading order (NNLO) calculations in the last few years. One important ingredient of this method is the NNLO soft function. We calculate this soft function for one massive colored particle production at hadron colliders. We select the color octet and color triplet cases to present the final results. We also discuss its application in NLO and NNLO differential calculations.

  6. A next-to-leading-order QCD analysis of neutrino-iron structure functions at the Tevatron

    International Nuclear Information System (INIS)

    Seligman, W.G.

    1997-01-01

    Nucleon structure functions measured in neutrino-iron and antineutrino-iron charged-current interactions are presented. The data were taken in two high-energy high-statistics runs by the LAB-E detector at the Fermilab Tevatron. Structure functions are extracted from a sample of 950,000 neutrino and 170,000 antineutrino events with neutrino energies from 30 to 360 GeV. The structure functions F 2 and xF 3 are compared with the predictions of perturbative Quantum Chromodynamics (PQCD). The combined non-singlet and singlet evolution in the context of PQCD gives value of ΛNLO,(4)/MS = 337 ± 28 (exp.) MeV, which corresponds to α S (M Z 2 ) = 0.119 ± 0.002 (exp.) ± 0.004 (theory), and with a gluon distribution given by xG(x,Q 0 2 = 5GeV 2 ) = (2.22 ± 0.34) x (1 - x) 4.65±0.68

  7. A next-to-leading-order QCD analysis of neutrino-iron structure functions at the Tevatron

    Energy Technology Data Exchange (ETDEWEB)

    Seligman, William Glenn [Columbia Univ., New York, NY (United States)

    1997-01-01

    Nucleon structure functions measured in neutrino-iron and antineutrino-iron charged-current interactions are presented. The data were taken in two high-energy high-statistics runs by the LAB-E detector at the Fermilab Tevatron. Structure functions are extracted from a sample of 950,000 neutrino and 170,000 antineutrino events with neutrino energies from 30 to 360 GeV. The structure functions F2 and xF3 are compared with the predictions of perturbative Quantum Chromodynamics (PQCD). The combined non-singlet and singlet evolution in the context of PQCD gives value of ΛNLO,(4)/MS = 337 ± 28 (exp.) MeV, which corresponds to αS(MZ2) = 0.119 ± 0.002 (exp.) ± 0.004 (theory), and with a gluon distribution given by xG(x,Q02 = 5GeV2) = (2.22 ± 0.34) x (1 - x)4.65±0.68.

  8. Test of the Flavour Independence of $\\alpha_{s}$ using Next-to-Leading Order Calculations for Heavy Quarks

    CERN Document Server

    Abbiendi, G.; Alexander, G.; Allison, John; Altekamp, N.; Anderson, K.J.; Anderson, S.; Arcelli, S.; Asai, S.; Ashby, S.F.; Axen, D.; Azuelos, G.; Ball, A.H.; Barberio, E.; Barlow, Roger J.; Batley, J.R.; Baumann, S.; Bechtluft, J.; Behnke, T.; Bell, Kenneth Watson; Bella, G.; Bellerive, A.; Bentvelsen, S.; Bethke, S.; Betts, S.; Biebel, O.; Biguzzi, A.; Bloodworth, I.J.; Bock, P.; Bohme, J.; Bonacorsi, D.; Boutemeur, M.; Braibant, S.; Bright-Thomas, P.; Brigliadori, L.; Brown, Robert M.; Burckhart, H.J.; Capiluppi, P.; Carnegie, R.K.; Carter, A.A.; Carter, J.R.; Chang, C.Y.; Charlton, David G.; Chrisman, D.; Ciocca, C.; Clarke, P.E.L.; Clay, E.; Cohen, I.; Conboy, J.E.; Cooke, O.C.; Couchman, J.; Couyoumtzelis, C.; Coxe, R.L.; Cuffiani, M.; Dado, S.; Dallavalle, G.Marco; Davis, R.; De Jong, S.; de Roeck, A.; Dervan, P.; Desch, K.; Dienes, B.; Dixit, M.S.; Dubbert, J.; Duchovni, E.; Duckeck, G.; Duerdoth, I.P.; Estabrooks, P.G.; Etzion, E.; Fabbri, F.; Fanfani, A.; Fanti, M.; Faust, A.A.; Fiedler, F.; Fierro, M.; Fleck, I.; Frey, A.; Furtjes, A.; Futyan, D.I.; Gagnon, P.; Gary, J.W.; Gascon-Shotkin, S.M.; Gaycken, G.; Geich-Gimbel, C.; Giacomelli, G.; Giacomelli, P.; Gibson, V.; Gibson, W.R.; Gingrich, D.M.; Glenzinski, D.; Goldberg, J.; Gorn, W.; Grandi, C.; Graham, K.; Gross, E.; Grunhaus, J.; Gruwe, M.; Hajdu, C.; Hanson, G.G.; Hansroul, M.; Hapke, M.; Harder, K.; Harel, A.; Hargrove, C.K.; Harin-Dirac, M.; Hauschild, M.; Hawkes, C.M.; Hawkings, R.; Hemingway, R.J.; Herndon, M.; Herten, G.; Heuer, R.D.; Hildreth, M.D.; Hill, J.C.; Hobson, P.R.; Hocker, James Andrew; Hoffman, Kara Dion; Homer, R.J.; Honma, A.K.; Horvath, D.; Hossain, K.R.; Howard, R.; Huntemeyer, P.; Igo-Kemenes, P.; Imrie, D.C.; Ishii, K.; Jacob, F.R.; Jawahery, A.; Jeremie, H.; Jimack, M.; Jones, C.R.; Jovanovic, P.; Junk, T.R.; Kanaya, N.; Kanzaki, J.; Karlen, D.; Kartvelishvili, V.; Kawagoe, K.; Kawamoto, T.; Kayal, P.I.; Keeler, R.K.; Kellogg, R.G.; Kennedy, B.W.; Kim, D.H.; Klier, A.; Kobayashi, T.; Kobel, M.; Kokott, T.P.; Kolrep, M.; Komamiya, S.; Kowalewski, Robert V.; Kress, T.; Krieger, P.; von Krogh, J.; Kuhl, T.; Kyberd, P.; Lafferty, G.D.; Landsman, H.; Lanske, D.; Lauber, J.; Lawson, I.; Layter, J.G.; Lellouch, D.; Letts, J.; Levinson, L.; Liebisch, R.; List, B.; Littlewood, C.; Lloyd, A.W.; Lloyd, S.L.; Loebinger, F.K.; Long, G.D.; Losty, M.J.; Lu, J.; Ludwig, J.; Lui, D.; Macchiolo, A.; Macpherson, A.; Mader, W.; Mannelli, M.; Marcellini, S.; Martin, A.J.; Martin, J.P.; Martinez, G.; Mashimo, T.; Mattig, Peter; McDonald, W.John; McKenna, J.; Mckigney, E.A.; McMahon, T.J.; McPherson, R.A.; Meijers, F.; Mendez-Lorenzo, P.; Merritt, F.S.; Mes, H.; Michelini, A.; Mihara, S.; Mikenberg, G.; Miller, D.J.; Mohr, W.; Montanari, A.; Mori, T.; Nagai, K.; Nakamura, I.; Neal, H.A.; Nisius, R.; O'Neale, S.W.; Oakham, F.G.; Odorici, F.; Ogren, H.O.; Okpara, A.; Oreglia, M.J.; Orito, S.; Pasztor, G.; Pater, J.R.; Patrick, G.N.; Patt, J.; Perez-Ochoa, R.; Petzold, S.; Pfeifenschneider, P.; Pilcher, J.E.; Pinfold, J.; Plane, David E.; Poffenberger, P.; Poli, B.; Polok, J.; Przybycien, M.; Quadt, A.; Rembser, C.; Rick, H.; Robertson, S.; Robins, S.A.; Rodning, N.; Roney, J.M.; Rosati, S.; Roscoe, K.; Rossi, A.M.; Rozen, Y.; Runge, K.; Runolfsson, O.; Rust, D.R.; Sachs, K.; Saeki, T.; Sahr, O.; Sang, W.M.; Sarkisian, E.K.G.; Sbarra, C.; Schaile, A.D.; Schaile, O.; Scharff-Hansen, P.; Schieck, J.; Schmitt, S.; Schoning, A.; Schroder, Matthias; Schumacher, M.; Schwick, C.; Scott, W.G.; Seuster, R.; Shears, T.G.; Shen, B.C.; Shepherd-Themistocleous, C.H.; Sherwood, P.; Siroli, G.P.; Sittler, A.; Skuja, A.; Smith, A.M.; Snow, G.A.; Sobie, R.; Soldner-Rembold, S.; Spagnolo, S.; Sproston, M.; Stahl, A.; Stephens, K.; Steuerer, J.; Stoll, K.; Strom, David M.; Strohmer, R.; Surrow, B.; Talbot, S.D.; Taras, P.; Tarem, S.; Teuscher, R.; Thiergen, M.; Thomas, J.; Thomson, M.A.; Torrence, E.; Towers, S.; Trigger, I.; Trocsanyi, Z.; Tsur, E.; Turner-Watson, M.F.; Ueda, I.; Van Kooten, Rick J.; Vannerem, P.; Verzocchi, M.; Voss, H.; Wackerle, F.; Wagner, A.; Ward, C.P.; Ward, D.R.; Watkins, P.M.; Watson, A.T.; Watson, N.K.; Wells, P.S.; Wermes, N.; Wetterling, D.; White, J.S.; Wilson, G.W.; Wilson, J.A.; Wyatt, T.R.; Yamashita, S.; Zacek, V.; Zer-Zion, D.

    1999-01-01

    We present a test of the flavour independence of the strong coupling constant for charm and bottom quarks with respect to light (uds) quarks, based on a hadronic event sample obtained with the OPAL detector at LEP. Five observables related to global event shapes were used to measure alpha_s in three flavour tagged samples (uds, c and b). The event shape distributions were fitted by Order(alpha_s**2) calculations of jet production taking into account mass effects for the c and b quarks. We find: = 0.997 +- 0.038(stat.) +- 0.030(syst.) +- 0.012(theory) and = 0.993 +- 0.008(stat.) +- 0.006(syst.) +- 0.011(theory) for the ratios alpha_s(charm)/alpha_s(uds) and alpha_s(b)/alpha_s(uds) respectively.

  9. Standard model Wilson coefficients for c → ul{sup +}l{sup -} transitions at next-to-leading order

    Energy Technology Data Exchange (ETDEWEB)

    Boer, Stefan de [TU Dortmund (Germany); Mueller, Bastian; Seidel, Dirk [Uni Siegen (Germany)

    2016-07-01

    The standard theoretical framework to deal with exclusive, weak decays of heavy mesons is the so-called weak effective Hamiltonian. It involves the short-distance Wilson coefficients, which depend on the renormalization scale μ. For specific calculations one has to evolve the Wilson coefficients down from the electroweak scale μ{sub W} to the typical mass scale of the decay under consideration. This is done by solving a renormalization group equation for the effective operator basis. In this talk the results of a consistent two-step running of the c → ul{sup +}l{sup -} Wilson coefficients are presented. This running involves the intermediate scale μ{sub b} (with μ{sub W} > μ{sub b} > μ{sub c}) where the bottom quark is integrated out. All the matching coefficients and anomalous dimensions are taken to the required order by generalizing and extending results from b → s or s → d transitions available in the literature.

  10. Mellin moments of the next-to-next-to leading order coefficient functions for the Drell-Yan process and hadronic Higgs-boson production

    International Nuclear Information System (INIS)

    Bluemlein, J.; Ravindran, V.

    2005-01-01

    We calculate the Mellin moments of the next-to-next-to leading order coefficient functions for the Drell-Yan and Higgs production cross sections. The results can be expressed in terms of multiple finite harmonic sums of maximal weight w=4. Using algebraic and structural relations between harmonic sums one finds that besides the single harmonic sums only five basic sums and their derivatives w.r.t. the summation index contribute. This representation reduces the large complexity being present in x-space calculations and is well suited for fast numerical implementations. (orig.)

  11. Inclusive photoproduction of D*± mesons at next-to-leading order in the general-mass variable-flavor-number scheme

    International Nuclear Information System (INIS)

    Kniehl, B.A.; Kramer, G.; Schienbein, I.; Spiesberger, H.

    2009-02-01

    We discuss the inclusive production of D *± mesons in γp collisions at DESY HERA, based on a calculation at next-to-leading order in the general-mass variable-flavor-number scheme. In this approach, MS subtraction is applied in such a way that large logarithmic corrections are resummed in universal parton distribution and fragmentation functions and finite mass terms are taken into account. We present detailed numerical results for a comparison with data obtained at HERA and discuss various sources of theoretical uncertainties. (orig.)

  12. Inclusive photoproduction of D{sup *{+-}} mesons at next-to-leading order in the general-mass variable-flavor-number scheme

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, B.A.; Kramer, G. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schienbein, I. [Univ. Joseph Fourier/CNRS-IN2P3, INPG, Grenoble (France). Lab. de Physique Subatomique et de Cosmologie; Spiesberger, H. [Mainz Univ. (Germany). Inst. fuer Physik

    2009-02-15

    We discuss the inclusive production of D{sup *{+-}} mesons in {gamma}p collisions at DESY HERA, based on a calculation at next-to-leading order in the general-mass variable-flavor-number scheme. In this approach, MS subtraction is applied in such a way that large logarithmic corrections are resummed in universal parton distribution and fragmentation functions and finite mass terms are taken into account. We present detailed numerical results for a comparison with data obtained at HERA and discuss various sources of theoretical uncertainties. (orig.)

  13. Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals

    Energy Technology Data Exchange (ETDEWEB)

    Levi, Michele [Institut d' Astrophysique de Paris, Université Pierre et Marie Curie, CNRS-UMR 7095, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@ist.utl.pt [Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

    2014-12-01

    The next-to-next-to-leading order spin1-spin2 potential for an inspiralling binary, that is essential for accuracy to fourth post-Newtonian order, if both components in the binary are spinning rapidly, has been recently derived independently via the ADM Hamiltonian and the Effective Field Theory approaches, using different gauges and variables. Here we show the complete physical equivalence of the two results, thereby we first prove the equivalence of the ADM Hamiltonian and the Effective Field Theory approaches at next-to-next-to-leading order with the inclusion of spins. The main difficulty in the spinning sectors, which also prescribes the manner in which the comparison of the two results is tackled here, is the existence of redundant unphysical spin degrees of freedom, associated with the spin gauge choice of a point within the extended spinning object for its representative worldline. After gauge fixing and eliminating the unphysical degrees of freedom of the spin and its conjugate at the level of the action, we arrive at curved spacetime generalizations of the Newton-Wigner variables in closed form, which can also be used to obtain further Hamiltonians, based on an Effective Field Theory formulation and computation. Finally, we make use of our validated result to provide gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to fourth post-Newtonian order, including all known sectors up to date.

  14. Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme

    Energy Technology Data Exchange (ETDEWEB)

    Levi, Michele [Université Pierre et Marie Curie, CNRS-UMR 7095, Institut d' Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@aei.mpg.de [Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Am Mühlenberg 1, 14476 Potsdam-Golm (Germany)

    2016-01-01

    We implement the effective field theory for gravitating spinning objects in the post-Newtonian scheme at the next-to-next-to-leading order level to derive the gravitational spin-orbit interaction potential at the third and a half post-Newtonian order for rapidly rotating compact objects. From the next-to-next-to-leading order interaction potential, which we obtain here in a Lagrangian form for the first time, we derive straightforwardly the corresponding Hamiltonian. The spin-orbit sector constitutes the most elaborate spin dependent sector at each order, and accordingly we encounter a proliferation of the relevant Feynman diagrams, and a significant increase of the computational complexity. We present in detail the evaluation of the interaction potential, going over all contributing Feynman diagrams. The computation is carried out in terms of the ''nonrelativistic gravitational'' fields, which are advantageous also in spin dependent sectors, together with the various gauge choices included in the effective field theory for gravitating spinning objects, which also optimize the calculation. In addition, we automatize the effective field theory computations, and carry out the automated computations in parallel. Such automated effective field theory computations would be most useful to obtain higher order post-Newtonian corrections. We compare our Hamiltonian to the ADM Hamiltonian, and arrive at a complete agreement between the ADM and effective field theory results. Finally, we provide Hamiltonians in the center of mass frame, and complete gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to third and a half post-Newtonian order. The derivation presented here is essential to obtain further higher order post-Newtonian corrections, and to reach the accuracy level required for the successful detection of gravitational radiation.

  15. Next-to-leading order prediction for the decay μ→e (e{sup +}e{sup −}) νν̄

    Energy Technology Data Exchange (ETDEWEB)

    Fael, M.; Greub, C. [Albert Einstein Center for Fundamental Physics,Institute for Theoretical Physics, University of Bern,CH-3012 Bern (Switzerland)

    2017-01-19

    We present the differential decay rates and the branching ratios of the muon decay with internal conversion, μ→e (e{sup +}e{sup −}) νν̄, in the Standard Model at next-to-leading order (NLO) in the on-shell scheme. This rare decay mode of the muon is among the main sources of background to the search for μ→eee decay. We found that in the phase space region where the neutrino energies are small, and the three-electron momenta have a similar signature as in the μ→eee decay, the NLO corrections decrease the leading-order prediction by about 10−20% depending on the applied cut.

  16. Top Quark Pair Production in Association with a Jet with Next-to-Leading-Order QCD Off-Shell Effects at the Large Hadron Collider.

    Science.gov (United States)

    Bevilacqua, G; Hartanto, H B; Kraus, M; Worek, M

    2016-02-05

    We present a complete description of top quark pair production in association with a jet in the dilepton channel. Our calculation is accurate to next-to-leading order (NLO) in QCD and includes all nonresonant diagrams, interferences, and off-shell effects of the top quark. Moreover, nonresonant and off-shell effects due to the finite W gauge boson width are taken into account. This calculation constitutes the first fully realistic NLO computation for top quark pair production with a final state jet in hadronic collisions. Numerical results for differential distributions as well as total cross sections are presented for the Large Hadron Collider at 8 TeV. With our inclusive cuts, NLO predictions reduce the unphysical scale dependence by more than a factor of 3 and lower the total rate by about 13% compared to leading-order QCD predictions. In addition, the size of the top quark off-shell effects is estimated to be below 2%.

  17. Leading and Next-to-Leading Order Gluon Polarization in the Nucleon and Longitudinal Double Spin Asymmetries from Open Charm Muoproduction

    CERN Document Server

    Adolph, C; Alexakhin, V Yu; Alexandrov, Yu; Alexeev, G D; Amoroso, A; Antonov, A A; Austregesilo, A; Badelek, B; Balestra, F; Barth, J; Baum, G; Bedfer, Y; Berlin, A; Bernhard, J; Bertini, R; Bettinelli, M; Bicker, K; Bieling, J; Birsa, R; Bisplinghoff, J; Bordalo, P; Bradamante, F; Braun, C; Bravar, A; Bressan, A; Buchele, M; Burtin, E; Capozza, L; Chiosso, M; Chung, S U; Cicuttin, A; Crespo, M L; Dalla Torre, S; Das, S; Dasgupta, S S; Dasgupta, S; Denisov, O Yu; Dhara, L; Donskov, S V; Doshita, N; Duic, V; Dunnweber, W; Dziewiecki, M; Efremov, A; Elia, C; Eversheim, P D; Eyrich, W; Faessler, M; Ferrero, A; Filin, A; Finger, M; Finger, M Jr; Fischer, H; Franco, C; du Fresne von Hohenesche, N; Friedrich, J M; Frolov, V; Garfagnini, R; Gautheron, F; Gavrichtchouk, O P; Gerassimov, S; Geyer, R; Giorgi, M; Gnesi, I; Gobbo, B; Goertz, S; Grabmuller, S; Grasso, A; Grube, B; Gushterski, R; Guskov, A; Guthorl, T; Haas, F; von Harrach, D; Heinsius, F H; Herrmann, F; Hess, C; Hinterberger, F; Horikawa, N; Hoppner, Ch; d'Hose, N; Huber, S; Ishimoto, S; Ivanov, O; Ivanshin, Yu; Iwata, T; Jahn, R; Jary, V; Jasinski, P; Joosten, R; Kabuss, E; Kang, D; Ketzer, B; Khaustov, G V; Khokhlov, Yu A; Kisselev, Yu; Klein, F; Klimaszewski, K; Koblitz, S; Koivuniemi, J H; Kolosov, V N; Kondo, K; Konigsmann, K; Konorov, I; Konstantinov, V F; Korzenev, A; Kotzinian, A M; Kouznetsov, O; Kramer, M; Kroumchtein, Z V; Kunne, F; Kurek, K; Lauser, L; Lednev, A A; Lehmann, A; Levorato, S; Lichtenstadt, J; Liska, T; Maggiora, A; Magnon, A; Makke, N; Mallot, G K; Mann, A; Marchand, C; Martin, A; Marzec, J; Matsuda, T; Meshcheryakov, G; Meyer, W; Michigami, T; Mikhailov, Yu V; Morreale, A; Mutter, A; Nagaytsev, A; Nagel, T; Nerling, F; Neubert, S; Neyret, D; Nikolaenko, V I; Nowak, W D; Nunes, A S; Olshevsky, A G; Ostrick, M; Padee, A; Panknin, R; Panzieri, D; Parsamyan, B; Paul, S; Perevalova, E; Pesaro, G; Peshekhonov, D V; Piragino, G; Platchkov, S; Pochodzalla, J; Polak, J; Polyakov, V A; Pretz, J; Quaresma, M; Quintans, C; Rajotte, J F; Ramos, S; Rapatsky, V; Reicherz, G; Rocco, E; Rondio, E; Rossiyskaya, N S; Ryabchikov, D I; Samoylenko, V D; Sandacz, A; Sapozhnikov, M G; Sarkar, S; Savin, I A; Sbrizzai, G; Schiavon, P; Schill, C; Schluter, T; Schmidt, A; Schmidt, K; Schmitt, L; Schmiden, H; Schonning, K; Schopferer, S; Schott, M; Shevchenko, O Yu; Silva, L; Sinha, L; Sissakian, A N; Slunecka, M; Smirnov, G I; Sosio, S; Sozzi, F; Srnka, A; Steiger, L; Stolarski, M; Sulc, M; Sulej, R; Suzuki, H; Sznajder, P; Takekawa, S; Ter Wolbeek, J; Tessaro, S; Tessarotto, F; Tkatchev, L G; Uhl, S; Uman, I; Vandenbroucke, M; Virius, M; Vlassov, N V; Wang, L; Weisrock, T; Wilfert, M; Windmolders, R; Wislicki, W; Wollny, H; Zaremba, K; Zavertyaev, M; Zemlyanichkina, E; Ziembicki, M; Zhuravlev, N; Zvyagin, A

    2013-01-01

    The gluon polarisation in the nucleon was measured using open charm production by scattering 160 GeV/c polarised muons off longitudinally polarised protons or deuterons. The data were taken by the COMPASS collaboration between 2002 and 2007. A detailed account is given of the analysis method that includes the application of neural networks. Several decay channels of $D^0$ mesons are investigated. Longitudinal spin asymmetries of the D meson production cross-sections are extracted in bins of $D^0$ transverse momentum and energy. At leading order QCD accuracy the average gluon polarisation is determined as $(\\Delta g/g)^{LO}=-0.06 \\pm 0.21 (stat.) \\pm 0.08 (syst.)$ at the scale $ \\approx 13$ (GeV/c)$^2$ and an average gluon momentum fraction $\\approx$ 0.11. The average gluon polarisation is also obtained at next-to-leading order QCD accuracy as $(\\Delta g/g) NLO = -0.13 \\pm 0.15 (stat.) \\pm 0.15 (syst.)$ at the scale $ \\approx $ 13 (GeV/c)$^2$ and $ \\approx $ 0.20.

  18. Next-to-leading order QCD-analysis of EMC deep inelastic μp and μd scattering data

    International Nuclear Information System (INIS)

    Bilen'kaya, S.I.; Stamenov, D.B.

    1987-01-01

    A combined next-to-leading order QCD analysis of the European Muon Collaboration (EMC) μH 2 and μD 2 scattering data is presented. The nucleon structure functions are given in terms of parton distributions. The Buras-Gaemers method is used to solve the QCD equations for these distributions. The higher twist corrections are not taken into account. As has been shown their contribution to the structure functions is negligible in the EMC kinematic region. Unlike most of the papers on this subject the cross section data (not the value for the structure functions obtained from these data by additional extrapolations and assumptions) are fitted. the following values for the QCD scale parameter Λ MS-bar are found: Λ MS-bar =218 ±73 MeV for the non-singlet fit to the data in the range x>0.3 and Λ MS-bar =65±20 MeV if the whole x data are fitted

  19. Next-to-leading order corrections to the spin-dependent energy spectrum of hadrons from polarized top quark decay in the general two Higgs doublet model

    Directory of Open Access Journals (Sweden)

    S. Mohammad Moosavi Nejad

    2017-08-01

    Full Text Available In recent years, searches for the light and heavy charged Higgs bosons have been done by the ATLAS and the CMS collaborations at the Large Hadron Collider (LHC in proton–proton collision. Nevertheless, a definitive search is a program that still has to be carried out at the LHC. The experimental observation of charged Higgs bosons would indicate physics beyond the Standard Model. In the present work, we study the scaled-energy distribution of bottom-flavored mesons (B inclusively produced in polarized top quark decays into a light charged Higgs boson and a massless bottom quark at next-to-leading order in the two-Higgs-doublet model; t(↑→bH+→BH++X. This spin-dependent energy distribution is studied in a specific helicity coordinate system where the polarization vector of the top quark is measured with respect to the direction of the Higgs momentum. The study of these energy distributions could be considered as a new channel to search for the charged Higgs bosons at the LHC. For our numerical analysis and phenomenological predictions, we restrict ourselves to the unexcluded regions of the MSSM mH+−tan⁡β parameter space determined by the recent results of the CMS [13] and ATLAS [14] collaborations.

  20. Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme

    Energy Technology Data Exchange (ETDEWEB)

    Levi, Michele [Université Pierre et Marie Curie, CNRS-UMR 7095, Institut d' Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@aei.mpg.de [Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Am Mühlenberg 1, 14476 Potsdam-Golm (Germany)

    2016-01-01

    The next-to-next-to-leading order spin-squared interaction potential for generic compact binaries is derived for the first time via the effective field theory for gravitating spinning objects in the post-Newtonian scheme. The spin-squared sector is an intricate one, as it requires the consideration of the point particle action beyond minimal coupling, and mainly involves the spin-squared worldline couplings, which are quite complex, compared to the worldline couplings from the minimal coupling part of the action. This sector also involves the linear in spin couplings, as we go up in the nonlinearity of the interaction, and in the loop order. Hence, there is an excessive increase in the number of Feynman diagrams, of which more are higher loop ones. We provide all the Feynman diagrams and their values. The beneficial ''nonrelativistic gravitational'' fields are employed in the computation. This spin-squared correction, which enters at the fourth post-Newtonian order for rapidly rotating compact objects, completes the conservative sector up to the fourth post-Newtonian accuracy. The robustness of the effective field theory for gravitating spinning objects is shown here once again, as demonstrated in a recent series of papers by the authors, which obtained all spin dependent sectors, required up to the fourth post-Newtonian accuracy. The effective field theory of spinning objects allows to directly obtain the equations of motion, and the Hamiltonians, and these will be derived for the potential obtained here in a forthcoming paper.

  1. Next-to-leading QCD calculation of the heavy quark fragmentation function

    International Nuclear Information System (INIS)

    Mele, B.; Nason, P.

    1990-01-01

    We present the results of a next-to-leading order QCD calculation of the fragmentation function of b flavoured hadrons at LEP. We find that the addition of the next-to-leading effects improves the stability of the result under changes of the evolution scale and does not alter drastically the leading order prediction. Our next-to-leading calculation suggests that, if we neglect non-perturbative effects, the b fragmentation function is peaked at fairly large values of x, even if the average value of x is not necessarily large. (orig.)

  2. Global analysis of nuclear parton distribution functions at leading and next-to-leading order perturbative QCD

    Science.gov (United States)

    Pesznyak, Csilla

    The aim of the investigation is to give answer to some questions of the QC in the mega-voltage therapy for the sake of making the treatments more trouble-free. We investigated the terms of the usage of CT and PET/CT equipments in treatment planning that were made originally for diagnostic purposes. We compared the calculation algorithms of the Varian CadPlan(TM) and CMS XiORTM treatment planning systems (TPS) for photon and electron radiations of different energy. We also investigated the terms of usage of the PTW EPID QC PHANTOMRTM in the quality control of the EPID's and the portal images, as well. We laid down the terms in a protocol that make the diagnostic CT and PET/CT equipments capable for radiation treatment planning. The protocols should contain the exact patient setup, the tube voltage, detailed directions for use of patient immobilization tools, the review and use of the necessary QA/QC devices, the time consumption of the procedure, the frequency of controls and the worksheet to be used during the measurements. On the base of the measurements, it can be stated that on photon energies the superposition algorithm can be used for patient treatments in the case of the CMS XiORTM TPS while in the case of Varian CadPlan(TM) TPS the PBMB algorithm is the proper choice. It is not allowed to use the TPS without inhomogeneity correction. The CIRS Thorax IMRT phantom can be used for electron measurement only at higher than 10 MeV since only the Farmer chamber can be inserted into the holes of the phantom. On the base of the electron measurements, it can be stated that both planning systems give good results in soft tissue. In lung equivalent material the calculated values of the Varian CadPlan(TM) are in better agreement with the measured values, but the calculated values behind the bones are not accurate enough. In the QA/QC process the PTW EPID QC PHANTOMRTM is usable not only for the amorphous silicon EPID's but the image quality can be analysed on the video based devices and on EPID's operating with liquid filled ionisation chamber array detector and even on port films. In the protocol for measurements, the usable file format should be given since the DICOM implementation is not complete in the case of these systems.

  3. An exploratory study of matrix elements of triangle I=3/2 K→ππ decays at next-to-leading order in the chiral expansion

    International Nuclear Information System (INIS)

    Boucaud, P.; Gimenez, V.; Lin, C.J.D.; Washington Univ., Seattle, WA; Lubicz, V.; Martinelli, G.; Papinutto, M.; Sachrajda, C.T.

    2004-12-01

    We present the first direct evaluation of ΔI=3/2 K → ππ matrix elements with the aim of determining all the low-energy constants at NLO in the chiral expansion. Our numerical investigation demonstrates that it is indeed possible to determine the K → ππ matrix elements directly for the masses and momenta used in the simulation with good precision. In this range however, we find that the matrix elements do not satisfy the predictions of NLO chiral perturbation theory. For the chiral extrapolation we therefore use a hybrid procedure which combines the observed polynomial behaviour in masses and momenta of our lattice results, with NLO chiral perturbation theory at lower masses. In this way we find stable results for the quenched matrix elements of the electroweak penguin operators ( I=2 left angle ππ vertical stroke O 8 vertical stroke K 0 right angle =(0.68±0.09) GeV 3 and I=2 left angle ππ vertical stroke O 7 vertical stroke K 0 right angle =(0.12±0.02) GeV 3 ), but not for the matrix elements of O 4 (for which there are too many low-energy constants at NLO for a reliable extrapolation). For all three operators we find that the effect of including the NLO corrections is significant (typically about 30%). We present a detailed discussion of the status of the prospects for the reduction of the systematic uncertainties. (orig.)

  4. Fixation of theoretical ambiguities in the improved fits to $xF_{3}$ CCFR data at the next-to-next-to-leading order and beyond

    CERN Document Server

    Kataev, A L; Sidorov, A V

    2003-01-01

    Using new theoretical information on the NNLO and N$^3$LO perturbative QCD corrections to renormalization-group quantities of odd $xF_3$ Mellin moments, we perform the reanalysis of the CCFR'97 data for $xF_3$ structure function. The fits were done without and with twist-4 power suppressed terms. Theoretical questions of applicability of the renormalon-inspired large-$\\beta_0$ approximation for estimating NNLO and N$^3$LO terms in the coefficient functions of odd $xF_3$ moments and even non-singlet moments of $F_2$ are considered. The comparison with [1/1] Pad\\'e estimates is presented. The small $x$ behaviour of the phenomenological model for $xF_3$ is compared with available theoretical predictions. The $x$-shape of the twist-4 contributions is determined. Indications of oscillating-type behaviour of $h(x)$ are obtained from more detailed NNLO fits when only statistical uncertainties are taken into account. The scale-dependent uncertainties of $\\alpha_s(M_Z)$ are analyzed. The obtained NNLO and approximate ...

  5. New insights into properties of large-N holographic thermal QCD at finite gauge coupling at (the non-conformal/next-to) leading order in N

    International Nuclear Information System (INIS)

    Sil, Karunava; Misra, Aalok

    2016-01-01

    It is believed that large-N thermal QCD laboratories like strongly coupled QGP (sQGP) require not only a large 't Hooft coupling but also a finite gauge coupling (Natsuume, String theory and quark-gluon plasma. arXiv:hep-ph/0701201, 2007). Unlike almost all top-down holographic models in the literature, holographic large-N thermal QCD models, based on this assumption, therefore necessarily require addressing this limit from M-theory. This was initiated in Dhuria and Misra (JHEP 1311:001, 2013) which presented a local M-theory uplift of the string theoretic dual of large-N thermal QCD-like theories at finite gauge/string coupling of Mia et al. (Nucl. Phys. B 839:187, arXiv:0902.1540 [hep-th], 2010) (g s perturbations and using the prescription of Kovtun and Starinets (Phys. Rev. D 72:086009, arXiv:hep-th/0506184, 2005) for constructing appropriate gauge-invariant perturbations, we obtain the non-conformal corrections to the conformal results (but at finite g s ), respectively, for the speed of sound, the shear mode diffusion constant, and the shear viscosity η (and (η)/(s)). The new insight gained is that it turns out

  6. New insights into properties of large-N holographic thermal QCD at finite gauge coupling at (the non-conformal/next-to) leading order in N

    Energy Technology Data Exchange (ETDEWEB)

    Sil, Karunava; Misra, Aalok [Indian Institute of Technology, Department of Physics, Roorkee, Uttarakhand (India)

    2016-11-15

    It is believed that large-N thermal QCD laboratories like strongly coupled QGP (sQGP) require not only a large 't Hooft coupling but also a finite gauge coupling (Natsuume, String theory and quark-gluon plasma. arXiv:hep-ph/0701201, 2007). Unlike almost all top-down holographic models in the literature, holographic large-N thermal QCD models, based on this assumption, therefore necessarily require addressing this limit from M-theory. This was initiated in Dhuria and Misra (JHEP 1311:001, 2013) which presented a local M-theory uplift of the string theoretic dual of large-N thermal QCD-like theories at finite gauge/string coupling of Mia et al. (Nucl. Phys. B 839:187, arXiv:0902.1540 [hep-th], 2010) (g{sub s} perturbations and using the prescription of Kovtun and Starinets (Phys. Rev. D 72:086009, arXiv:hep-th/0506184, 2005) for constructing appropriate gauge-invariant perturbations, we obtain the non-conformal corrections to the conformal results (but at finite g{sub s}), respectively, for the speed of sound, the shear mode diffusion constant, and the shear viscosity η (and (η)/(s)). The new insight gained is that it

  7. Next-to-next-to-leading order QCD analysis of combined data for xF3 structure function and higher-twist contribution

    International Nuclear Information System (INIS)

    Sidorov, A.V.

    1996-01-01

    The simultaneous QCD analysis of the xF 3 structure function measured in deep-inelastic scattering by several collaborations is done up to 3-loop order of QCD. The x dependence of the higher-twist contribution is evaluated and turns out to be in a qualitative agreement with the results of 'old' CCFR data analysis and with renormalon approach predictions. The Gross-Llewellyn Smith sum rule and its higher-twist corrections are evaluated. 32 refs., 1 figs., 1 tab

  8. Photoproduction of the J/{psi} meson at HERA at next-to-leading order within the framework of nonrelativistic QCD

    Energy Technology Data Exchange (ETDEWEB)

    Butenschoen, Mathias

    2009-06-15

    Nonrelativistic QCD (NRQCD) provides a rigorous factorization scheme which describes the production and decay of heavy quarkonia. It has been a desire for 13 years to know the NRQCD NLO predictions for both J/{psi} hadroproduction and photoproduction, in order to be able to check the universality of the color octet long distance matrix elements (MEs) by comparing Tevatron and HERA data. In this work we calculate for the rst time the NRQCD NLO prediction for direct photoproduction at HERA and compare our result with recent H1 data. Our results show clear evidence that the color octet mechanism of NRQCD is indeed realized in J/{psi} photoproduction at HERA. We solved a number of open conceptual problems, probably the most important one being the issue of Coulomb singularities. We found a way to evaluate the virtual corrections without having to deal with them. (orig.)

  9. Next-to-Leading Order Differential Cross Sections for J/ψ, ψ(2S), and Υ Production in Proton-Proton Collisions at a Fixed-Target Experiment Using the LHC Beams

    OpenAIRE

    Yu Feng; Jian-Xiong Wang

    2015-01-01

    Using nonrelativistic QCD (NRQCD) factorization, we calculate the yields for J/ψ , ψ(2S) , and Υ(1S) hadroproduction at s=72  GeV and 115 GeV including the next-to-leading order QCD corrections. Both these center-of-mass energies correspond to those obtained with 7 TeV and 2.76 TeV nucleon beam impinging a fixed target. We study the cross section integrated in pt as a function of the (center-of-mass) rapidity as well as the pt differential cross section in the central rapidity region. Using d...

  10. Next-to-leading order γγ+2-jet production at the LHC

    Energy Technology Data Exchange (ETDEWEB)

    Bern, Z.; Dixon, L. J.; Febres Cordero, F.; Höche, S.; Ita, H.; Kosower, D. A.; Lo Presti, N. A.; Maître, D.

    2014-09-01

    We present next-to-leading-order QCD predictions for cross sections and for a comprehensive set of distributions in γγ+2-jet production at the Large Hadron Collider. We consider the contributions from loop amplitudes for two photons and four gluons, but we neglect top quarks. We use BlackHat together with SHERPA to carry out the computation. We use a Frixione cone isolation for the photons. We study standard sets of cuts on the jets and the photons and also sets of cuts appropriate for studying backgrounds to Higgs-boson production via vector-boson fusion.

  11. Determination of the strong coupling constant α{sub s}(m{sub Z}) in next-to-next-to-leading order QCD using H1 jet cross section measurements

    Energy Technology Data Exchange (ETDEWEB)

    Andreev, V.; Belousov, A.; Fomenko, A.; Gogitidze, N.; Lebedev, A.; Malinovski, E.; Soloviev, Y.; Vazdik, Y. [Lebedev Physical Institute, Moscow (Russian Federation); Baghdasaryan, A.; Zohrabyan, H. [Yerevan Physics Institute, Yerevan (Armenia); Begzsuren, K.; Ravdandorj, T. [Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar (Mongolia); Bertone, V. [Vrije University, Department of Physics and Astronomy, Amsterdam (Netherlands); National Institute for Subatomic Physics (NIKHEF), Amsterdam (Netherlands); Bolz, A.; Britzger, D.; Huber, F.; Sauter, M.; Schoening, A. [Universitaet Heidelberg, Physikalisches Institut, Heidelberg (Germany); Boudry, V.; Specka, A. [LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau (France); Brandt, G. [Universitaet Goettingen, II. Physikalisches Institut, Goettingen (Germany); Brisson, V.; Jacquet, M.; Pascaud, C.; Zhang, Z.; Zomer, F. [LAL, Universite Paris-Sud, CNRS/IN2P3, Orsay (France); Buniatyan, A.; Newman, P.R.; Thompson, P.D. [University of Birmingham, School of Physics and Astronomy, Birmingham (United Kingdom); Bylinkin, A. [Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region (Russian Federation); Bystritskaya, L.; Fedotov, A. [Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Campbell, A.J.; Dodonov, V.; Eckerlin, G.; Elsen, E.; Fleischer, M.; Gayler, J.; Ghazaryan, S.; Haidt, D.; Jung, H.; Katzy, J.; Kleinwort, C.; Kruecker, D.; Krueger, K.; Levonian, S.; Lipka, K.; List, B.; List, J.; Meyer, A.B.; Meyer, J.; Niebuhr, C.; Olsson, J.E.; Pirumov, H.; Pitzl, D.; Placakyte, R.; Schmitt, S.; Sefkow, F.; South, D.; Steder, M.; Wuensch, E.; Zlebcik, R. [DESY, Hamburg (Germany); Cantun Avila, K.B.; Contreras, J.G. [CINVESTAV, Departamento de Fisica Aplicada, Merida, Yucatan (Mexico); Cerny, K.; Salek, D.; Valkarova, A.; Zacek, J. [Charles University, Faculty of Mathematics and Physics, Prague (Czech Republic); Chekelian, V.; Grindhammer, G.; Kiesling, C.; Lobodzinski, B. [Max-Planck-Institut fuer Physik, Munich (Germany); Cvach, J.; Hladky, J.; Reimer, P. [Academy of Sciences of the Czech Republic, Institute of Physics, Prague (Czech Republic); Currie, J. [Durham University, Institute for Particle Physics Phenomenology, Ogden Centre for Fundamental Physics, Durham (United Kingdom); Dainton, J.B.; Gabathuler, E.; Greenshaw, T.; Klein, M.; Kostka, P.; Kretzschmar, J.; Laycock, P.; Maxfield, S.J.; Mehta, A.; Patel, G.D. [University of Liverpool, Department of Physics, Liverpool (United Kingdom); Daum, K.; Meyer, H. [Fachbereich C, Universitaet Wuppertal, Wuppertal (Germany); Diaconu, C.; Hoffmann, D.; Vallee, C. [Aix Marseille Universite, CNRS/IN2P3, CPPM UMR 7346, Marseille (France); Dobre, M.; Rotaru, M. [Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering (IFIN-HH), Bucharest (Romania); Egli, S.; Horisberger, R.; Ozerov, D. [Paul Scherrer Institute, Villigen (Switzerland); Favart, L.; Grebenyuk, A.; Hreus, T.; Janssen, X.; Roosen, R.; Mechelen, P.Van [Brussels and Universiteit Antwerpen, Inter-University Institute for High Energies ULB-VUB, Antwerp (Belgium); Feltesse, J.; Schoeffel, L. [Irfu/SPP, CE Saclay, Gif-sur-Yvette (France); Gehrmann, T.; Mueller, K.; Niehues, J.; Robmann, P.; Straumann, U.; Truoel, P. [Physik-Institut der Universitaet Zuerich, Zurich (Switzerland); Goerlich, L.; Mikocki, S.; Nowak, G.; Sopicki, P. [Polish Academy of Sciences, Institute of Nuclear Physics, Krakow (Poland); Gouzevitch, M.; Petrukhin, A. [IPNL, Universite Claude Bernard Lyon 1, CNRS/IN2P3, Villeurbanne (France); Grab, C.; Huss, A. [ETH Zuerich, Institut fuer Teilchenphysik, Zurich (Switzerland); Gwenlan, C.; Radescu, V. [Oxford University, Department of Physics, Oxford (United Kingdom); Henderson, R.C.W. [University of Lancaster, Department of Physics, Lancaster (United Kingdom); Jung, A.W. [Purdue University, Department of Physics and Astronomy, West Lafayette, IN (United States); Kapichine, M.; Morozov, A.; Spaskov, V. [Joint Institute for Nuclear Research, Dubna (Russian Federation); Kogler, R. [Universitaet Hamburg, Institut fuer Experimentalphysik, Hamburg (Germany); Landon, M.P.J.; Rizvi, E.; Traynor, D. [Queen Mary University of London, School of Physics and Astronomy, London (United Kingdom); Lange, W.; Naumann, T. [DESY, Zeuthen (Germany); Martyn, H.U. [I. Physikalisches Institut der RWTH, Aachen (Germany); Perez, E. [CERN, Geneva (Switzerland); Picuric, I.; Raicevic, N. [University of Montenegro, Faculty of Science, Podgorica (Montenegro); Polifka, R. [Charles University, Faculty of Mathematics and Physics, Prague (Czech Republic); University of Toronto, Department of Physics, Toronto, ON (Canada); Rabbertz, K. [Karlsruher Institut fuer Technologie (KIT), Institut fuer Experimentelle Teilchenphysik (ETP), Karlsruhe (Germany); Rostovtsev, A. [Institute for Information Transmission Problems RAS, Moscow (Russian Federation); Sankey, D.P.C. [STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire (United Kingdom); Sauvan, E. [Aix Marseille Universite, CNRS/IN2P3, CPPM UMR 7346, Marseille (France); Universite de Savoie, CNRS/IN2P3, LAPP, Annecy-le-Vieux (France); Shushkevich, S. [Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, Moscow (Russian Federation); Stella, B. [Universita di Roma Tre, Dipartimento di Fisica, Rome (Italy); INFN Roma 3 (Italy); Sutton, M.R. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom); Sykora, T. [Brussels and Universiteit Antwerpen, Inter-University Institute for High Energies ULB-VUB, Antwerp (Belgium); Charles University, Faculty of Mathematics and Physics, Prague (Czech Republic); Tsakov, I. [Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria); Tseepeldorj, B. [Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar (MN); Ulaanbaatar University, Ulaanbaatar (MN); Wegener, D. [TU Dortmund, Institut fuer Physik, Dortmund (DE); Collaboration: H1 Collaboration

    2017-11-15

    The strong coupling constant α{sub s} is determined from inclusive jet and dijet cross sections in neutral-current deep-inelastic ep scattering (DIS) measured at HERA by the H1 collaboration using next-to-next-to-leading order (NNLO) QCD predictions. The dependence of the NNLO predictions and of the resulting value of α{sub s}(m{sub Z}) at the Z-boson mass m{sub Z} are studied as a function of the choice of the renormalisation and factorisation scales. Using inclusive jet and dijet data together, the strong coupling constant is determined to be α{sub s}(m{sub Z}) = 0.1157(20){sub exp}(29){sub th}. Complementary, α{sub s}(m{sub Z}) is determined together with parton distribution functions of the proton (PDFs) from jet and inclusive DIS data measured by the H1 experiment. The value α{sub s}(m{sub Z}) = 0.1142(28){sub tot} obtained is consistent with the determination from jet data alone. The impact of the jet data on the PDFs is studied. The running of the strong coupling is tested at different values of the renormalisation scale and the results are found to be in agreement with expectations. (orig.)

  12. Singularity-free next-to-leading order ΔS=1 renormalization group evolution and ϵ{sub K}{sup ′}/ϵ{sub K} in the Standard Model and beyond

    Energy Technology Data Exchange (ETDEWEB)

    Kitahara, Teppei [Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology,Engesserstraße 7, Karlsruhe, D-76128 (Germany); Institute for Nuclear Physics (IKP), Karlsruhe Institute of Technology,Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen, D-76344 (Germany); Nierste, Ulrich; Tremper, Paul [Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology,Engesserstraße 7, Karlsruhe, D-76128 (Germany)

    2016-12-16

    The standard analytic solution of the renormalization group (RG) evolution for the ΔS=1 Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of ϵ{sub K}{sup ′}, the measure of direct CP violation in K→ππ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio ϵ{sub K}{sup ′}/ϵ{sub K} (with ϵ{sub K} quantifying indirect CP violation) in the Standard Model (SM) at NLO to ϵ{sub K}{sup ′}/ϵ{sub K}=(1.06±5.07)×10{sup −4}, which is 2.8 σ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: if the new contribution is generated at the scale of 1–10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50–100%. Our solution contains a term of order α{sub EM}{sup 2}/α{sub s}{sup 2}, which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.

  13. Next-to-next-to-leading logarithms in four-fermion electroweak processes at high energy

    International Nuclear Information System (INIS)

    Kuehn, J.H.; Moch, S.; Penin, A.A.; Smirnov, V.A.

    2001-01-01

    We sum up the next-to-next-to-leading logarithmic virtual electroweak corrections to the high energy asymptotics of the neutral current four-fermion processes for light fermions to all orders in the coupling constants using the evolution equation approach. From this all order result we derive finite order expressions through next-to-next-to leading order for the total cross section and various asymmetries. We observe an amazing cancellation between the sizable leading, next-to-leading and next-to-next-to-leading logarithmic contributions at TeV energies

  14. Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions

    NARCIS (Netherlands)

    Duca, Vittorio del; Laenen, E.; Magnea, L.; Vernazza, L.; White, C.D.

    2017-01-01

    We consider the production of an arbitrary number of colour-singlet particles near partonic threshold, and show that next-to-leading order cross sections for this class of processes have a simple universal form at next-to-leading power (NLP) in the energy of the emitted gluon radiation. Our analysis

  15. Next to Leading Logarithms and the PHOTOS Monte Carlo

    CERN Document Server

    Golonka, P

    2007-01-01

    With the approaching start-up of the experiments at LHC, the urgency to quantify systematic uncertainties of the generators, used in the interpretation of the data, is becoming pressing. The PHOTOS Monte Carlo program is often used for the simulationof experimental, selection-sensitive, QED radiative corrections in decays of Z bosons and other heavy resonances and particles. Thanks to its complete phase-space coverage it is possible, with no approximations for any decay channel, to implement the matrix-element. The present paper will be devoted to those parts of the next-to-leading order corrections for Z decays which are normally missing in PHOTOS. The analytical form of the exact and truncated (standard) kernel used in PHOTOS will be explicitly given. The correction, being the ratio of the exact to the approximate kernel, can be activated as an optional contribution to the internal weight of PHOTOS. To calculate the weight, the information on the effective Born-level Z/gamma* couplings and even directions o...

  16. Next to leading order analysis of DVCS and TCS

    Directory of Open Access Journals (Sweden)

    Wagner J.

    2014-03-01

    Full Text Available The study of O(αs QCD contributions to the timelike and spacelike virtual Compton scattering amplitudes in the generalized Bjorken scaling regime demonstrates that gluonic contributions are by no means negligible even in the medium energy range which will be studied intensely at JLab12 and in the COMPASS-II experiment at CERN.

  17. Large-order perturbation theory

    International Nuclear Information System (INIS)

    Wu, T.T.

    1982-01-01

    The original motivation for studying the asymptotic behavior of the coefficients of perturbation series came from quantum field theory. An overview is given of some of the attempts to understand quantum field theory beyond finite-order perturbation series. At least is the case of the Thirring model and probably in general, the full content of a relativistic quantum field theory cannot be recovered from its perturbation series. This difficulty, however, does not occur in quantum mechanics, and the anharmonic oscillator is used to illustrate the methods used in large-order perturbation theory. Two completely different methods are discussed, the first one using the WKB approximation, and a second one involving the statistical analysis of Feynman diagrams. The first one is well developed and gives detailed information about the desired asymptotic behavior, while the second one is still in its infancy and gives instead information about the distribution of vertices of the Feynman diagrams

  18. Perturbation theory in large order

    International Nuclear Information System (INIS)

    Bender, C.M.

    1978-01-01

    For many quantum mechanical models, the behavior of perturbation theory in large order is strikingly simple. For example, in the quantum anharmonic oscillator, which is defined by -y'' + (x 2 /4 + ex 4 /4 - E) y = 0, y ( +- infinity) = 0, the perturbation coefficients, A/sub n/, in the expansion for the ground-state energy, E(ground state) approx. EPSILON/sub n = 0//sup infinity/ A/sub n/epsilon/sup n/, simplify dramatically as n → infinity: A/sub n/ approx. (6/π 3 )/sup 1/2/(-3)/sup n/GAMMA(n + 1/2). Methods of applied mathematics are used to investigate the nature of perturbation theory in quantum mechanics and show that its large-order behavior is determined by the semiclassical content of the theory. In quantum field theory the perturbation coefficients are computed by summing Feynman graphs. A statistical procedure in a simple lambda phi 4 model for summing the set of all graphs as the number of vertices → infinity is presented. Finally, the connection between the large-order behavior of perturbation theory in quantum electrodynamics and the value of α, the charge on the electron, is discussed. 7 figures

  19. Topics in perturbative QCD beyond the leading order

    International Nuclear Information System (INIS)

    Buras, A.J.

    1979-08-01

    The basic structure of QCD formulae for various inclusive and semi-inclusive processes is presented. Next to leading order QCD corrections to inclusive deep-inelastic scattering are discussed in some detail. The methods for calculations of QCD corrections (leading, next to leading) to semi-inclusive processes are outlined. Some results of these calculations are discussed. 58 references

  20. Next-to-leading-logarithmic power corrections for N -jettiness subtraction in color-singlet production

    Science.gov (United States)

    Boughezal, Radja; Isgrò, Andrea; Petriello, Frank

    2018-04-01

    We present a detailed derivation of the power corrections to the factorization theorem for the 0-jettiness event shape variable T . Our calculation is performed directly in QCD without using the formalism of effective field theory. We analytically calculate the next-to-leading logarithmic power corrections for small T at next-to-leading order in the strong coupling constant, extending previous computations which obtained only the leading-logarithmic power corrections. We address a discrepancy in the literature between results for the leading-logarithmic power corrections to a particular definition of 0-jettiness. We present a numerical study of the power corrections in the context of their application to the N -jettiness subtraction method for higher-order calculations, using gluon-fusion Higgs production as an example. The inclusion of the next-to-leading-logarithmic power corrections further improves the numerical efficiency of the approach beyond the improvement obtained from the leading-logarithmic power corrections.

  1. Heavy Quark Impact Factor at Next-to-leading Level

    OpenAIRE

    Ciafaloni, Marcello; Rodrigo, German

    2000-01-01

    We further analyze the definition and the calculation of the heavy quark impact factor at next-to-leading (NL) log(s) level, and we provide its analytical expression in a previously proposed k-factorization scheme. Our results indicate that k-factorization holds at NL level with a properly chosen energy scale, and with the same gluonic Green's function previously found in the massless probe case.

  2. BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY

    Energy Technology Data Exchange (ETDEWEB)

    Fadin, V.S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Budker Nuclear Physics Institute, Novosibirsk (Russian Federation); Novosibirskij Gosudarstvennyj Univ., Novosibirsk (Russian Federation); Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); St. Petersburg State Univ., Gatchina (Russian Federation)

    2011-12-15

    We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group SU(N{sub c}) in the N=4 supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this anzatz are chosen in an appropriate way.

  3. Mueller–Navelet small-cone jets at LHC in next-to-leading BFKL

    Energy Technology Data Exchange (ETDEWEB)

    Caporale, F., E-mail: francesco.caporale@fis.unical.it [Dipartimento di Fisica, Università della Calabria and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Ivanov, D.Yu., E-mail: d-ivanov@math.nsc.ru [Sobolev Institute of Mathematics and Novosibirsk State University, 630090 Novosibirsk (Russian Federation); Murdaca, B., E-mail: beatrice.murdaca@fis.unical.it [Dipartimento di Fisica, Università della Calabria and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Papa, A., E-mail: alessandro.papa@fis.unical.it [Dipartimento di Fisica, Università della Calabria and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy)

    2013-12-01

    We consider within QCD collinear factorization the process p+p→jet+jet+X, where two forward high-p{sub T} jets are produced with a large separation in rapidity Δy (Mueller–Navelet jets). In this case the (calculable) hard part of the reaction receives large higher-order corrections ∼α{sub s}{sup n}(Δy){sup n}, which can be accounted for in the BFKL approach with next-to-leading logarithmic accuracy, including contributions ∼α{sub s}{sup n}(Δy){sup n−1}. We calculate several observables related with this process, using the next-to-leading order jet vertices, recently calculated in the approximation of small aperture of the jet cone in the pseudorapidity–azimuthal angle plane.

  4. Cosmological perturbations beyond linear order

    CERN Multimedia

    CERN. Geneva

    2013-01-01

    Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.

  5. The next-next-to-leading QCD approximation for non-singlet moments of deep inelastic structure functions

    Energy Technology Data Exchange (ETDEWEB)

    Larin, S.A.; Ritbergen, T. van; Vermaseren, J.A.M.

    1993-12-01

    We obtain the analytic next-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N = 2, 4, 6, 8 of the non-singlet deep inelastic structure functions F{sub 2} and F{sub L}. We calculate the three-loop anomalous dimensions of the corresponding non-singlet operators and the three-loop coefficient functions of the structure function F{sub L}. (orig.).

  6. The next-next-to-leading QCD approximation for non-singlet moments of deep inelastic structure functions

    International Nuclear Information System (INIS)

    Larin, S.A.; Ritbergen, T. van; Vermaseren, J.A.M.

    1993-12-01

    We obtain the analytic next-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N = 2, 4, 6, 8 of the non-singlet deep inelastic structure functions F 2 and F L . We calculate the three-loop anomalous dimensions of the corresponding non-singlet operators and the three-loop coefficient functions of the structure function F L . (orig.)

  7. Non-abelian factorisation for next-to-leading-power threshold logarithms

    International Nuclear Information System (INIS)

    Bonocore, D.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C.D.

    2016-01-01

    Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a non-abelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.

  8. Non-abelian factorisation for next-to-leading-power threshold logarithms

    Energy Technology Data Exchange (ETDEWEB)

    Bonocore, D. [Nikhef, Science Park 105, NL-1098 XG Amsterdam (Netherlands); Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen University, Sommerfeldstr. 16, 52074 Aachen (Germany); Laenen, E. [Nikhef, Science Park 105, NL-1098 XG Amsterdam (Netherlands); ITFA, University of Amsterdam, Science Park 904, Amsterdam (Netherlands); ITF, Utrecht University, Leuvenlaan 4, Utrecht (Netherlands); Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 (United States); Magnea, L. [Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino, Via P. Giuria 1, I-10125 Torino (Italy); Vernazza, L. [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); White, C.D. [Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, 327 Mile End Road, London E1 4NS (United Kingdom)

    2016-12-22

    Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a non-abelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.

  9. Gravitational clustering to all perturbative orders

    International Nuclear Information System (INIS)

    Abdalla, E.; Mohayaee, R.

    1999-04-01

    We derive the time evolution of the density contrast to all orders of perturbation theory, by solving the Einstein equation for scale-invariant fluctuations. These fluctuations are represented by an infinite series in inverse powers of the radial parameter. In addition to the standard growing modes, we find infinitely many more new growing modes for open and closed universes. (author)

  10. Factorization for groomed jet substructure beyond the next-to-leading logarithm

    International Nuclear Information System (INIS)

    Frye, Christopher; Larkoski, Andrew J.; Schwartz, Matthew D.; Yan, Kai

    2016-01-01

    Jet grooming algorithms are widely used in experimental analyses at hadron colliders to remove contaminating radiation from within jets. While the algorithms perform a great service to the experiments, their intricate algorithmic structure and multiple parameters has frustrated precision theoretic understanding. In this paper, we demonstrate that one particular groomer called soft drop actually makes precision jet substructure easier. In particular, we derive a factorization formula for a large class of soft drop jet substructure observables, including jet mass. The essential observation that allows for this factorization is that, without the soft wide-angle radiation groomed by soft drop, all singular contributions are collinear. The simplicity and universality of the collinear limit in QCD allows us to show that to all orders, the normalized differential cross section has no contributions from non-global logarithms. It is also independent of process, up to the relative fraction of quark and gluon jets. In fact, soft drop allows us to define this fraction precisely. The factorization theorem also explains why soft drop observables are less sensitive to hadronization than their ungroomed counterparts. Using the factorization theorem, we resum the soft drop jet mass to next-to-next-to-leading logarithmic accuracy. This requires calculating some clustering effects that are closely related to corresponding effects found in jet veto calculations. We match our resummed calculation to fixed order results for both e + e − → dijets and pp→Z+j events, producing the first jet substructure predictions (groomed or ungroomed) to this accuracy for the LHC.

  11. Factorization for groomed jet substructure beyond the next-to-leading logarithm

    Energy Technology Data Exchange (ETDEWEB)

    Frye, Christopher; Larkoski, Andrew J.; Schwartz, Matthew D.; Yan, Kai [Center for the Fundamental Laws of Nature, Harvard University,17 Oxford Street, Cambridge, MA 02138 (United States)

    2016-07-12

    Jet grooming algorithms are widely used in experimental analyses at hadron colliders to remove contaminating radiation from within jets. While the algorithms perform a great service to the experiments, their intricate algorithmic structure and multiple parameters has frustrated precision theoretic understanding. In this paper, we demonstrate that one particular groomer called soft drop actually makes precision jet substructure easier. In particular, we derive a factorization formula for a large class of soft drop jet substructure observables, including jet mass. The essential observation that allows for this factorization is that, without the soft wide-angle radiation groomed by soft drop, all singular contributions are collinear. The simplicity and universality of the collinear limit in QCD allows us to show that to all orders, the normalized differential cross section has no contributions from non-global logarithms. It is also independent of process, up to the relative fraction of quark and gluon jets. In fact, soft drop allows us to define this fraction precisely. The factorization theorem also explains why soft drop observables are less sensitive to hadronization than their ungroomed counterparts. Using the factorization theorem, we resum the soft drop jet mass to next-to-next-to-leading logarithmic accuracy. This requires calculating some clustering effects that are closely related to corresponding effects found in jet veto calculations. We match our resummed calculation to fixed order results for both e{sup +}e{sup −}→ dijets and pp→Z+j events, producing the first jet substructure predictions (groomed or ungroomed) to this accuracy for the LHC.

  12. Non-abelian factorisation for next-to-leading-power threshold logarithms

    NARCIS (Netherlands)

    Bonocore, D.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C.D.

    2016-01-01

    Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this

  13. The gluon Green's function in the BFKL approach at next-to-leading logarithmic accuracy

    International Nuclear Information System (INIS)

    Andersen, Jeppe R.; Sabio Vera, Agustin

    2004-01-01

    We investigate the gluon Green's function in the high energy limit of QCD using a recently proposed iterative solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation at next-to-leading logarithmic (NLL) accuracy. To establish the applicability of this method in the NLL approximation we solve the BFKL equation as originally written by Fadin and Lipatov, and compare the results with previous studies in the leading logarithmic (LL) approximation

  14. Next-to-next-to-leading order calculation of the strong coupling ...

    Indian Academy of Sciences (India)

    Pramana – J. Phys., Vol. 81, No. ... of the higher moments of the different shape variable is similar to what was observed for the first moments. Although ... Figure 1. First moment of four event-shape variables: (a) 1 − T, (b) ρ, (c) BT,. (d) Bw. 3.

  15. SU(N)-QCD2 meson equation in next-to-leading order

    International Nuclear Information System (INIS)

    Durgut, M.; Pak, N.K.

    1982-08-01

    We compute the 1/N corrections to the meson equation in the regular cut-off scheme. We illustrate that although the quark and gluon self energy and vertex corrections do not vanish explicitly as in the singular cut-off scheme, their contributions to the meson Bethe-Salpeter equation get cancelled within the whole set of contributing diagrams. We also argue that 0(1/N) corrections to the meson equation remove the massless boson from the spectrum in accordance with the Coleman theorem. (author)

  16. The quark induced Mueller-Tang jet impact factor at next-to-leading order

    CERN Document Server

    Hentschinski, M.; Murdaca, B.; Vera, A. Sabio

    2014-01-01

    We present the NLO corrections for the quark induced forward production of a jet with an associated rapidity gap. We make use of Lipatov's QCD high energy effective action to calculate the real emission contributions to the so-called Mueller-Tang impact factor. We combine them with the previously calculated virtual corrections and verify ultraviolet and collinear finiteness of the final result.

  17. Next-to-leading order QCD corrections to five jet production at the LHC

    DEFF Research Database (Denmark)

    David Badger, Simon; Biedermann, Benedikt; Uwer, Peter

    2014-01-01

    -to-two ratio and are promising candidates for future αs measurements. Furthermore, we present a detailed analysis of uncertainties related to parton distribution functions. The full color virtual matrix elements used in the computation were obtained with the NJet package [1], a publicly available library...

  18. Next-to-next-to-leading order calculation of the strong coupling ...

    Indian Academy of Sciences (India)

    It is observed that the NNLO correction gives a better agreement between the theory and the experimental data. Also, by using the above observables, the strong coupling constant () is determined and how much its value is affected by the NNLO correction is demonstrated. By combining the results for all variables at ...

  19. Next-to-leading order effective field theory Lambda N -> NN potential in coordinate space

    Czech Academy of Sciences Publication Activity Database

    Peréz-Obiol Castaneda, Axel; Entem, D. R.; Julia-Diaz, B.; Parreno, A.

    2016-01-01

    Roč. 954, OCT (2016), s. 213-241 ISSN 0375-9474 R&D Projects: GA ČR(CZ) GA15-04301S Institutional support: RVO:61389005 Keywords : non-mesonic weak decay * effective field theory * hypernuclei Subject RIV: BE - Theoretical Physics Impact factor: 1.916, year: 2016

  20. Extra dimension searches at hadron colliders to next-to-leading order-QCD

    Science.gov (United States)

    Kumar, M. C.; Mathews, Prakash; Ravindran, V.

    2007-11-01

    The quantitative impact of NLO-QCD corrections for searches of large and warped extra dimensions at hadron colliders are investigated for the Drell-Yan process. The K-factor for various observables at hadron colliders are presented. Factorisation, renormalisation scale dependence and uncertainties due to various parton distribution functions are studied. Uncertainties arising from the error on experimental data are estimated using the MRST parton distribution functions.

  1. First order normalization in the perturbed restricted three–body ...

    African Journals Online (AJOL)

    This paper performs the first order normalization that will be employed in the study of the nonlinear stability of triangular points of the perturbed restricted three – body problem with variable mass. The problem is perturbed in the sense that small perturbations are given in the coriolis and centrifugal forces. It is with variable ...

  2. Higher order corrections in perturbative quantum chromodynamics

    Indian Academy of Sciences (India)

    Since the discovery of asymptotic freedom in non-abelian gauge field theories, like quan- tum chromodynamics (QCD), many perturbative calculations have been performed to ..... The integral above appears in the partial integration with respect to the momentum. &½ of the expression below (see figure 2). ¼. Т&½. ґѕπµТ.

  3. Very high order lattice perturbation theory for Wilson loops

    International Nuclear Information System (INIS)

    Horsley, R.

    2010-10-01

    We calculate perturbativeWilson loops of various sizes up to loop order n=20 at different lattice sizes for pure plaquette and tree-level improved Symanzik gauge theories using the technique of Numerical Stochastic Perturbation Theory. This allows us to investigate the behavior of the perturbative series at high orders. We observe differences in the behavior of perturbative coefficients as a function of the loop order. Up to n=20 we do not see evidence for the often assumed factorial growth of the coefficients. Based on the observed behavior we sum this series in a model with hypergeometric functions. Alternatively we estimate the series in boosted perturbation theory. Subtracting the estimated perturbative series for the average plaquette from the non-perturbative Monte Carlo result we estimate the gluon condensate. (orig.)

  4. The BFKL high energy asymptotic in the next-to-leading approximation

    International Nuclear Information System (INIS)

    Levin, Eugene

    1999-01-01

    We discuss the high energy asymptotic in the next-to-leading (NLO) BFKL equation. We find a general solution for the Green functions and consider two properties of the NLO BFKL kernel: running QCD coupling and large NLO corrections to the conformal part of the kernel. Both these effects lead to Regge-BFKL asymptotic only in the limited range of energy (y = ln(s/qq 0 ) ≤ (α S ) ((-5)/(3)) ) and change the energy behaviour of the amplitude for higher values of energy. We confirm the oscillation in the total cross section found by D.A. Ross [SHEP-98-06, hep-ph/9804332] in the NLO BFKL asymptotic, which shows that the NLO BFKL has a serious pathology

  5. Wilson loops in very high order lattice perturbation theory

    International Nuclear Information System (INIS)

    Ilgenfritz, E.M.; Nakamura, Y.; Perlt, H.; Schiller, A.; Rakow, P.E.L.; Schierholz, G.; Regensburg Univ.

    2009-10-01

    We calculate Wilson loops of various sizes up to loop order n=20 for lattice sizes of L 4 (L=4,6,8,12) using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the perturbative series at high orders. We discuss three models to estimate the perturbative series: a renormalon inspired fit, a heuristic fit based on an assumed power-law singularity and boosted perturbation theory. We have found differences in the behavior of the perturbative series for smaller and larger Wilson loops at moderate n. A factorial growth of the coefficients could not be confirmed up to n=20. From Monte Carlo measured plaquette data and our perturbative result we estimate a value of the gluon condensate left angle (α)/(π)GG right angle. (orig.)

  6. Higher order perturbation theory - An example for discussion

    International Nuclear Information System (INIS)

    Lewins, J.D.; Parks, G.; Babb, A.L.

    1986-01-01

    Higher order perturbation theory is developed in the form of a Taylor series expansion to third order to calculate the thermal utilization of a nonuniform cell. The development takes advantage of the self-adjoint property of the diffusion operator to provide a simple development of this illustration of generalized perturbation theory employing scalar perturbation parameters. The results show how a designer might employ a second-order theory to quantify proposed design improvements, together with the limitations of second- and third-order theory. The chosen example has an exact optimization solution and thus provides a clear understanding of the role of perturbation theory at its various orders. Convergence and the computational advantages and disadvantages of the method are discussed

  7. A factorization approach to next-to-leading-power threshold logarithms

    Energy Technology Data Exchange (ETDEWEB)

    Bonocore, D. [Nikhef,Science Park 105, NL-1098 XG Amsterdam (Netherlands); Laenen, E. [Nikhef,Science Park 105, NL-1098 XG Amsterdam (Netherlands); ITFA, University of Amsterdam,Science Park 904, Amsterdam (Netherlands); ITF, Utrecht University,Leuvenlaan 4, Utrecht (Netherlands); Magnea, L. [Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino,Via P. Giuria 1, I-10125, Torino (Italy); Melville, S. [School of Physics and Astronomy, University of Glasgow,Glasgow, G12 8QQ (United Kingdom); Vernazza, L. [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh,Edinburgh, EH9 3JZ, Scotland (United Kingdom); White, C.D. [School of Physics and Astronomy, University of Glasgow,Glasgow, G12 8QQ (United Kingdom)

    2015-06-03

    Threshold logarithms become dominant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear. Such radiation factorizes at the level of scattering amplitudes, and this leads to the resummation of threshold logarithms which appear at leading power in the threshold variable. In this paper, we consider the extension of this factorization to include effects suppressed by a single power of the threshold variable. Building upon the Low-Burnett-Kroll-Del Duca (LBKD) theorem, we propose a decomposition of radiative amplitudes into universal building blocks, which contain all effects ultimately responsible for next-to-leading-power (NLP) threshold logarithms in hadronic cross sections for electroweak annihilation processes. In particular, we provide a NLO evaluation of the radiative jet function, responsible for the interference of next-to-soft and collinear effects in these cross sections. As a test, using our expression for the amplitude, we reproduce all abelian-like NLP threshold logarithms in the NNLO Drell-Yan cross section, including the interplay of real and virtual emissions. Our results are a significant step towards developing a generally applicable resummation formalism for NLP threshold effects, and illustrate the breakdown of next-to-soft theorems for gauge theory amplitudes at loop level.

  8. Perturbative reduction of derivative order in EFT

    Science.gov (United States)

    Glavan, Dražen

    2018-02-01

    Higher derivative corrections are ubiquitous in effective field theories, which seemingly introduces new degrees of freedom at successive orders. This is actually an artefact of the implicit local derivative expansion defining effective field theories. We argue that higher derivative corrections that introduce additional degrees of freedom should be removed and their effects captured either by lower derivative corrections, or special combinations of higher derivative corrections not propagating extra degrees of freedom. Three methods adapted for this task are examined and field redefinitions are found to be most appropriate. First order higher derivative corrections in a scalar tensor theory are removed by field redefinition and it is found that their effects are captured by a subset of Horndeski theories. A case is made for restricting the effective field theory expansions in principle to only terms not introducing additional degrees of freedom.

  9. Quasipotential in the fourth order of perturbation theory

    International Nuclear Information System (INIS)

    Bojkova, N.A.; Dvoeglazov, V.V.; Tyukhtyaev, Yu.N.; Faustov, R.N.

    1992-01-01

    The quasipotential in the fourth order of perturbation theory is calculated in the Coulomb gauge for the unequal mass particles. It could be used for the future calculations of energy spectra in two-body systems. 15 refs.; 1 fig

  10. High-order perturbations of a spherical collapsing star

    International Nuclear Information System (INIS)

    Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich; Kokkotas, Kostas D.

    2010-01-01

    A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.

  11. Wilson loops to 20th order numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Hotzel, G.; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Ilgenfritz, E.M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Joint Institute for Nuclear Research, VBLHEP, Dubna (Russian Federation); Millo, R.; Rakow, P.E.L. [Liverpool Univ. (Germany). Theoretical Physics Div.; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe, Hyogo (Japan); Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2012-05-15

    We calculate Wilson loops of various sizes up to 20 loops in SU(3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high loop orders. We observe differences in the behavior of those series as function of the loop order. Up to n=20 we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. Alternatively we estimate the total series in boosted perturbation theory using information from the first 14 loops. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their non-perturbative parts.

  12. Second-order gauge-invariant perturbations during inflation

    International Nuclear Information System (INIS)

    Finelli, F.; Marozzi, G.; Vacca, G. P.; Venturi, G.

    2006-01-01

    The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second-order gauge-invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second-order gauge-invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections with respect to the first order spectrum. For all scales of interest the amplitude of these spectra depends on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable

  13. Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

    Science.gov (United States)

    Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

    2015-10-02

    The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

  14. Improving predictions for collider observables by consistently combining fixed order calculations with resummed results in perturbation theory

    International Nuclear Information System (INIS)

    Schoenherr, Marek

    2011-01-01

    With the constantly increasing precision of experimental data acquired at the current collider experiments Tevatron and LHC the theoretical uncertainty on the prediction of multiparticle final states has to decrease accordingly in order to have meaningful tests of the underlying theories such as the Standard Model. A pure leading order calculation, defined in the perturbative expansion of said theory in the interaction constant, represents the classical limit to such a quantum field theory and was already found to be insufficient at past collider experiments, e.g. LEP or HERA. Such a leading order calculation can be systematically improved in various limits. If the typical scales of a process are large and the respective coupling constants are small, the inclusion of fixed-order higher-order corrections then yields quickly converging predictions with much reduced uncertainties. In certain regions of the phase space, still well within the perturbative regime of the underlying theory, a clear hierarchy of the inherent scales, however, leads to large logarithms occurring at every order in perturbation theory. In many cases these logarithms are universal and can be resummed to all orders leading to precise predictions in these limits. Multiparticle final states now exhibit both small and large scales, necessitating a description using both resummed and fixed-order results. This thesis presents the consistent combination of two such resummation schemes with fixed-order results. The main objective therefor is to identify and properly treat terms that are present in both formulations in a process and observable independent manner. In the first part the resummation scheme introduced by Yennie, Frautschi and Suura (YFS), resumming large logarithms associated with the emission of soft photons in massive QED, is combined with fixed-order next-to-leading matrix elements. The implementation of a universal algorithm is detailed and results are studied for various precision

  15. On high-order perturbative calculations at finite density

    CERN Document Server

    Ghisoiu, Ioan; Kurkela, Aleksi; Romatschke, Paul; Säppi, Matias; Vuorinen, Aleksi

    2017-01-01

    We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes. Applications of these rules will be discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbative orders.

  16. On high-order perturbative calculations at finite density

    Energy Technology Data Exchange (ETDEWEB)

    Ghişoiu, Ioan, E-mail: ioan.ghisoiu@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland); Gorda, Tyler, E-mail: tyler.gorda@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland); Department of Physics, University of Colorado Boulder, Boulder, CO (United States); Kurkela, Aleksi, E-mail: aleksi.kurkela@cern.ch [Theoretical Physics Department, CERN, Geneva (Switzerland); Faculty of Science and Technology, University of Stavanger, Stavanger (Norway); Romatschke, Paul, E-mail: paul.romatschke@colorado.edu [Department of Physics, University of Colorado Boulder, Boulder, CO (United States); Center for Theory of Quantum Matter, University of Colorado, Boulder, CO (United States); Säppi, Matias, E-mail: matias.sappi@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland); Vuorinen, Aleksi, E-mail: aleksi.vuorinen@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland)

    2017-02-15

    We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes — a result reminiscent of a previously proposed “naive real-time formalism” for vacuum diagrams. Applications of these rules are discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbative orders.

  17. Nonlinear singular perturbation problems of arbitrary real orders

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-10-01

    Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

  18. A simple extrapolation of thermodynamic perturbation theory to infinite order

    International Nuclear Information System (INIS)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2015-01-01

    Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A 3 /A 2 , where A i is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT)

  19. Cosmological perturbation theory at three-loop order

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-09-15

    We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

  20. Cosmological perturbation theory at three-loop order

    International Nuclear Information System (INIS)

    Blas, Diego; Garny, Mathias; Konstandin, Thomas

    2013-09-01

    We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

  1. Singular perturbations introduction to system order reduction methods with applications

    CERN Document Server

    Shchepakina, Elena; Mortell, Michael P

    2014-01-01

    These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...

  2. Hamiltonian approach to second order gauge invariant cosmological perturbations

    Science.gov (United States)

    Domènech, Guillem; Sasaki, Misao

    2018-01-01

    In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.

  3. A next-to-leading determination of the singlet axial charge and the polarized gluon content of the nucleon

    CERN Document Server

    Ball, R D; Ridolfi, G

    1996-01-01

    We perform a full next-to-leading analysis of the the available experimental data on the polarized structure function g_1 of the nucleon, and give a precise determination of its singlet axial charge together with a thorough assessment of the theoretical uncertainties. We find that the data are now sufficient to separately determine first moments of the polarized quark and gluon distributions and show in particular that the gluon contribution is large and positive.

  4. Driven similarity renormalization group: Third-order multireference perturbation theory.

    Science.gov (United States)

    Li, Chenyang; Evangelista, Francesco A

    2017-03-28

    A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6 ) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2 , H 2 O 2 , C 2 H 6 , and N 2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST =E T -E S ) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol -1 , a value that is within 0.1 kcal mol -1 from multireference coupled cluster results.

  5. An integral for second-order multiple scattering perturbation theory

    International Nuclear Information System (INIS)

    Hoffman, G.G.

    1997-01-01

    This paper presents the closed form evaluation of a six-dimensional integral. The integral arises in the application to many-electron systems of a multiple scattering perturbation expansion at second order when formulated in fourier space. The resulting function can be used for the calculation of both the electron density and the effective one-electron potential in an SCF calculations. The closed form expression derived here greatly facilitates these calculations. In addition, the evaluated integral can be used for the computation of second-order corrections to the open-quotes optimized Thomas-Fermi theory.close quotes 10 refs., 2 figs

  6. Quark mass relations to four-loop order in perturbative QCD.

    Science.gov (United States)

    Marquard, Peter; Smirnov, Alexander V; Smirnov, Vladimir A; Steinhauser, Matthias

    2015-04-10

    We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS[over ¯] quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS[over ¯] heavy quark masses.

  7. Next-to-leading order QCD corrections to the decay of Higgs to vector meson and Z boson

    Science.gov (United States)

    Sun, Qing-Feng; Wang, An-Min

    2018-02-01

    The exclusive decay of the Higgs boson to a vector meson (J/ψ or Υ(1S)) and Z boson is studied in this work. The decay amplitudes are separated into two parts in a gauge invariant manner. The first part comes from the direct coupling of the Higgs boson to the charm (bottom) quark and the other from the HZZ* or the loop-induced HZ γ* vertexes in the standard model. While the branching ratios from the direct channel are much smaller than those of the indirect channel, their interference terms give nontrivial contributions. We further calculate the QCD radiative corrections to both channels, which reduce the total branching ratios by around 20% for both (J/ψ or Υ(1S)) production. Our results provide a possible chance to check the SM predictions of the {{Hc}}\\bar{{{c}}}({{Hb}}\\bar{{{b}}}) coupling and to seek for hints of new physics at the High Luminosity LHC or future hadron colliders. Supported by National Natural Science Foundation of China (11375168)

  8. Next-to-leading order corrections to e+e-→W+W-Z and e+e-→ZZZ

    International Nuclear Information System (INIS)

    Boudjema, Fawzi; Hao Sun; Ninh, Le Duc; Weber, Marcus M.

    2010-01-01

    We calculate the one-loop electroweak corrections to e + e - →W + W - Z and e + e - →ZZZ and analyze their impacts on both the total cross section and some key distributions. These processes are important for the measurements of the quartic couplings of the massive gauge bosons which can be a window on the mechanism of spontaneous symmetry breaking. We find that even after subtracting the leading QED corrections, the electroweak corrections can still be large, especially as the energy increases. We compare and implement different methods of dealing with potential instabilities in the routines pertaining to the loop integrals. For the real corrections we apply a dipole subtraction formalism and compare it to a phase-space slicing method.

  9. Spin-dependent hadro- and photoproduction of heavy quarks at next-to-leading order of QCD

    International Nuclear Information System (INIS)

    Riedl, Johann

    2014-01-01

    In this thesis, we have studied heavy quark hadro- and photoproduction in detail and examined the possibilities of using heavy quark production for the extraction of the polarised parton distribution functions. All calculations are performed at O(α s 3 ) and O(αα s 2 ) accuracy, respectively, and theoretical uncertainties due to the choice of scales μ f,r and the heavy quark mass m Q have been discussed in detail. Based on our theoretical results we have presented detailed phenomenological studies for the existing PHENIX and STAR experiments at BNL-RHIC and the COMPASS experiment at CERN. Predictions have been made for possible future experiments at a low-energy antiproton-proton collider at GSI-FAIR, a proton-proton collider at J-PARC and an upcoming high-energy electron-ion collider (EIC).

  10. Estimation of uncertainties from missing higher orders in perturbative calculations

    International Nuclear Information System (INIS)

    Bagnaschi, E.

    2015-05-01

    In this proceeding we present the results of our recent study (hep-ph/1409.5036) of the statistical performances of two different approaches, Scale Variation (SV) and the Bayesian model of Cacciari and Houdeau (CH)(hep-ph/1105.5152) (which we also extend to observables with initial state hadrons), to the estimation of Missing Higher-Order Uncertainties (MHOUs)(hep-ph/1307.1843) in perturbation theory. The behavior of the models is determined by analyzing, on a wide set of observables, how the MHOU intervals they produce are successful in predicting the next orders. We observe that the Bayesian model behaves consistently, producing intervals at 68% Degree of Belief (DoB) comparable with the scale variation intervals with a rescaling factor r larger than 2 and closer to 4. Concerning SV, our analysis allows the derivation of a heuristic Confidence Level (CL) for the intervals. We find that assigning a CL of 68% to the intervals obtained with the conventional choice of varying the scales within a factor of two with respect to the central scale could potentially lead to an underestimation of the uncertainties in the case of observables with initial state hadrons.

  11. High orders of perturbation theory. Are renormalons significant?

    International Nuclear Information System (INIS)

    Suslov, I.M.

    1999-01-01

    According to Lipatov [Sov. Phys. JETP 45, 216 (1977)], the high orders of perturbation theory are determined by saddle-point configurations, i.e., instantons, which correspond to functional integrals. According to another opinion, the contributions of individual large diagrams, i.e., renormalons, which, according to t'Hooft [The Whys of Subnuclear Physics: Proceedings of the 1977 International School of Subnuclear Physics (Erice, Trapani, Sicily, 1977), A. Zichichi (Ed.), Plenum Press, New York (1979)], are not contained in the Lipatov contribution, are also significant. The history of the conception of renormalons is presented, and the arguments in favor of and against their existence are discussed. The analytic properties of the Borel transforms of functional integrals, Green's functions, vertex parts, and scaling functions are investigated in the case of φ 4 theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou-Zinn-Justin hypothesis [Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980)] is proved. It rules out the existence of the renormalon singularities pointed out by t'Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of φ 4 theory

  12. Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

    Science.gov (United States)

    Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

    2017-12-07

    We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

  13. SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim; Gong, Jinn-Ouk

    2012-01-01

    We present the growing mode solutions of cosmological perturbations to the second order in the matter-dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in the most general fluid context. Based on these solutions, we study the Newtonian correspondence of relativistic perturbations to the second order. In addition to the previously known exact relativistic/Newtonian correspondence of density and velocity perturbations to the second order in the comoving gauge, here we show that in the sub-horizon limit we have the correspondences for density, velocity, and potential perturbations in the zero-shear gauge and in the uniform-expansion gauge to the second order. Density perturbation in the uniform-curvature gauge also shows the correspondence to the second order in the sub-horizon scale. We also identify the relativistic gravitational potential that shows exact correspondence to the Newtonian one to the second order.

  14. Contribution of higher order terms in the reductive perturbation theory, 2

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.

    1977-01-01

    Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)

  15. On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar N=4 SYM

    Energy Technology Data Exchange (ETDEWEB)

    Bondarenko, Sergey; Prygarin, Alex [Physics Department, Ariel University,Ariel 40700, territories administered by (Israel)

    2016-07-15

    We discuss a residual freedom of the next-to-leading BFKL eigenvalue that originates from ambiguity in redistributing the next-to-leading (NLO) corrections between the adjoint BFKL eigenvalue and eigenfunctions in planar N=4 super-Yang-Mills (SYM) Theory. In terms of the remainder function of the Bern-Dixon-Smirnov (BDS) amplitude this freedom is translated to reshuffling correction between the eigenvalue and the impact factors in the multi-Regge kinematics (MRK) in the next-to-leading logarithm approximation (NLA). We show that the modified NLO BFKL eigenvalue suggested by the authors in ref. http://arxiv.org/abs/1510.00589 can be introduced in the MRK expression for the remainder function by shifting the anomalous dimension in the impact factor in such a way that the two and three loop remainder function is left unchanged to the NLA accuracy.

  16. Virial theorem and the Born-Oppenheimer approximation at different orders of perturbation

    International Nuclear Information System (INIS)

    Olivier, Gabriel; Weislinger, Edmond

    1977-01-01

    The link between the virial theorem and the adiabatic approximation is studied for a few orders of perturbation. It is shown that the total energy of the system is distributed between the mean values of kinetic and potential energy of the nuclei and the electrons in each order of perturbation. No static approximation connected with the Hellmann-Feynman theorem is made [fr

  17. Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim

    2007-01-01

    We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

  18. Limit cycles via higher order perturbations for some piecewise differential systems

    Science.gov (United States)

    Buzzi, Claudio A.; Lima, Maurício Firmino Silva; Torregrosa, Joan

    2018-05-01

    A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x‧ ,y‧) =(- y + εf(x , y , ε) , x + εg(x , y , ε)) . In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n , no more than Nn - 1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Liénard differential systems providing better upper bounds for higher order perturbation in ε, showing also when they are reached. The Poincaré-Pontryagin-Melnikov theory is the main technique used to prove all the results.

  19. Resummation of the QCD perturbative series for hard processes

    International Nuclear Information System (INIS)

    Catani, S.

    1989-01-01

    We study the region of inhibited radiation in hard hadronic processes, as for jet cross sections and heavy flavour production near threshold. The cases of deep inelastic scattering and Drell-Yan annihilation are explicitly considered. A general method to exponentiate leading and next-to-leading logarithms to all orders in perturbation theory is developed. A complete formula for the large N-moments is given and shown to agree with previous two-loop calculations. The resummation procedure suggests how to connect the perturbative and nonperturbative regions. The natural limit within the perturbative phase is shown to be the intrinsic transverse momentum. (orig.)

  20. A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

    International Nuclear Information System (INIS)

    Adam, G.

    1979-01-01

    A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

  1. Perturbative construction of self-dual configurations on the torus

    International Nuclear Information System (INIS)

    Garcia Perez, M.; Gonzalez-Arroyo, A.; Pena, C.

    2000-01-01

    We develop a perturbative expansion which allows the construction of non-abelian self-dual SU(2) Yang-Mills field configurations on the four-dimensional torus with topological charge 1/2. The expansion is performed around the constant field strength abelian solutions found by 't Hooft. Next to leading order calculations are compared with numerical results obtained with lattice gauge theory techniques. (author)

  2. Fourth-order Perturbed Eigenvalue Equation for Stepwise Damage Detection of Aeroplane Wing

    Directory of Open Access Journals (Sweden)

    Wong Chun Nam

    2016-01-01

    Full Text Available Perturbed eigenvalue equations up to fourth-order are established to detect structural damage in aeroplane wing. Complete set of perturbation terms including orthogonal and non-orthogonal coefficients are computed using perturbed eigenvalue and orthonormal equations. Then the perturbed eigenparameters are optimized using BFGS approach. Finite element model with small to large stepwise damage is used to represent actual aeroplane wing. In small damaged level, termination number is the same for both approaches, while rms errors and termination d-norms are very close. For medium damaged level, termination number is larger for third-order perturbation with lower d-norm and smaller rms error. In large damaged level, termination number is much larger for third-order perturbation with same d-norm and larger rms error. These trends are more significant as the damaged level increases. As the stepwise damage effect increases with damage level, the increase in stepwise effect leads to the increase in model order. Hence, fourth-order perturbation is more accurate to estimate the model solution.

  3. Protein-induced bilayer Perturbations: Lipid ordering and hydrophobic coupling

    DEFF Research Database (Denmark)

    Petersen, Frederic Nicolas Rønne; Laursen, Ib; Bohr, Henrik

    2009-01-01

    The host lipid bilayer is increasingly being recognized as an important non-specific regulator of membrane protein function. Despite considerable progress the interplay between hydrophobic coupling and lipid ordering is still elusive. We use electron spin resonance (ESR) to study the interaction...... between the model protein gramicidin and lipid bilayers of varying thickness. The free energy of the interaction is up to −6 kJ/mol; thus not strongly favored over lipid–lipid interactions. Incorporation of gramicidin results in increased order parameters with increased protein concentration...... and hydrophobic mismatch. Our findings also show that at high protein:lipid ratios the lipids are motionally restricted but not completely immobilized. Both exchange on and off rate values for the lipid ↔ gramicidin interaction are lowest at optimal hydrophobic matching. Hydrophobic mismatch of few Å results...

  4. Second-order generalized perturbation theory for source-driven systems

    International Nuclear Information System (INIS)

    Greenspan, E.; Gilai, D.; Oblow, E.M.

    1978-01-01

    A second-order generalized perturbation theory (GPT) for the effect of multiple system variations on a general flux functional in source-driven systems is derived. The derivation is based on a functional Taylor series in which second-order derivatives are retained. The resulting formulation accounts for the nonlinear effect of a given variation accurate to third order in the flux and adjoint perturbations. It also accounts for the effect of interaction between any number of variations. The new formulation is compared with exact perturbation theory as well as with perturbation theory for altered systems. The usefulnes of the second-order GPT formulation is illustrated by applying it to optimization problems. Its applicability to areas of cross-section sensitivity analysis and system design and evaluation is also discussed

  5. Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

    Science.gov (United States)

    Matsubara, Takahiko

    2003-02-01

    We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

  6. Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim

    2005-01-01

    We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon

  7. Correlation effects of third-order perturbation in the extended Hubbard model

    International Nuclear Information System (INIS)

    Wei, G.Z.; Nie, H.Q.; Li, L.; Zhang, K.Y.

    1989-01-01

    Using the local approach, a third-order perturbation calculation has been performed to investigate the effects of intra-atomic electron correlation and electron and spin correlation between nearest neighbour sites in the extended Hubbard model. It was found that significant correction of the third order over the second order results and, in comparison with the results of the third-order perturbation where only the intra-atomic electron correlation is included, the influence of the electron and spin correlation between nearest neighbour sites on the correlation energy is non-negligible. 17 refs., 3 figs

  8. Higher order perturbation theory applied to radiative transfer in non-plane-parallel media

    International Nuclear Information System (INIS)

    Box, M.A.; Polonsky, I.N.; Davis, A.B.

    2003-01-01

    Radiative transfer in non-plane-parallel media is a very challenging problem, which is currently the subject of concerted efforts to develop computational techniques which may be used to tackle different tasks. In this paper we develop the full formalism for another technique, based on radiative perturbation theory. With this approach, one starts with a plane-parallel 'base model', for which many solution techniques exist, and treat the horizontal variability as a perturbation. We show that under the most logical assumption as to the base model, the first-order perturbation term is zero for domain-average radiation quantities, so that it is necessary to go to higher order terms. This requires the computation of the Green's function. While this task is by no means simple, once the various pieces have been assembled they may be re-used for any number of perturbations--that is, any horizontal variations

  9. SIMP model at NNLO in chiral perturbation theory

    Science.gov (United States)

    Hansen, Martin; Langæble, Kasper; Sannino, Francesco

    2015-10-01

    We investigate the phenomenological viability of a recently proposed class of composite dark matter models where the relic density is determined by 3 →2 number-changing processes in the dark sector. Here the pions of the strongly interacting field theory constitute the dark matter particles. By performing a consistent next-to-leading- and next-to-next-to-leading-order chiral perturbative investigation we demonstrate that the leading-order analysis cannot be used to draw conclusions about the viability of the model. We further show that higher-order corrections substantially increase the tension with phenomenological constraints challenging the viability of the simplest realization of the strongly interacting massive particle paradigm.

  10. On the all-order perturbative finiteness of the deformed N=4 SYM theory

    International Nuclear Information System (INIS)

    Rossi, G.C.; Sokatchev, E.; Stanev, Ya.S.

    2006-01-01

    We prove that the chiral propagator of the deformed N=4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g 6

  11. SAMPO: a code system giving different orders of approximation for sensitivity and perturbation analysis

    International Nuclear Information System (INIS)

    Estiot, J.C.; Salvatores, M.; Palmiotti, G.

    1981-01-01

    We present the characteristics of SAMPO, a one dimension transport theory code system, which is used for the following types of calculation: sensitivity analysis for functional linear or bi-linear on the direct or adjoint flux and their ratios; classic perturbation analysis. First order calculations, as well higher order, can be presented

  12. A higher order depletion perturbation theory with application to in-core fuel management optimization

    International Nuclear Information System (INIS)

    Kropaczek, D.J.; Turinsky, P.J.

    1990-01-01

    Perturbation techniques utilized in reactor analysis have recently been applied in the solution of the in-core nuclear fuel management optimization problem. The use of such methods is motivated by the need to evaluate many times over, the core physics characteristics of loading pattern solutions obtained through an optimization process, which is typically iterative. Perturbation theory provides an efficient alternative to the prohibitively expensive, repetitive solutions of the system few-group neutron diffusion equations required in solving the fuel placement problem. A primary concern in the use of such methods is the control of perturbation errors arising during the fuel shuffling process. First-order accurate models inevitably resort to undue restriction of fuel movement during the optimization process to control these errors. Higher order perturbation theory models have the potential to overcome such limitations, which may result in the identification of local versus global optima. An accurate, computationally efficient reactor physics model based on higher order perturbation theory and geared toward the needs of large-scale in-core fuel management optimization is presented in this paper

  13. Energy correlations in perturbative quantum chromodynamics: a conjecture for all orders

    International Nuclear Information System (INIS)

    Basham, C.L.; Brown, L.S.; Ellis, S.D.; Love, S.T.

    1979-01-01

    The hadronic energy produced in high-energy electron-positron annihilation has an angular correlation which can be computed by the asymptotically free perturbation theory of quantum chromodynamics. In finite orders, the correlation is not well behaved as the detectors become anti-collinear. The leading behaviour has been calculated to fourth order and an exponential expression for the sum of all orders is discussed. This expression obeys a non-trivial sum rule which lends support for its validity. (Auth.)

  14. Numerical studies of QCD renormalons in high-order perturbative expansions

    International Nuclear Information System (INIS)

    Bauer, Clemens

    2013-01-01

    Perturbative expansions in four-dimensional non-Abelian gauge theories such as Quantum Chromodynamics (QCD) are expected to be divergent, at best asymptotic. One reason is that it is impossible to strictly exclude from the relevant Feynman diagrams those energy regions in which a perturbative treatment is inapplicable. The divergent nature of the series is then signaled by a rapid (factorial) growth of the perturbative expansion coefficients, commonly referred to as a renormalon. In QCD, the most severe divergences occur in the infrared (IR) limit and therefore they are classified as IR renormalons. Their appearance can be understood within the well-accepted Operator Product Expansion (OPE) framework. According to the OPE, the perturbative calculation of a physical observable must be amended by non-perturbative power corrections that come in the form of condensates, universal characteristics of the rich QCD vacuum structure. Adding up perturbative and non-perturbative contributions, the ambiguity due to the renormalon cancels and the physical observable is well-defined. Although the field has made considerable progress in the last twenty years, a proof of renormalon existence is still pending. It has only been tested assuming strong simplifications or in toy models. The aim of this thesis is to provide the first numerical evidence for renormalon existence in the gauge sector of QCD. We use Numerical Stochastic Perturbation Theory (NSPT) to directly obtain perturbative coefficients within lattice regularization, a means to replace continuum spacetime by a four-dimensional hypercubic lattice. A peculiar feature of NSPT are comparatively low simulation costs when reaching high expansion orders. We examine two distinct observables: the static self-energy of an isolated quark and the elementary plaquette. Following the OPE classification, the static quark self-energy is ideally suited for a renormalon study. Taking into account peculiarities of the lattice approach such

  15. The width of the Δ-resonance at two loop order in baryon chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Gegelia, Jambul, E-mail: j.gegelia@fz-juelich.de [Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany); Tbilisi State University, 0186 Tbilisi, Georgia (United States); Meißner, Ulf-G., E-mail: meissner@hiskp.uni-bonn.de [Helmholtz Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany); Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany); Siemens, Dmitrij, E-mail: dmitrij.siemens@rub.de [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Yao, De-Liang, E-mail: d.yao@fz-juelich.de [Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany)

    2016-12-10

    We calculate the width of the delta resonance at leading two-loop order in baryon chiral perturbation theory. This gives a correlation between the leading pion–nucleon–delta and pion–delta couplings, which is relevant for the analysis of pion–nucleon scattering and other processes.

  16. Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

    Science.gov (United States)

    Xu, Enhua; Zhao, Dongbo; Li, Shuhua

    2015-10-13

    A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

  17. Effects of next-to-leading order DGLAP evolution on generalized parton distributions of the proton and deeply virtual Compton scattering at high energy

    Energy Technology Data Exchange (ETDEWEB)

    Khanpour, Hamzeh [University of Science and Technology of Mazandaran, Department of Physics, Behshahr (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of); Goharipour, Muhammad [Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of); Guzey, Vadim [Petersburg Nuclear Physics Institute (PNPI), National Research Center ' ' Kurchatov Institute' ' , Gatchina (Russian Federation)

    2018-01-15

    We studied the effects of NLO Q{sup 2} evolution of generalized parton distributions (GPDs) using the aligned-jet model for the singlet quark and gluon GPDs at an initial evolution scale. We found that the skewness ratio for quarks is a slow logarithmic function of Q{sup 2}, reaching r{sup S} = 1.5-2 at Q{sup 2} = 100 GeV{sup 2} and r{sup g} ∼ 1 for gluons in a wide range of Q{sup 2}. Using the resulting GPDs, we calculated the DVCS cross section on the proton in NLO pQCD and found that this model in conjunction with modern parameterizations of proton PDFs (CJ15 and CT14) provides a good description of the available H1 and ZEUS data in a wide kinematic range. (orig.)

  18. Leading and Next-to-Leading Order Gluon Polarisation in the Nucleon and Longitudinal Double Spin Asymmetries from Open Charm Muoproduction

    Czech Academy of Sciences Publication Activity Database

    Adolph, C.; Alekseev, M.; Alexakhin, V. Yu.; Alexandrov, Yu.; Alexeev, G. D.; Amoroso, A.; Antonov, A. A.; Austregisilio, A.; Badelek, B.; Balestra, F.; Barth, J.; Baum, G.; Bedfer, Y.; Berlin, A.; Bernhard, J.; Bertini, R.; Bettinelli, M.; Bicker, K.; Bieling, J.; Birsa, R.; Bisplinghoff, J.; Bordalo, P.; Bradamante, F.; Braun, C.; Bravar, A.; Bressan, A.; Büchele, M.; Burtin, E.; Capozza, L.; Chiosso, M.; Chung, S.U.; Cicuttin, A.; Crespo, M.; Dalla Torre, S.; Das, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O.; Dhara, L.; Donskov, S.; Doshita, N.; Duic, V.; Dünnweber, W.; Dziewiecki, M.; Efremov, A.V.; Elia, C.; Eversheim, P.; Eyrich, W.; Faessler, M.; Ferrero, A.; Filin, A.; Finger, M.; Finger jr., M.; Fischer, H.; Franco, C.; Fresne von Hohenesche, N.; Friedrich, J.; Frolov, V.; Garfagnini, R.; Gautheron, F.; Gavrichtchouk, O.; Gerassimov, S.; Geyer, R.; Giorgi, M.; Gnesi, I.; Gobbo, B.; Goertz, S.; Grabmüller, S.; Grasso, A.; Grube, B.; Gushterski, R.; Guskov, A.; Guthörl, T.; Haas, F.; von Harrach, D.; Heinsius, F.; Herrmann, F.; Hess, C.; Hinterberger, F.; Horikawa, N.; Höppner, Ch.; d'Hose, N.; Huber, S.; Ishimoto, S.; Ivanov, O.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jasinski, P.; Joosten, R.; Kabuss, E.; Kang, D.; Ketzer, B.; Khaustov, G.; Khokhlov, Y.; Kisselev, Y.; Klein, F.; Klimaszewski, K.; Koblitz, S.; Koivuniemi, J.; Kolosov, V.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V.; Korzenev, A.; Kotzinian, A.; Kouznetsov, O.; Krämer, M.; Kroumchtein, Z.; Kunne, F.; Kurek, K.; Lauser, L.; Lednev, A.; Lehmann, A.; Levorato, S.; Lichtenstadt, J.; Liska, T.; Maggiora, A.; Magnon, A.; Makke, N.; Mallot, G.; Mann, A.; Marchand, C.; Martin, A.; Marzec, J.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Y.; Morreale, A.; Mutter, A.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neubert, S.; Neyret, D.; Nikolaenko, V.; Nowak, W. D.; Nunes, A.S.; Olshevsky, A.; Ostrick, M.; Padee, A.; Panknin, R.; Panzieri, D.; Parsamyan, B.; Paul, S.; Perevalova, E.; Pesaro, G.; Peshekhonov, D.; Piragino, G.; Platchkov, S.; Pochodzalla, J.; Polak, J.; Polyakov, V.; Pretz, J.; Quaresma, M.; Quintans, C.; Rajotte, J.; Ramos, S.; Rapatsky, V.; Reicherz, G.; Rocco, E.; Rondio, E.; Rossiyskaya, N. S.; Ryabchikov, D.; Samoylenko, V.; Sandacz, A.; Sapozhnikov, M.; Sarkar, S.; Savin, I.; Sbrizzai, G.; Schiavon, P.; Schill, C.; Schlütter, T.; Schmidt, A.; Schmidt, K.; Schmiden, H.; Schmitt, L.; Schönning, K.; Schopferer, S.; Schott, M.; Shevchenko, O.; Silva, L.; Sinha, L.; Sissakian, A.; Slunecka, M.; Smirnov, G.; Sosio, S.; Sozzi, F.; Srnka, Aleš; Steiger, L.; Stolarski, M.; Sulc, M.; Sulej, R.; Suzuki, H.; Sznajder, P.; Takekawa, S.; Ter Wolbeek, J.; Tessaro, S.; Tessarotto, F.; Tkatchev, L.; Uhl, S.; Uman, I.; Vandenbroucke, M.; Virius, M.; Vlassov, N.; Wang, L.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Wislicki, W.; Wollny, H.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Zhuravlev, N.; Ziembicki, M.; Zvyagin, A.

    2013-01-01

    Roč. 87, č. 5 (2013), 052018:1-22 ISSN 1550-7998 Institutional support: RVO:68081731 Keywords : dependent structure-function * Monte-Carlo generator Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 4.864, year: 2013

  19. Improving the theoretical prediction for the Bs - B̅s width difference: matrix elements of next-to-leading order ΔB = 2 operators

    Science.gov (United States)

    Davies, Christine; Harrison, Judd; Lepage, G. Peter; Monahan, Christopher; Shigemitsu, Junko; Wingate, Matthew

    2018-03-01

    We present lattice QCD results for the matrix elements of R2 and other dimension-7, ΔB = 2 operators relevant for calculations of Δs, the Bs - B̅s width difference. We have computed correlation functions using 5 ensembles of the MILC Collaboration's 2+1 + 1-flavour gauge field configurations, spanning 3 lattice spacings and light sea quarks masses down to the physical point. The HISQ action is used for the valence strange quarks, and the NRQCD action is used for the bottom quarks. Once our analysis is complete, the theoretical uncertainty in the Standard Model prediction for ΔΓs will be substantially reduced.

  20. Fourth-order perturbative extension of the single-double excitation coupled-cluster method

    International Nuclear Information System (INIS)

    Derevianko, Andrei; Emmons, Erik D.

    2002-01-01

    Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed

  1. Second-order Cosmological Perturbations Engendered by Point-like Masses

    Energy Technology Data Exchange (ETDEWEB)

    Brilenkov, Ruslan [Institute for Astro- and Particle Physics, University of Innsbruck, Technikerstrasse 25/8, A‐6020 Innsbruck (Austria); Eingorn, Maxim, E-mail: ruslan.brilenkov@gmail.com, E-mail: maxim.eingorn@gmail.com [North Carolina Central University, CREST and NASA Research Centers, 1801 Fayetteville St., Durham, NC 27707 (United States)

    2017-08-20

    In the ΛCDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second‐order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second‐order scalar, vector, and tensor metric corrections are suitable at arbitrary distances, including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfillment of all Einstein equations, as well as self‐consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological back-reaction manifestations by means of relativistic simulations are also outlined.

  2. GAPER-1D, 1-D Multigroup 1. Order Perturbation Transport Theory for Reactivity Coefficient

    International Nuclear Information System (INIS)

    Koch, P.K.

    1976-01-01

    1 - Description of problem or function: Reactivity coefficients are computed using first-order transport perturbation theory for one- dimensional multi-region reactor assemblies. The number of spatial mesh-points and energy groups is arbitrary. An elementary synthesis scheme is employed for treatment of two- and three-dimensional problems. The contributions to the change in inverse multiplication factor, delta(1/k), from perturbations in the individual capture, net fission, total scattering, (n,2n), inelastic scattering, and leakage cross sections are computed. A multi-dimensional prompt neutron lifetime calculation is also available. 2 - Method of solution: Broad group cross sections for the core and perturbing or sample materials are required as input. Scalar neutron fluxes and currents, as computed by SN transport calculations, are then utilized to solve the first-order transport perturbation theory equations. A synthesis scheme is used, along with independent SN calculations in two or three dimensions, to treat a multi- dimensional assembly. Spherical harmonics expansions of the angular fluxes and scattering source terms are used with leakage and anisotropic scattering treated in a P1 approximation. The angular integrations in the perturbation theory equations are performed analytically. Various reactivity coefficients and material worths are then easily computed at specified positions in the assembly. 3 - Restrictions on the complexity of the problem: The formulation of the synthesis scheme used for two- and three-dimensional problems assumes that the fluxes and currents were computed by the DTF4 code (NESC Abstract 209). Therefore, fluxes and currents from two- or three-dimensional transport or diffusion theory codes cannot be used

  3. HQET at order 1/m. Pt. 1. Non-perturbative parameters in the quenched approximation

    Energy Technology Data Exchange (ETDEWEB)

    Blossier, Benoit [Paris XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Della Morte, Michele [Mainz Univ. (Germany). Inst. fuer Kernphysik; Garron, Nicolas [Universidad Autonoma de Madrid (Spain). Dept. Fisica Teorica y Inst. de Fisica Teorica UAM/CSIC; Edinburgh Univ. (United Kingdom). School of Physics and Astronomy - SUPA; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2010-01-15

    We determine non-perturbatively the parameters of the lattice HQET Lagrangian and those of heavy-light axial-vector and vector currents in the quenched approximation. The HQET expansion includes terms of order 1/m{sub b}. Our results allow to compute, for example, the heavy-light spectrum and B-meson decay constants in the static approximation and to order 1/m{sub b} in HQET. The determination of the parameters is separated into universal and non-universal parts. The universal results can be used to determine the parameters for various discretizations. The computation reported in this paper uses the plaquette gauge action and the ''HYP1/2'' action for the b-quark described by HQET. The parameters of the currents also depend on the light-quark action, for which we choose non-perturbatively O(a)-improved Wilson fermions. (orig.)

  4. HQET at order 1/m. Pt. 1. Non-perturbative parameters in the quenched approximation

    International Nuclear Information System (INIS)

    Blossier, Benoit; Della Morte, Michele; Garron, Nicolas; Edinburgh Univ.; Sommer, Rainer

    2010-01-01

    We determine non-perturbatively the parameters of the lattice HQET Lagrangian and those of heavy-light axial-vector and vector currents in the quenched approximation. The HQET expansion includes terms of order 1/m b . Our results allow to compute, for example, the heavy-light spectrum and B-meson decay constants in the static approximation and to order 1/m b in HQET. The determination of the parameters is separated into universal and non-universal parts. The universal results can be used to determine the parameters for various discretizations. The computation reported in this paper uses the plaquette gauge action and the ''HYP1/2'' action for the b-quark described by HQET. The parameters of the currents also depend on the light-quark action, for which we choose non-perturbatively O(a)-improved Wilson fermions. (orig.)

  5. Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

    Science.gov (United States)

    Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

    2016-07-12

    A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

  6. Propagation of perturbations for a sixth-order thin film equation

    Directory of Open Access Journals (Sweden)

    Zhenbang Li

    2012-07-01

    Full Text Available We consider an initial-boundary problem for a sixth-order thin film equation, which arises in the industrial application of the isolation oxidation of silicon. Relying on some necessary uniform estimates of the approximate solutions, we prove the existence of radial symmetric solutions to this problem in the two-dimensional space. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.

  7. Keldysh meets Lindblad: Correlated Gain and Loss in Higher Order Perturbation Theory

    Science.gov (United States)

    Stace, Tom; Mueller, Clemens

    Motivated by correlated decay processes driving gain, loss and lasing in driven artificial quantum systems, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behaviour at the same order of perturbation theory. We then apply these results to analyse the phonon-assisted steady-state gain of a microwave field driving a double quantum-dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing- assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.

  8. A calculation methodology applied for fuel management in PWR type reactors using first order perturbation theory

    International Nuclear Information System (INIS)

    Rossini, M.R.

    1992-01-01

    An attempt has been made to obtain a strategy coherent with the available instruments and that could be implemented with future developments. A calculation methodology was developed for fuel reload in PWR reactors, which evolves cell calculation with the HAMMER-TECHNION code and neutronics calculation with the CITATION code.The management strategy adopted consists of fuel element position changing at the beginning of each reactor cycle in order to decrease the radial peak factor. The bi-dimensional, two group First Order perturbation theory was used for the mathematical modeling. (L.C.J.A.)

  9. A next-to-leading-log Monte Carlo study of photon pairs and the search for the intermediate mass Higgs Boson

    International Nuclear Information System (INIS)

    Bailey, B.R.

    1993-01-01

    Symmetry breaking and the question of the origin of mass are the reasons the Superconducting Super Collider and the Large Hadron Collider are being built. The Standard Model of particle physics provides a solution to this problem by proposing the existence of a neutral scalar particle, the Higgs boson. This particle, via its interactions, gives mass to all of the particles in the Standard Model. The question of whether the Higgs boson can be detected at these machines depends critically on its final state decays. These decays in turn depend crucially on the mass of the Higgs boson, an unknown parameter of the theory. A lower bound of the Higgs mass has been set by experiment and a upper bound via theoretical arguments. Throughout much of the mass range Higgs decays via weak gauge bosons yield a clear signal. However, near the lower limit, the so-called intermediate mass region, the situation is less clear. In this region Higgs decays into photon pairs have been suggested as a viable signal. The significance of such a signal depends on other competing processes or backgrounds. This dissertation attempts to answer the question, open-quotes Can the Intermediate mass Higgs boson be detected via its electromagnetic decays?close quotes To answer this question various Standard Model processes are calculated to the leading-log and next-to-leading-log level in a Monte Carlo environment

  10. New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory

    International Nuclear Information System (INIS)

    Chung-Wen Kao; Barbara Pasquini; Marc Vanderhaeghen

    2004-01-01

    We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering (VCS) at Ο(p 4 ) in heavy baryon chiral perturbation theory. At this order, no unknown low energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the VCS amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double polarization experiments which allow to access these spin-flip GPs of the nucleon

  11. Magnetic dipole moment of the Δ(1232) in chiral perturbation theory

    International Nuclear Information System (INIS)

    Hacker, C.; Wies, N.; Scherer, S.; Gegelia, J.

    2006-01-01

    The magnetic dipole moment of the Δ(1232) is calculated in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop contribution. Moreover, due to the unstable nature of the Δ(1232), at next-to-leading order the isovector anomalous magnetic moment not only receives a real but also an imaginary loop contribution. (orig.)

  12. Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

    Science.gov (United States)

    Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

    2012-01-21

    We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

  13. Higher order generalized perturbation theory for boiling water reactor in-core fuel management optimization

    International Nuclear Information System (INIS)

    Moore, B.R.; Turinsky, P.J.

    1998-01-01

    Boiling water reactor (BWR) loading pattern assessment requires solving the two-group, nodal form of the neutron diffusion equation and drift-flux form of the fluid equations simultaneously because these equation sets are strongly coupled via nonlinear feedback. To reduce the computational burden associated with the calculation of the core attributes (that is, core eigenvalue and thermal margins) of a perturbed BWR loading pattern, the analytical and numerical aspects of a higher order generalized perturbation theory (GPT) method, which correctly addresses the strong nonlinear feedbacks of two-phase flow, have been established. Inclusion of Jacobian information in the definition of the generalized flux adjoints provides for a rapidly convergent iterative method for solution of the power distribution and eigenvalue of a loading pattern perturbed from a reference state. Results show that the computational speedup of GPT compared with conventional forward solution methods demanding consistent accuracy is highly dependent on the number of spatial nodes utilized by the core simulator, varying from superior to inferior performance as the number of nodes increases

  14. MULTIPOLE GRAVITATIONAL LENSING AND HIGH-ORDER PERTURBATIONS ON THE QUADRUPOLE LENS

    Energy Technology Data Exchange (ETDEWEB)

    Chu, Z.; Lin, W. P. [Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030 (China); Li, G. L. [Purple Mountain Observatory, 2 West Beijing Road, Nanjing 210008 (China); Kang, X., E-mail: chuzhe@shao.ac.cn, E-mail: linwp@shao.ac.cn [Partner Group of MPI for Astronomy, Purple Mountain Observatory, 2 West Beijing Road, Nanjing 210008 (China)

    2013-03-10

    An arbitrary surface mass density of the gravitational lens can be decomposed into multipole components. We simulate the ray tracing for the multipolar mass distribution of the generalized Singular Isothermal Sphere model based on deflection angles, which are analytically calculated. The magnification patterns in the source plane are then derived from an inverse shooting technique. As has been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses this kind of overlapping caustics, the image numbers change by {+-}4, rather than {+-}2. There are two kinds of caustic images. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4, and 5 mode components and found that one, two, and three butterfly or swallowtail singularities can be produced, respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails make contact, then eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.

  15. Periodic Solution and Stationary Distribution of Stochastic Predator-Prey Models with Higher-Order Perturbation

    Science.gov (United States)

    Liu, Qun; Jiang, Daqing

    2018-04-01

    In this paper, two stochastic predator-prey models with general functional response and higher-order perturbation are proposed and investigated. For the nonautonomous periodic case of the system, by using Khasminskii's theory of periodic solution, we show that the system admits a nontrivial positive T-periodic solution. For the system disturbed by both white and telegraph noises, sufficient conditions for positive recurrence and the existence of an ergodic stationary distribution to the solutions are established. The existence of stationary distribution implies stochastic weak stability to some extent.

  16. Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

    Science.gov (United States)

    Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

    1994-01-01

    Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

  17. Block correlated second order perturbation theory with a generalized valence bond reference function

    International Nuclear Information System (INIS)

    Xu, Enhua; Li, Shuhua

    2013-01-01

    The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multi-orbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods

  18. First and higher order, heuristically based generalized perturbation theory (HGPT) with optional control reset variable

    International Nuclear Information System (INIS)

    Gandini, A.

    1996-01-01

    The heuristically based generalized perturbation theory (HGPT), to first and higher order, applied to the neutron field of a reactor system, is discussed in relation to the criticality reset procedure. This procedure is implicit within the GPT methodology, corresponding to the so called filtering of the importance function relevant to the neutron field from the fundamental mode contamination. It is common practice to use the so called ''lambda''-mode filter. In order to account for any possible reset option, a general definition is introduced of an intensive control variable (ρ) entering into the governing equations, and correspondingly a fundamental ρ-mode filtering of the importance function is defined, relevant to the real criticality reset (control) mechanism adopted. A simple example illustrates the need to take into account the correct filtering, so as to avoid significant inaccuracies in the sensitivity calculation results. The extension of this filtering technique to other functions entering into the GPT perturbative formulations at first and higher order is also discussed. (author)

  19. Block correlated second order perturbation theory with a generalized valence bond reference function.

    Science.gov (United States)

    Xu, Enhua; Li, Shuhua

    2013-11-07

    The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

  20. First order mean field games - explicit solutions, perturbations and connection with classical mechanics

    KAUST Repository

    Gomes, Diogo A.

    2016-01-06

    We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.

  1. First order mean field games - explicit solutions, perturbations and connection with classical mechanics

    KAUST Repository

    Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana

    2016-01-01

    We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.

  2. Efficient analytic computation of higher-order QCD amplitudes

    International Nuclear Information System (INIS)

    Bern, Z.; Chalmers, G.; Dunbar, D.C.; Kosower, D.A.

    1995-01-01

    The authors review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints

  3. Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory.

    Science.gov (United States)

    Lao, Ka Un; Herbert, John M

    2012-03-22

    We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA. © 2012 American Chemical Society

  4. The Interaction Between Control Rods as Estimated by Second-Order One-Group Perturbation Theory

    International Nuclear Information System (INIS)

    Persson, Rolf

    1966-10-01

    The interaction effect between control rods is an important problem for the reactivity control of a reactor. The approach of second order one-group perturbation theory is shown to be attractive due to its simplicity. Formulas are derived for the fully inserted control rods in a bare reactor. For a single rod we introduce a correction parameter b, which with good approximation is proportional to the strength of the absorber. For two and more rods we introduce an interaction function g(r ij ), which is assumed to depend only on the distance r ij between the rods. The theoretical expressions are correlated with the results of several experiments in R0, ZEBRA and the Aagesta reactor, as well as with more sophisticated calculations. The approximate formulas are found to give quite good agreement with exact values, but in the case of about 8 or more rods higher-order effects are likely to be important

  5. The Interaction Between Control Rods as Estimated by Second-Order One-Group Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Persson, Rolf

    1966-10-15

    The interaction effect between control rods is an important problem for the reactivity control of a reactor. The approach of second order one-group perturbation theory is shown to be attractive due to its simplicity. Formulas are derived for the fully inserted control rods in a bare reactor. For a single rod we introduce a correction parameter b, which with good approximation is proportional to the strength of the absorber. For two and more rods we introduce an interaction function g(r{sub ij}), which is assumed to depend only on the distance r{sub ij} between the rods. The theoretical expressions are correlated with the results of several experiments in R0, ZEBRA and the Aagesta reactor, as well as with more sophisticated calculations. The approximate formulas are found to give quite good agreement with exact values, but in the case of about 8 or more rods higher-order effects are likely to be important.

  6. A porous flow model of flank eruptions on Mt. Etna: second-order perturbation theory

    Directory of Open Access Journals (Sweden)

    N. Cenni

    1997-06-01

    Full Text Available A porous flow model for magma migration from a deep source within a volcanic edifice is developed. The model is based on the assumption that an isotropic and homogeneous system of fractures allows magma migration from one localized feeding dyke up to the surface of the volcano. The maximum level that magma can reach within the volcano (i.e., the «free surface» of magma, where fluid pressure equals the atmospheric pressure is reproduced through a second-order perturbation approach to the non-linear equations governing the migration of incompressible fluids through a porous medium. The perturbation parameter is found to depend on the ratio of the volumic discharge rate at the source (m3/s divided by the product of the hydraulic conductivity of the medium (m1/s times the square of the source depth. The second-order corrections for the free surface of Mt. Etna are found to be small but not negligible; from the comparison between first-order and second-order free surfaces it appears that the former is higher near the summit, slightly lower at intermediate altitudes and slightly higher far away from the axis of the volcano. Flank eruptions in the southern sector are found to be located in regions where the topography is actually lower than the theoretical free surface of magma. In this sector, modulations in the eruption site density correlate well with even minor differences between free surface and topography. In the northern and western sectors similar good fits are found, while the NE rift and the eastern sector seem to require mechanisms or structures respectively favouring and inhibiting magma migration.

  7. New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

    Directory of Open Access Journals (Sweden)

    Heonjong Yoo

    2017-01-01

    Full Text Available The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III–(V, they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.

  8. Second order classical perturbation theory for atom surface scattering: Analysis of asymmetry in the angular distribution

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Yun, E-mail: zhou.yun.x@gmail.com; Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il [Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovot (Israel); Miret-Artés, Salvador, E-mail: s.miret@iff.csic.es [Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain)

    2014-01-14

    A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to “soft” corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.

  9. Stochastic evaluation of second-order many-body perturbation energies.

    Science.gov (United States)

    Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So

    2012-11-28

    With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.

  10. Second order classical perturbation theory for atom surface scattering: analysis of asymmetry in the angular distribution.

    Science.gov (United States)

    Zhou, Yun; Pollak, Eli; Miret-Artés, Salvador

    2014-01-14

    A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to "soft" corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.

  11. CITATION, 3-D Multigroup Diffusion with 1. Order Perturbation and Criticality Search

    International Nuclear Information System (INIS)

    Fowler, T.B.; Vondy, D.R.; Cunningham, G.W.

    1995-01-01

    1 - Description of problem or function: CITATION is designed to solve problems using the finite-difference representation of neutron diffusion theory, treating up to three space dimensions with arbitrary group-to-group scattering. X-y-z, theta-r-z, hexagonal-z, and trigonal-z geometries may be treated. Depletion problems may be solved and fuel managed for multi-cycle analysis. Extensive first-order perturbation results may be obtained given microscopic data and nuclide concentrations. Statics problems may be solved and perturbation results obtained with microscopic data. CITATION-2-3-VP2 is a vectorized version for FACOM VP-100 and VP-200 vector computers. 2 - Method of solution: Explicit, finite-difference approximations in space and time have been implemented. The neutron-flux-eigenvalue problems are solved by direct iteration to determine the multiplication factor or the nuclide densities required for a critical system. CITATION-2-3-VP2: Algorithms for the inner-outer iterative calculations are adapted to vector computers. The SLOR method, which is used in the original CITATION code, and the SOR method, which is adopted in the revised code, are vectorized by odd-even mesh ordering. 3 - Restrictions on the complexity of the problem: CITATION has been designed to attack problems which can be run in a reasonable amount of time. Storage of data is allocated dynamically to give the user flexibility in dimensioning. Typically, a finite-difference diffusion problem could have 200 depleting zones, 10,000 nuclide densities, and 30,000 space-energy point flux values

  12. Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

    Science.gov (United States)

    Sayevand, K.; Pichaghchi, K.

    2018-04-01

    In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

  13. Degenerate Perturbation Theory for Electronic g Tensors: Leading-Order Relativistic Effects.

    Science.gov (United States)

    Rinkevicius, Zilvinas; de Almeida, Katia Julia; Oprea, Cornel I; Vahtras, Olav; Ågren, Hans; Ruud, Kenneth

    2008-11-11

    A new approach for the evaluation of the leading-order relativistic corrections to the electronic g tensors of molecules with a doublet ground state is presented. The methodology is based on degenerate perturbation theory and includes all relevant contributions to the g tensor shift up to order O(α(4)) originating from the one-electron part of the Breit-Pauli Hamiltonian-that is, it allows for the treatment of scalar relativistic, spin-orbit, and mixed corrections to the spin and orbital Zeeman effects. This approach has been implemented in the framework of spin-restricted density functional theory and is in the present paper, as a first illustration of the theory, applied to study relativistic effects on electronic g tensors of dihalogen anion radicals X2(-) (X = F, Cl, Br, I). The results indicate that the spin-orbit interaction is responsible for the large parallel component of the g tensor shift of Br2(-) and I2(-), and furthermore that both the leading-order scalar relativistic and spin-orbit corrections are of minor importance for the perpendicular component of the g tensor in these molecules since they effectively cancel each other. In addition to investigating the g tensors of dihalogen anion radicals, we also critically examine the importance of various relativistic corrections to the electronic g tensor of linear molecules with Σ-type ground states and present a two-state model suitable for an approximate estimation of the g tensor in such molecules.

  14. Linear perturbation of spherically symmetric flows: a first-order upwind scheme for the gas dynamics equations in Lagrangian coordinates

    International Nuclear Information System (INIS)

    Clarisse, J.M.

    2007-01-01

    A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)

  15. A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

    Directory of Open Access Journals (Sweden)

    R. C. Domingos

    2013-01-01

    Full Text Available The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. The disturbing function is expanded in Legendre polynomials up to the second order in both cases. The equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.

  16. Determination of the strong coupling constant αs(MZ2) under regardment of completely resummed leading and next-to-leading logarithms. Analysis of global event variables measured in hadronic Z decays

    International Nuclear Information System (INIS)

    Wehr, A.

    1994-06-01

    The value of the strong coupling constant α s is determined from a combined analysis of the global event shape variables thrust, heavy jet mass and total and wide jet broadening. The extraction of α s includes the full calculation of O(α s 2 ) terms and leading and next-to-leading logarithms resummed to all orders of α s . The analysis is based on data taken with the DELPHI detector at LEP during 1991 and 1992. The dependence of the result on the detailed matching of the resummed and fixed order terms is studied. The result from the combined theory is compared with values coming from a pure NLLA analysis and as pure O(α s 2 ) analysis, respectively. It is found that the inclusion of the resummed logarithms allows the description of the data in the two jet range and reduces the scale dependence of α s (M Z 2 ) compared to pure O(α s 2 ) theory. The value using the combined NLLA+O(α s 2 ) theory at the scale μ 2 =M Z 2 is α S (M Z 2 )=0.118±0.007. The running of α s is measured from the 1991 data in an energy range from 88.5 to 93.7 GeV. The slope of α s obtained at the Z peak is dα s /dQ/ Q=Mz =-(2.9±2.8)x10 -4 GeV -1 . This value is compatible with QCD and exludes an abelian gluon model with more than two standard deviations. (orig.)

  17. Combining higher-order resummation with multiple NLO calculations and parton showers in the Geneva Monte Carlo framework

    International Nuclear Information System (INIS)

    Alioli, Simone; Bauer, Christian W.; Berggren, Calvin; Vermilion, Christopher K.; Walsh, Jonathan R.; Zuberi, Saba; Hornig, Andrew; Tackmann, Frank J.

    2013-05-01

    We discuss the GENEVA Monte Carlo framework, which combines higher-order resummation (NNLL) of large Sudakov logarithms with multiple next-to-leading-order (NLO) matrix-element corrections and parton showering (using PYTHIA 8) to give a complete description at the next higher perturbative accuracy in α s at both small and large jet resolution scales. Results for e + e - →jets compared to LEP data and pp→(Z/γ * →l + l - )+jets are presented.

  18. The electric dipole form factor of the nucleon in chiral perturbation theory to sub-leading order

    NARCIS (Netherlands)

    Mereghetti, E.; de Vries, J.; Hockings, W. H.; Maekawa, C. M.; van Kolck, U.

    2011-01-01

    The electric dipole form factor (EDFF) of the nucleon stemming from the QCD (theta) over bar term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable,

  19. The Fubini-Furlan-Rosetti sum rule and related aspects in light of covariant baryon chiral perturbation theory

    International Nuclear Information System (INIS)

    Bernard, V.; Kubis, B.; Meissner, U.G.

    2005-01-01

    We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading-order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E 0+ . (orig.)

  20. O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory

    CERN Document Server

    Grimbach, A; Knechtli, F; Palombi, Filippo

    2008-01-01

    We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schroedinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.

  1. Hydrogen atom with a Yukawa potential: Perturbation theory and continued-fractions--Pade approximants at large order

    International Nuclear Information System (INIS)

    Vrscay, E.R.

    1986-01-01

    A simple power-series method is developed to calculate to large order the Rayleigh-Schroedinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Pade approximants to these series generally avoid the region of the positive real axis 0 < lambda < lambda(, where lambda( represents the coupling constant threshold. As a result, the Pade sums afford accurate approximations to E(lambda) in this domain. The continued-fraction representations to these perturbation series have been accurately calculated to large (100th) order and demonstrate a curious ''quasioscillatory,'' but non-Stieltjes, behavior. Accurate values of E(lambda) as well as lambda( for the 1s, 2s, and 2p levels are reported

  2. Analyzing Bs - anti Bs mixing. Non-perturbative contributions to bag parameters from sum rules

    International Nuclear Information System (INIS)

    Mannel, T.; Pivovarov, A.A.; Russian Academy of Sciecnes, Moscow

    2007-03-01

    We use QCD sum rules to compute matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the B s mass eigenstates. Our analysis includes the leading-order operators Q and Q S , as well as the subleading operators R 2 and R 3 , which appear at next-to-leading order in the 1/m b expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)

  3. Influence of stochastic perturbations on the cluster explosive synchronization of second-order Kuramoto oscillators on networks.

    Science.gov (United States)

    Cao, Liang; Tian, Changhai; Wang, Zhenhua; Zhang, Xiyun; Liu, Zonghua

    2018-02-01

    Explosive synchronization in networked second-order Kuramoto oscillators has been well studied recently and it is revealed that the synchronization process is featured by cluster explosive synchronization. However, little attention has been paid to the influence of noise or perturbation. We here study this problem and discuss the influences of noise and perturbation. For the former, we interestingly find that noise has significant influence on the cluster explosive synchronization of those nodes with smaller degrees, i.e., their synchronization will change from the first-order to second-order transition and the critical points for both the forward and backward synchronization depend on the strength of noise. Especially, when the strength of noise is in an optimal range, a synchronization of the nodes with smaller degrees will be induced in the region of coupling strength where they do not display synchronization in the absence of noise. For the latter, we find that the effect of perturbation is similar to that of noise when its duration W is small. However, the perturbation will induce a change from cluster explosive synchronization to explosive synchronization when W is large. Furthermore, a brief theory is provided to explain the influence of perturbations on the critical points.

  4. Fourth-order terms in the diagrammatic perturbation expansion for the electronic energy of atoms and molecules

    International Nuclear Information System (INIS)

    Wilson, S.; Silver, D.M.

    1979-01-01

    Third-order diagrammatic perturbation theory provides a simple and accurate description of the electronic structure of atoms and molecules beyond that afforded by independent electron models. The largest corrections to such treatments, the fourth-order terms, are presented and discussed. All of the diagrams, which arise when the closed-shell Hartree--Fock function is utilized as a reference function, are given through fourth order. 18 references

  5. Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis

    NARCIS (Netherlands)

    Helmich-Paris, B.; Knecht, Stefan

    2017-01-01

    In the present article, we show how to formulate the partially contracted n-electron valence second-order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of orbital-energy denominators (OEDs). As atomic-orbital (AO) basis

  6. Investigation of solutions of boundary-value singular perturbated problem for Schroedinger equation of 4th order

    International Nuclear Information System (INIS)

    Amirkhanov, I.V.; Zhidkov, E.P.; Konnova, S.V.

    2000-01-01

    For the case of spherical-symmetrical potential we have considered the convergence of the solution of singular-perturbated Schroedinger equation of the 4th order to the solution of the corresponding standard nonrelativistic Schroedinger equation by numerical and analytical methods. The questions of existence of the solutions are explored. Numerical results are given. (author)

  7. Perturbative quantum chromodynamic analysis of deep inelastic scattering

    International Nuclear Information System (INIS)

    Herrod, R.T.

    1982-01-01

    This is an account of the field theoretic description of the deep inelastic scattering of leptons from nucleons. Starting from simple parton model description, using the assumption of an SU(3) colour confining field theory, for the quarks comprising hadronic matter, the well known prediction of Bjorken scaling is obtained. Field theoretic predictions for deviations from Bjorken scaling are formally introduced, with particular reference to quantum chromodynamics (QCD). This treatment is purely perturbative, although the renormalisation group is used to improve convergence. Scaling violations at both leading order, and next-to-leading order are discussed, and it is shown how these lead to predictions regarding the dependence of the moments of observable structure functions, on the square of the 4-momentum transferred (Q 2 ). Evolution equations for the moments of structure functions are then derived. The intuitive approach of Altarelli and Parisi (AP), which leads to predictions for the Q 2 dependence of the structure functions themselves, is introduced. The corresponding equations are derived to next-to-leading order. The results of an extensive analysis of current data are presented.. Both weak and electromagnetic structure functions are compared with the predictions of leading order, and higher order formulae. Methods for incorporating heavy quark flavours into the AP equations are discussed. (author)

  8. Development of parallellized higher-order generalized depletion perturbation theory for application in equilibrium cycle optimization

    Energy Technology Data Exchange (ETDEWEB)

    Geemert, R. van E-mail: rene.vangeemert@psi.ch; Hoogenboom, J.E. E-mail: j.e.hoogenboom@iri.tudelft.nl

    2001-09-01

    As nuclear fuel economy is basically a multi-cycle issue, a fair way of evaluating reload patterns is to consider their performance in the case of an equilibrium cycle. The equilibrium cycle associated with a reload pattern is defined as the limit fuel cycle that eventually emerges after multiple successive periodic refueling, each time implementing the same reload scheme. Since the equilibrium cycle is the solution of a reload operation invariance equation, it can in principle be found with sufficient accuracy only by applying an iterative procedure, simulating the emergence of the limit cycle. For a design purpose such as the optimization of reload patterns, in which many different equilibrium cycle perturbations (resulting from many different limited changes in the reload operator) must be evaluated, this requires far too much computational effort. However, for very fast calculation of these many different equilibrium cycle perturbations it is also possible to set up a generalized variational approach. This approach results in an iterative scheme that yields the exact perturbation in the equilibrium cycle solution as well, in an accelerated way. Furthermore, both the solution of the adjoint equations occurring in the perturbation theory formalism and the implementation of the optimization algorithm have been parallellized and executed on a massively parallel machine. The combination of parallellism and generalized perturbation theory offers the opportunity to perform very exhaustive, fast and accurate sampling of the solution space for the equilibrium cycle reload pattern optimization problem.

  9. Perturbation theory for nematic liquid crystals of axially symmetric molecules: Evaluation of fourth rank orientational order parameter

    International Nuclear Information System (INIS)

    Singh, K.

    1993-11-01

    Using a statistical mechanical perturbation theory for isotropic-nematic transition we report a calculation of second and fourth rank orientation order parameters and thermodynamic properties for a model system of prolate ellipsoids of revolution parameterized by its length-to-width ratio. The influence of attractive potential represented by dispersion interaction on a variety of thermodynamic properties is analysed. Inclusion of fourth rank orientational order parameter in calculation slightly changes the transition parameter. (author). 7 refs, 1 tab

  10. Estimation of high orders of the perturbation theory in quantum mechanics

    International Nuclear Information System (INIS)

    Seznec, Reynald.

    1978-01-01

    First of all the simple case of an integral of one variable (zero-dimensional model) is examined to illustrate the methods and concepts used. A system n quantum oscillators 0(n) (spherical model) is then studied. A theory of perturbations around the saddle point dominating the functional integral is developed (theory of perturbations around the instanton). The fluctuation propagator is calculated explicitly. Some properties of the corresponding Feynman diagrams are also investigated. Methods are proposed to generalize the calculations to more complicated potentials. As an example of application the calculations of the first correction to the Lipatovian term are given for the spherical model [fr

  11. Perturbative QCD for the LHC

    International Nuclear Information System (INIS)

    Glover, N.

    2008-01-01

    The need for predictions of standard model processes at the LHC at leading order and beyond is motivated. Recent developments in computing scattering amplitudes are reviewed. I describe the limitations of tree-level predictions, and how they may be improved at next-to-leading order. The current status of the field is discussed. (author)

  12. Complex-plane strategy for computing rotating polytropic models - efficiency and accuracy of the complex first-order perturbation theory

    International Nuclear Information System (INIS)

    Geroyannis, V.S.

    1988-01-01

    In this paper, a numerical method is developed for determining the structure distortion of a polytropic star which rotates either uniformly or differentially. This method carries out the required numerical integrations in the complex plane. The method is implemented to compute indicative quantities, such as the critical perturbation parameter which represents an upper limit in the rotational behavior of the star. From such indicative results, it is inferred that this method achieves impressive improvement against other relevant methods; most important, it is comparable to some of the most elaborate and accurate techniques on the subject. It is also shown that the use of this method with Chandrasekhar's first-order perturbation theory yields an immediate drastic improvement of the results. Thus, there is no neeed - for most applications concerning rotating polytropic models - to proceed to the further use of the method with higher order techniques, unless the maximum accuracy of the method is required. 31 references

  13. Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients

    Science.gov (United States)

    Shiozaki, Toru; Győrffy, Werner; Celani, Paolo; Werner, Hans-Joachim

    2011-08-01

    The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented.

  14. A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

    2017-02-01

    The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.

  15. Higher order statistics of curvature perturbations in IFF model and its Planck constraints

    International Nuclear Information System (INIS)

    Fujita, Tomohiro; Yokoyama, Shuichiro

    2013-01-01

    We compute the power spectrum P ζ and non-linear parameters f NL and τ NL of the curvature perturbation induced during inflation by the electromagnetic fields in the kinetic coupling model (IFF model). By using the observational result of P ζ ,f NL and τ NL reported by the Planck collaboration, we study the constraint on the model comprehensively. Interestingly, if the single slow-rolling inflaton is responsible for the observed P ζ , the constraint from τ NL is most stringent. We also find a general relationship between f NL and τ NL generated in this model. Even if f NL ∼ O(1), a detectable τ NL can be produced

  16. Calculation of neutron flux and reactivity by perturbation theory at high order

    International Nuclear Information System (INIS)

    Silva, W.L.P. da; Silva, F.C. da; Thome Filho, Z.D.

    1982-01-01

    A high order pertubation theory is studied, independent of time, applied to integral parameter calculation of a nuclear reactor. A pertubative formulation, based on flux difference technique, which gives directy the reactivity and neutron flux up to the aproximation order required, is presented. As an application of the method, global pertubations represented by fuel temperature variations, are used. Tests were done aiming to verify the relevancy of the approximation order for several intensities of the pertubations considered. (E.G.) [pt

  17. Covariant second-order perturbations in generalized two-field inflation

    International Nuclear Information System (INIS)

    Tzavara, Eleftheria; Tent, Bartjan van; Mizuno, Shuntaro

    2014-01-01

    We examine the covariant properties of generalized models of two-field inflation, with non-canonical kinetic terms and a possibly non-trivial field metric. We demonstrate that kinetic-term derivatives and covariant field derivatives do commute in a proper covariant framework, which was not realized before in the literature. We also define a set of generalized slow-roll parameters, using a unified notation. Within this framework, we study the most general class of models that allows for well-defined adiabatic and entropic sound speeds, which we identify as the models with parallel momentum and field velocity vectors. For these models we write the exact cubic action in terms of the adiabatic and isocurvature perturbations. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale for these generalized models. We illustrate our general results by considering their long-wavelength limit, as well as with the example of two-field DBI inflation

  18. Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions.

    Science.gov (United States)

    Vlaisavljevich, Bess; Shiozaki, Toru

    2016-08-09

    We report the development of the theory and computer program for analytical nuclear energy gradients for (extended) multistate complete active space perturbation theory (CASPT2) with full internal contraction. The vertical shifts are also considered in this work. This is an extension of the fully internally contracted CASPT2 nuclear gradient program recently developed for a state-specific variant by us [MacLeod and Shiozaki, J. Chem. Phys. 2015, 142, 051103]; in this extension, the so-called λ equation is solved to account for the variation of the multistate CASPT2 energies with respect to the change in the amplitudes obtained in the preceding state-specific CASPT2 calculations, and the Z vector equations are modified accordingly. The program is parallelized using the MPI3 remote memory access protocol that allows us to perform efficient one-sided communication. The optimized geometries of the ground and excited states of a copper corrole and benzophenone are presented as numerical examples. The code is publicly available under the GNU General Public License.

  19. Perturbation theory at large order in more than one coupling constant for a field theory with fermions

    International Nuclear Information System (INIS)

    Chowdhury, A.R.; Roy, T.

    1980-01-01

    We have considered the problem of evaluating the large order estimates of perturbation theory in a quantum field theory with more than one coupling constant. The theory considered is four dimensional and possesses instanton-type solutions. It contains a Boson field coupled with a Fermion through the usual g anti psi psi phi type interaction, along with the self-interaction of the Boson lambda phi 4 . Our analysis reveals a phenomenon not observed in a theory with only one coupling constant. One gets different kinds of behavior in different regions of the (lambda, g) plane. The results are quite encouraging for the application to more realistic field theories

  20. Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe

    OpenAIRE

    Takahashi, Ryuichi

    2008-01-01

    We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in a quasi-nonlinear regime ($k \\approx 0.1h$/Mpc). Analytical solutions and simple fitting formulae are presented for the dark-energy model with the general time-varying equation of state $w(a)$. It turns out that the power spectrum coincides with the approx...

  1. Perturbation series at large orders in quantum mechanics and field theories: application to the problem of resummation

    International Nuclear Information System (INIS)

    Zinn-Justin, J.; Freie Univ. Berlin

    1981-01-01

    In this review I present a method to estimate the large order behavior of perturbation theory in quantum mechanics and field theory. The basic idea, due to Lipatov, is to relate the large order behavior to (in general complex) instanton contributions to the path integral representation of Green's functions. I explain the method first in the case of a simple integral and of the anharmonic oscillator and recover the results of Bender and Wu. I apply it then to the PHI 4 field theory. I study general potentials and boson field theories. I show, following Parisi, how the method can be generalized to theories with fermions. Finally I outline the implications of these results for the summability of the series. In particular I explain a method to sum divergent series based on a Borel transformation. In a last section I compare the larger order behavior predictions to actual series calculation. I present also some numerical examples of series summation. (orig.)

  2. Can the second order multireference perturbation theory be considered a reliable tool to study mixed-valence compounds?

    Science.gov (United States)

    Pastore, Mariachiara; Helal, Wissam; Evangelisti, Stefano; Leininger, Thierry; Malrieu, Jean-Paul; Maynau, Daniel; Angeli, Celestino; Cimiraglia, Renzo

    2008-05-07

    In this paper, the problem of the calculation of the electronic structure of mixed-valence compounds is addressed in the frame of multireference perturbation theory (MRPT). Using a simple mixed-valence compound (the 5,5(') (4H,4H('))-spirobi[ciclopenta[c]pyrrole] 2,2('),6,6(') tetrahydro cation), and the n-electron valence state perturbation theory (NEVPT2) and CASPT2 approaches, it is shown that the ground state (GS) energy curve presents an unphysical "well" for nuclear coordinates close to the symmetric case, where a maximum is expected. For NEVPT, the correct shape of the energy curve is retrieved by applying the MPRT at the (computationally expensive) third order. This behavior is rationalized using a simple model (the ionized GS of two weakly interacting identical systems, each neutral system being described by two electrons in two orbitals), showing that the unphysical well is due to the canonical orbital energies which at the symmetric (delocalized) conformation lead to a sudden modification of the denominators in the perturbation expansion. In this model, the bias introduced in the second order correction to the energy is almost entirely removed going to the third order. With the results of the model in mind, one can predict that all MRPT methods in which the zero order Hamiltonian is based on canonical orbital energies are prone to present unreasonable energy profiles close to the symmetric situation. However, the model allows a strategy to be devised which can give a correct behavior even at the second order, by simply averaging the orbital energies of the two charge-localized electronic states. Such a strategy is adopted in a NEVPT2 scheme obtaining a good agreement with the third order results based on the canonical orbital energies. The answer to the question reported in the title (is this theoretical approach a reliable tool for a correct description of these systems?) is therefore positive, but care must be exercised, either in defining the orbital

  3. Analytic solution to leading order coupled DGLAP evolution equations: A new perturbative QCD tool

    International Nuclear Information System (INIS)

    Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.

    2011-01-01

    We have analytically solved the LO perturbative QCD singlet DGLAP equations [V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)][G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977)][Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)] using Laplace transform techniques. Newly developed, highly accurate, numerical inverse Laplace transform algorithms [M. M. Block, Eur. Phys. J. C 65, 1 (2010)][M. M. Block, Eur. Phys. J. C 68, 683 (2010)] allow us to write fully decoupled solutions for the singlet structure function F s (x,Q 2 ) and G(x,Q 2 ) as F s (x,Q 2 )=F s (F s0 (x 0 ),G 0 (x 0 )) and G(x,Q 2 )=G(F s0 (x 0 ),G 0 (x 0 )), where the x 0 are the Bjorken x values at Q 0 2 . Here F s and G are known functions--found using LO DGLAP splitting functions--of the initial boundary conditions F s0 (x)≡F s (x,Q 0 2 ) and G 0 (x)≡G(x,Q 0 2 ), i.e., the chosen starting functions at the virtuality Q 0 2 . For both G(x) and F s (x), we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy--a computational fractional precision of O(10 -9 ). Armed with this powerful new tool in the perturbative QCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet F s distributions [A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009)], starting from their initial values at Q 0 2 =1 GeV 2 and 1.69 GeV 2 , respectively, using their choice of α s (Q 2 ). This allows an important independent check on the accuracies of their evolution codes and, therefore, the computational accuracies of their published parton distributions. Our method completely decouples the two LO distributions, at the same time guaranteeing that both G and F s satisfy the singlet coupled DGLAP equations. It also allows one to easily obtain the effects of the starting functions on the evolved gluon and singlet structure functions, as functions of both Q

  4. Perturbative theory of higher-order collision-enhanced wave mixing

    International Nuclear Information System (INIS)

    Trebino, R.; Rahn, L.A.

    1989-01-01

    This paper reports on collision-enhanced resonances which represent an interesting class of nonlinear- optical processes. They occur because collisional dephasing can rephase quantum-mechanical amplitudes that ordinarily cancel out exactly, thereby allowing otherwise unobservable wave-mixing resonances to be seen. This is an especially interesting phenomenon because these resonances are coherent effects that are induced by an incoherent process (collisional dephasing). First predicted in the late 1970s and eventually observed in 1981, these novel effects have now been seen in a wide variety of four-wave-mixing experiments, ranging from self-focusing to coherent anti-Stokes Raman spectroscopy. Recently, the authors have extended these observations to higher order, where the authors have shown both experimentally and theoretically the higher-order, collision-enhanced effects exist in nonlinear optics, appearing as subharmonics of two-photon resonances. Indeed, the authors have found that collision-enhanced processes are ideal systems for studying higher-order, nonlinear-optical effects because very high orders can be made to contribute with little or no saturation braodening. Experiments on sodium in a flame using six- and eight-wave-mixing geometries have revealed still higher-order effects (at least as high- order as χ (13) )

  5. Identification of fractional-order systems via a switching differential evolution subject to noise perturbations

    International Nuclear Information System (INIS)

    Zhu, Wu; Fang, Jian-an; Tang, Yang; Zhang, Wenbing; Xu, Yulong

    2012-01-01

    In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.

  6. Identification of fractional-order systems via a switching differential evolution subject to noise perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Zhu, Wu, E-mail: dtzhuwu@gmail.com [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Fang, Jian-an [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Tang, Yang, E-mail: yang.tang@pik-potsdam.de [Institute of Physics, Humboldt University, Berlin 12489 (Germany); Potsdam Institute for Climate Impact Research, Potsdam 14415 (Germany); Research Institute for Intelligent Control and System, Harbin Institute of Technology, Harbin 150006 (China); Zhang, Wenbing [Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong (China); Xu, Yulong [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)

    2012-10-01

    In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.

  7. Analyzing B{sub s} - anti B{sub s} mixing. Non-perturbative contributions to bag parameters from sum rules

    Energy Technology Data Exchange (ETDEWEB)

    Mannel, T. [Siegen Univ. (Germany). FB 7, Theoretische Physik; Pecjak, B.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pivovarov, A.A. [Siegen Univ. (Germany). FB 7, Theoretische Physik]|[Russian Academy of Sciecnes, Moscow (Russian Federation). Inst. for Nuclear Research

    2007-03-15

    We use QCD sum rules to compute matrix elements of the {delta}B=2 operators appearing in the heavy-quark expansion of the width difference of the B{sub s} mass eigenstates. Our analysis includes the leading-order operators Q and Q{sub S}, as well as the subleading operators R{sub 2} and R{sub 3}, which appear at next-to-leading order in the 1/m{sub b} expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)

  8. Perturbation theory

    International Nuclear Information System (INIS)

    Bartlett, R.; Kirtman, B.; Davidson, E.R.

    1978-01-01

    After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references

  9. Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

    International Nuclear Information System (INIS)

    Chingangbam, Pravabati; Park, Changbom

    2009-01-01

    We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter g NL . The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of g NL and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for g NL > 0 and less of both for g NL NL and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of g NL that are clearly distinct from the quadratic order perturbations, encoded in the parameter f NL . Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between g NL and f NL type non-Gaussianities

  10. Computation of External Quality Factors for RF Structures by Means of Model Order Reduction and a Perturbation Approach

    CERN Document Server

    Flisgen, Thomas; van Rienen, Ursula

    2016-01-01

    External quality factors are significant quantities to describe losses via waveguide ports in radio frequency resonators. The current contribution presents a novel approach to determine external quality factors by means of a two-step procedure: First, a state-space model for the lossless radio frequency structure is generated and its model order is reduced. Subsequently, a perturbation method is applied on the reduced model so that external losses are accounted for. The advantage of this approach results from the fact that the challenges in dealing with lossy systems are shifted to the reduced order model. This significantly saves computational costs. The present paper provides a short overview on existing methods to compute external quality factors. Then, the novel approach is introduced and validated in terms of accuracy and computational time by means of commercial software.

  11. The Electric Dipole Form Factor of the Nucleon in Chiral Perturbation Theory to Sub-leading Order

    CERN Document Server

    Mereghetti, E; Hockings, W H; Maekawa, C M; van Kolck, U

    2011-01-01

    The electric dipole form factor (EDFF) of the nucleon stemming from the QCD theta term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable, non-analytic contribution from the pion cloud. In the case of the theta term, the expected lower bound on the deuteron electric dipole moment is |d_d| > 1.4 10^(-4) \\theta e fm. The momentum dependence of the isovector EDFF is proportional to a non-derivative time-reversal-violating pion-nucleon coupling, and the scale for momentum variation ---appearing, in particular, in the radius of the form factor--- is the pion mass.

  12. Extension of the chiral perturbation theory meson Lagrangian to order p{sup 6}

    Energy Technology Data Exchange (ETDEWEB)

    Fearing, H W; Scherer, S

    1994-08-01

    We have derived the most general chirally invariant Lagrangian L{sub 6} for the meson sector at order p{sup 6}. The result provides an extension of the standard Gasser-Leutwyler Lagrangian L{sub 4} to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The equation of motion terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating p{sup 6} contributions to simple processes. (author). 53 refs., 10 tabs.

  13. ERRATUM: ON THE AUBIN PROPERTY OF CRITICAL POINTS TO PERTURBED SECOND-ORDER CONE PROGRAMS

    Czech Academy of Sciences Publication Activity Database

    Opazo, F.; Outrata, Jiří; Ramírez, H. C.

    2017-01-01

    Roč. 27, č. 3 (2017), s. 2143-2151 ISSN 1052-6234 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : second-order cone programming * Aubin property * nondegeneracy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.968, year: 2016 http://library.utia.cas.cz/separaty/2017/MTR/outrata-0481868.pdf

  14. Third-order perturbation theory for van der Waals interaction coefficients

    International Nuclear Information System (INIS)

    Tang Liyan; Shi Tingyun; Yan Zongchao; Mitroy, J.

    2011-01-01

    The third-order expression for the dispersion interaction between two atoms is written as a sum over lists of transition matrix elements. Particular attention is given to the C 9 /R 9 interaction which occurs in the homonuclear case when one atom is in an S state and the other is in a P state. Numerical values of the C 9 coefficient are given for the homonuclear alkali-metal dimers. The size of the C 9 :C 3 dispersion coefficient ratio increases for the heavier alkali-metal atoms. The C 11 and C 13 coefficients between two helium atoms and lithium atoms in their ground states are also given.

  15. Extension of the chiral perturbation theory meson Lagrangian to order p6

    International Nuclear Information System (INIS)

    Fearing, H.W.; Scherer, S.

    1996-01-01

    We have constructed the most general chirally invariant Lagrangian scrL 6 for the meson sector at order p 6 . The result provides an extension of the standard Gasser-Leutwyler Lagrangian scrL 4 to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the construction was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The claim to have obtained the most general Lagrangian relies on this systematic construction and on the elimination of redundant quantities using relations of which we are aware, rather than on a general formal proof of either completeness or independence. The open-quote open-quote equation-of-motion close-quote close-quote terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating p 6 contributions to simple processes. copyright 1995 The American Physical Society

  16. Exploration of zeroth-order wavefunctions and energies as a first step toward intramolecular symmetry-adapted perturbation theory

    Science.gov (United States)

    Gonthier, Jérôme F.; Corminboeuf, Clémence

    2014-04-01

    Non-covalent interactions occur between and within all molecules and have a profound impact on structural and electronic phenomena in chemistry, biology, and material science. Understanding the nature of inter- and intramolecular interactions is essential not only for establishing the relation between structure and properties, but also for facilitating the rational design of molecules with targeted properties. These objectives have motivated the development of theoretical schemes decomposing intermolecular interactions into physically meaningful terms. Among the various existing energy decomposition schemes, Symmetry-Adapted Perturbation Theory (SAPT) is one of the most successful as it naturally decomposes the interaction energy into physical and intuitive terms. Unfortunately, analogous approaches for intramolecular energies are theoretically highly challenging and virtually nonexistent. Here, we introduce a zeroth-order wavefunction and energy, which represent the first step toward the development of an intramolecular variant of the SAPT formalism. The proposed energy expression is based on the Chemical Hamiltonian Approach (CHA), which relies upon an asymmetric interpretation of the electronic integrals. The orbitals are optimized with a non-hermitian Fock matrix based on two variants: one using orbitals strictly localized on individual fragments and the other using canonical (delocalized) orbitals. The zeroth-order wavefunction and energy expression are validated on a series of prototypical systems. The computed intramolecular interaction energies demonstrate that our approach combining the CHA with strictly localized orbitals achieves reasonable interaction energies and basis set dependence in addition to producing intuitive energy trends. Our zeroth-order wavefunction is the primary step fundamental to the derivation of any perturbation theory correction, which has the potential to truly transform our understanding and quantification of non

  17. Exploration of zeroth-order wavefunctions and energies as a first step toward intramolecular symmetry-adapted perturbation theory

    International Nuclear Information System (INIS)

    Gonthier, Jérôme F.; Corminboeuf, Clémence

    2014-01-01

    Non-covalent interactions occur between and within all molecules and have a profound impact on structural and electronic phenomena in chemistry, biology, and material science. Understanding the nature of inter- and intramolecular interactions is essential not only for establishing the relation between structure and properties, but also for facilitating the rational design of molecules with targeted properties. These objectives have motivated the development of theoretical schemes decomposing intermolecular interactions into physically meaningful terms. Among the various existing energy decomposition schemes, Symmetry-Adapted Perturbation Theory (SAPT) is one of the most successful as it naturally decomposes the interaction energy into physical and intuitive terms. Unfortunately, analogous approaches for intramolecular energies are theoretically highly challenging and virtually nonexistent. Here, we introduce a zeroth-order wavefunction and energy, which represent the first step toward the development of an intramolecular variant of the SAPT formalism. The proposed energy expression is based on the Chemical Hamiltonian Approach (CHA), which relies upon an asymmetric interpretation of the electronic integrals. The orbitals are optimized with a non-hermitian Fock matrix based on two variants: one using orbitals strictly localized on individual fragments and the other using canonical (delocalized) orbitals. The zeroth-order wavefunction and energy expression are validated on a series of prototypical systems. The computed intramolecular interaction energies demonstrate that our approach combining the CHA with strictly localized orbitals achieves reasonable interaction energies and basis set dependence in addition to producing intuitive energy trends. Our zeroth-order wavefunction is the primary step fundamental to the derivation of any perturbation theory correction, which has the potential to truly transform our understanding and quantification of non

  18. Third-order perturbation theory for van der Waals interaction coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Tang Liyan; Shi Tingyun [State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China); Yan Zongchao [Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071 (China); Department of Physics, Wuhan University, Wuhan 430072 (China); Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 (Canada); Mitroy, J. [School of Engineering, Charles Darwin University, Darwin NT 0909 (Australia)

    2011-11-15

    The third-order expression for the dispersion interaction between two atoms is written as a sum over lists of transition matrix elements. Particular attention is given to the C{sub 9}/R{sup 9} interaction which occurs in the homonuclear case when one atom is in an S state and the other is in a P state. Numerical values of the C{sub 9} coefficient are given for the homonuclear alkali-metal dimers. The size of the C{sub 9}:C{sub 3} dispersion coefficient ratio increases for the heavier alkali-metal atoms. The C{sub 11} and C{sub 13} coefficients between two helium atoms and lithium atoms in their ground states are also given.

  19. Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory

    Science.gov (United States)

    Győrffy, Werner; Knizia, Gerald; Werner, Hans-Joachim

    2017-12-01

    We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.

  20. Inversion of the perturbation GPS-TEC data induced by tsunamis in order to estimate the sea level anomaly.

    Science.gov (United States)

    Rakoto, Virgile; Lognonné, Philippe; Rolland, Lucie; Coïsson, Pierdavide; Drilleau, Mélanie

    2017-04-01

    Large underwater earthquakes (Mw > 7) can transmit part of their energy to the surrounding ocean through large sea-floor motions, generating tsunamis that propagate over long distances. The forcing effect of tsunami waves on the atmosphere generate internal gravity waves which produce detectable ionospheric perturbations when they reach the upper atmosphere. Theses perturbations are frequently observed in the total electron content (TEC) measured by the multi-frequency Global navigation Satellite systems (GNSS) data (e.g., GPS,GLONASS). In this paper, we performed for the first time an inversion of the sea level anomaly using the GPS TEC data using a least square inversion (LSQ) through a normal modes summation modeling technique. Using the tsunami of the 2012 Haida Gwaii in far field as a test case, we showed that the amplitude peak to peak of the sea level anomaly inverted using this method is below 10 % error. Nevertheless, we cannot invert the second wave arriving 20 minutes later. This second wave is generaly explain by the coastal reflection which the normal modeling does not take into account. Our technique is then applied to two other tsunamis : the 2006 Kuril Islands tsunami in far field, and the 2011 Tohoku tsunami in closer field. This demonstrates that the inversion using a normal mode approach is able to estimate fairly well the amplitude of the first arrivals of the tsunami. In the future, we plan to invert in real the TEC data in order to retrieve the tsunami height.

  1. Some phenomenological consequences of the time-ordered perturbation theory of QED on non-commutative spacetime

    CERN Document Server

    Liao, Y

    2003-01-01

    A framework was recently proposed for doing perturbation theory on non-commutative (NC) spacetime. It preserves the unitarity of the S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does not commute with space. In this work, we investigate its phenomenological implications at linear colliders, especially the TESLA at DESY, through the processes of e sup + e sup --> mu sup +mu sup - ,H sup + H sup - ,H sup 0 H sup 0. We find that some NC effects computed previously are now modified and that there are new processes which now exhibit NC effects. Indeed, the first two processes get corrected at tree level as opposed to the null result in the naive approach, while the third one coincides with the naive result only in the low energy limit. The impact of the earth's rotation is incorporated. The NC signals are generally significant when the NC scale is comparable to the collider energy. If this is not the case, the non-trivial azimuthal angle distribution an...

  2. Stochastic multi-scale analysis of homogenised properties considering uncertainties in cellular solid microstructures using a first-order perturbation

    Directory of Open Access Journals (Sweden)

    Khairul Salleh Basaruddin

    Full Text Available Randomness in the microstructure due to variations in microscopic properties and geometrical information is used to predict the stochastically homogenised properties of cellular media. Two stochastic problems at the micro-scale level that commonly occur due to fabrication inaccuracies, degradation mechanisms or natural heterogeneity were analysed using a stochastic homogenisation method based on a first-order perturbation. First, the influence of Young's modulus variation in an adhesive on the macroscopic properties of an aluminium-adhesive honeycomb structure was investigated. The fluctuations in the microscopic properties were then combined by varying the microstructure periodicity in a corrugated-core sandwich plate to obtain the variation of the homogenised property. The numerical results show that the uncertainties in the microstructure affect the dispersion of the homogenised property. These results indicate the importance of the presented stochastic multi-scale analysis for the design and fabrication of cellular solids when considering microscopic random variation.

  3. Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

    Science.gov (United States)

    Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan

    2017-03-01

    Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  4. Second-order contributions to the structure functions in deep inelastic scattering III The singlet

    CERN Document Server

    González-Arroyo, A

    1980-01-01

    For pt.II see ibid., vol.159, p.512 (1979). Pointlike QCD predictions for the singlet part of the structure functions are given up to next- to-leading order of perturbation theory. This generalises the result obtained in pt.I (see ibid., vol.153, p.161, 1979) which deals with the non-singlet case. An interesting by-product is an exact and simple analytical expression for the anomalous dimension matrix to second non-trivial order in the QCD coupling constant. (18 refs).

  5. The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

    Science.gov (United States)

    Mcclelland, J.; Silk, J.

    1978-01-01

    Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.

  6. Use of density functional theory orbitals in the GVVPT2 variant of second-order multistate multireference perturbation theory.

    Science.gov (United States)

    Hoffmann, Mark R; Helgaker, Trygve

    2015-03-05

    A new variation of the second-order generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structure is suggested. In contrast to the established procedure, in which CASSCF or MCSCF orbitals are first obtained and subsequently used to define a many-electron model (or reference) space, the use of an orbital space obtained from the local density approximation (LDA) variant of density functional theory is considered. Through a final, noniterative diagonalization of an average Fock matrix within orbital subspaces, quasicanonical orbitals that are otherwise indistinguishable from quasicanonical orbitals obtained from a CASSCF or MCSCF calculation are obtained. Consequently, all advantages of the GVVPT2 method are retained, including use of macroconfigurations to define incomplete active spaces and rigorous avoidance of intruder states. The suggested variant is vetted on three well-known model problems: the symmetric stretching of the O-H bonds in water, the dissociation of N2, and the stretching of ground and excited states C2 to more than twice the equilibrium bond length of the ground state. It is observed that the LDA-based GVVPT2 calculations yield good results, of comparable quality to conventional CASSCF-based calculations. This is true even for the C2 model problem, in which the orbital space for each state was defined by the LDA orbitals. These results suggest that GVVPT2 can be applied to much larger problems than previously accessible.

  7. Numerical-analytic implementation of the higher-order canonical Van Vleck perturbation theory for the interpretation of medium-sized molecule vibrational spectra.

    Science.gov (United States)

    Krasnoshchekov, Sergey V; Isayeva, Elena V; Stepanov, Nikolay F

    2012-04-12

    Anharmonic vibrational states of semirigid polyatomic molecules are often studied using the second-order vibrational perturbation theory (VPT2). For efficient higher-order analysis, an approach based on the canonical Van Vleck perturbation theory (CVPT), the Watson Hamiltonian and operators of creation and annihilation of vibrational quanta is employed. This method allows analysis of the convergence of perturbation theory and solves a number of theoretical problems of VPT2, e.g., yields anharmonic constants y(ijk), z(ijkl), and allows the reliable evaluation of vibrational IR and Raman anharmonic intensities in the presence of resonances. Darling-Dennison and higher-order resonance coupling coefficients can be reliably evaluated as well. The method is illustrated on classic molecules: water and formaldehyde. A number of theoretical conclusions results, including the necessity of using sextic force field in the fourth order (CVPT4) and the nearly vanishing CVPT4 contributions for bending and wagging modes. The coefficients of perturbative Dunham-type Hamiltonians in high-orders of CVPT are found to conform to the rules of equality at different orders as earlier proven analytically for diatomic molecules. The method can serve as a good substitution of the more traditional VPT2.

  8. Three-nucleon scattering by using chiral perturbation theory potential

    International Nuclear Information System (INIS)

    Kamata, Hiroyuki

    2003-01-01

    Three-nucleon scattering problems are studied by using two-nucleon and three-nucleon potentials derived from chiral perturbation theory. The three-nucleon term is shown to appear in the effective potential of the rank of next-to-next-to-leading order (NNLO). New three-nucleon forces are taken into consideration in addition to the conventional Fujita-Miyazawa (FM) type three-nucleon potential. Two-nucleon potential of the chiral perturbation theory is as precise as the conventional ones in low energy region. The FM type three-nucleon force which explains Sagara discrepancy in high energy region is introduced automatically. Concerning the Ay puzzle, the results seems to behave as if the puzzle has been solved at the level of NLO, but at the NNLO (without three-nucleon force) level the result is similar to the cases of conventional potential indicating the need of three-nucleon force. In contrast to the FM type three-nucleon force, five free parameters exist in the new D and E type three-nucleon forces introduced by the NNLO, but they are reduced to two independent parameters by antisymmetrization, which are found to be sensitive to the coupling energy of tritons and to the nd scattering length (spin doublet state). Parameters determined from them cannot give satisfactory answer to the A y puzzle. It seems, however, too hasty to conclude that A y puzzle cannot be solved by the chiral perturbation theory. (S. Funahashi)

  9. Development of a sensitivity analysis systems in nuclear reactors through generalized perturbation theory at first order in 2 D geometries

    International Nuclear Information System (INIS)

    Garcia, Juan Matias

    2005-01-01

    Perturbation Methods represent a powerful tool to do sensitivity analysis, and they found many aplications in nuclear engineering.As an introduction to this kind of analysis, we develope a program that apply the Generalized Perturbation Theory or GPT Method to bidimensional system of rectangular geometry.We first consider an homogeneous system of non-multiplying material and then an heterogeneous system with region of multiplying material, with the intention of make concret aplications of perturbation method to nuclear engineering problems.The program, that we called Pert, determines neutron fluxes and importance functions applying the Multigroup Diffusion Theory; and also solves the integrals required to calculate sensitivity coefficients.Using this perturbation methods we could verify the low computational cost required to make this kind of analysis and the simplicity of the equations systems involved, allowing us to make elaborates sensitivity analysis for the responses of our interest

  10. Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

    Energy Technology Data Exchange (ETDEWEB)

    Herbert, John M. [Kansas State Univ., Manhattan, KS (United States). Dept. of Chemistry

    1997-01-01

    Rayleigh-Schroedinger perturbation theory is an effective and popular tool for describing low-lying vibrational and rotational states of molecules. This method, in conjunction with ab initio techniques for computation of electronic potential energy surfaces, can be used to calculate first-principles molecular vibrational-rotational energies to successive orders of approximation. Because of mathematical complexities, however, such perturbation calculations are rarely extended beyond the second order of approximation, although recent work by Herbert has provided a formula for the nth-order energy correction. This report extends that work and furnishes the remaining theoretical details (including a general formula for the Rayleigh-Schroedinger expansion coefficients) necessary for calculation of energy corrections to arbitrary order. The commercial computer algebra software Mathematica is employed to perform the prohibitively tedious symbolic manipulations necessary for derivation of generalized energy formulae in terms of universal constants, molecular constants, and quantum numbers. As a pedagogical example, a Hamiltonian operator tailored specifically to diatomic molecules is derived, and the perturbation formulae obtained from this Hamiltonian are evaluated for a number of such molecules. This work provides a foundation for future analyses of polyatomic molecules, since it demonstrates that arbitrary-order perturbation theory can successfully be applied with the aid of commercially available computer algebra software.

  11. The Fubini-Furlan-Rosetti sum rule and related aspects in light of covariant baryon chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Bernard, V. [Universite Louis Pasteur, Laboratoire de Physique Theorique, Strasbourg Cedex 2 (France); Kubis, B. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie), Bonn (Germany); Meissner, U.G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie), Bonn (Germany); Forschungszentrum Juelich, Institut fuer Kernphysik (Theorie), Juelich (Germany)

    2005-09-01

    We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading-order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E{sub 0+}. (orig.)

  12. Time-Sliced Perturbation Theory II: Baryon Acoustic Oscillations and Infrared Resummation

    CERN Document Server

    Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-01-01

    We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.

  13. Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory

    Science.gov (United States)

    Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.

    2015-11-01

    We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

  14. Prospects of using the second-order perturbation theory of the MP2 type in the theory of electron scattering by polyatomic molecules

    Energy Technology Data Exchange (ETDEWEB)

    Čársky, Petr [J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.i.i., Dolejškova 3, 18223 Prague 8 (Czech Republic)

    2015-01-22

    So far the second-order perturbation theory has been only applied to the hydrogen molecule. No application was attempted for another molecule, probably because of technical difficulties of such calculations. The purpose of this contribution is to show that the calculations of this type are now feasible on larger polyatomic molecules even on commonly used computers.

  15. Boson-fermion and boson-boson scattering in a Yang-Mills theory at high energy: Sixth-order perturbation theory

    International Nuclear Information System (INIS)

    McCoy, B.M.; Wu, T.T.

    1976-01-01

    Our previous study of Yang-Mills fields is extended by calculating the high-energy behavior of the boson-fermion and of the boson-boson amplitude in sixth-order perturbation theory. In the isovector and isoscalar channels of both these processes the behavior of the amplitude is the same as that found in fermion-fermion scattering

  16. Application of Homotopy-Perturbation Method to Nonlinear Ozone Decomposition of the Second Order in Aqueous Solutions Equations

    DEFF Research Database (Denmark)

    Ganji, D.D; Miansari, Mo; B, Ganjavi

    2008-01-01

    In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...

  17. A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves

    Science.gov (United States)

    Giner, Emmanuel; Angeli, Celestino; Garniron, Yann; Scemama, Anthony; Malrieu, Jean-Paul

    2017-06-01

    The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the Appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double, and triple bond breaking together with an excited state calculation. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

  18. Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: theory and test calculations of second order approximation.

    Science.gov (United States)

    Chen, Zhenhua; Hoffmann, Mark R

    2012-07-07

    A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4

  19. Applicability of perturbative QCD and NLO power corrections for the pion form factor

    International Nuclear Information System (INIS)

    Yeh Tsungwen

    2002-01-01

    As is well recognized, the asymptotic of the perturbative QCD prediction for the pion form factor is much smaller than the upper end of the data. We investigate this problem. We first evaluate the next-to-leading-order (NLO) power correction for the pion form factor. The corrected form factor contains nonperturbative parameters which are determined from a χ 2 fit to the data. Interpreting these parameters leads to the fact that the involved strong interaction coupling constant should be identified as an effective coupling constant under a nonperturbative QCD vacuum. If the scale associated with the effective coupling constant is identified as 2 Q 2 , then Q 2 , the momentum transfer square for the pion form factor to be measured, can have a value about 1 GeV 2 , and , the averaged momentum fraction variable, can locate around 0.5. This circumstance is consistent with the asymptotic model for the pion wave function

  20. πK scattering in chiral perturbation theory to one loop

    International Nuclear Information System (INIS)

    Bernard, V.; Kaiser, N.; Strasbourg-1 Univ., 67; Meissner, U.G.

    1991-01-01

    We evaluate the πK scattering amplitude at next-to-leading order in the framework of chiral perturbation theory. All low-energy constants appearing in the effective lagrangian of the pseudoscalars have previously been determined. We calculate the scattering lengths of the S- and P-waves as well as the expansion parameters around the point ν triple bond (s-u)/4M K = t = 0 in the unphysical region. Furthermore, phase-shifts of the low partial ways are presented and compared to the data. In most cases, the chiral predictions are comparable to the trends set by the empirical information. For a precise comparison, however, more accurate experimental determinations of the πK scattering process at low and moderate energies would be necessary. We urge the experimenters to perform these. (orig.)

  1. Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

    Science.gov (United States)

    Kurashige, Yuki; Yanai, Takeshi

    2011-09-07

    We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

  2. Some physical properties of GaX (X=P, As and Sb) semiconductor compounds using higher-order perturbation theory

    International Nuclear Information System (INIS)

    Jivani, A.R.; Trivedi, H.J.; Gajjar, P.N.; Jani, A.R.

    2005-01-01

    Recently proposed model potential for describing the electron-ion interaction is employed to calculate total energy, energy band gap at Jones-zone face at X, equation of state and bulk modulus of GaP, GaAs and GaSb compounds using higher-order perturbation theory. The covalent correction term corresponding to third- and fourth-order perturbation energy terms are used to take account of covalent bonding effect in such semiconductors. The significant value of the covalent bonding term shows the essentiality of higher-order correction for zincblende-type crystals. We have employed five different screening functions along with the latest screening function proposed by Sarkar et al. in the present work. The numerical results for the total energy, energy band gap at Jones-zone face and bulk modulus of these compounds are in good agreement with the experimental data and found better than other such theoretical findings. The pressure and bulk modulus at different volumes are obtained by using such higher-order perturbation theory with the application of our model potential. The pressure obtained by this method is compared with pressure obtained by equations proposed by Murnarghan and Vinet et al. The present study also shows that the incorporation of different screening functions generates distinct effects

  3. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    Energy Technology Data Exchange (ETDEWEB)

    Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J [Intelligent System Research Group, Faculty of Electrical and Computer Engineering, Babol, Noushirvani University of Technology, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Department of Mathematics, Mutah University, PO Box 7, Al-Karak (Jordan)], E-mail: h.hoseinnia@stu.nit.ac.ir, E-mail: a.ranjbar@nit.ac.ir, E-mail: shahermm@yahoo.com

    2009-10-15

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  4. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    International Nuclear Information System (INIS)

    Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J; Ranjbar, A; Momani, S

    2009-01-01

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  5. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    Science.gov (United States)

    Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

    2009-10-01

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  6. Prospects of using the second-order perturbation theory of the MP2 type in the theory of electron scattering by polyatomic molecules

    Czech Academy of Sciences Publication Activity Database

    Čársky, Petr

    2015-01-01

    Roč. 191, č. 2015 (2015), s. 191-192 ISSN 1551-7616 R&D Projects: GA MŠk OC09079; GA MŠk(CZ) OC10046; GA ČR GA202/08/0631 Grant - others:COST(XE) CM0805; COST(XE) CM0601 Institutional support: RVO:61388955 Keywords : electron-scattering * calculation of cross sections * second-order perturbation theory Subject RIV: CF - Physical ; Theoretical Chemistry

  7. Adiabaticity and gravity theory independent conservation laws for cosmological perturbations

    Science.gov (United States)

    Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao

    2016-04-01

    We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.

  8. Average gluon and quark jet multiplicities at higher orders

    Energy Technology Data Exchange (ETDEWEB)

    Bolzoni, Paolo; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kotikov, Anatoly V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics

    2013-05-15

    We develop a new formalism for computing and including both the perturbative and nonperturbative QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new method is motivated by recent progress in timelike small-x resummation obtained in the MS factorization scheme. We obtain next-to-next-to-leading-logarithmic (NNLL) resummed expressions, which represent generalizations of previous analytic results. Our expressions depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets that are compatible with regard to the jet algorithms demonstrates by its goodness how our results solve a longstanding problem of QCD. We show that the statistical and theoretical uncertainties both do not exceed 5% for scales above 10 GeV. We finally propose to use the jet multiplicity data as a new way to extract the strong-coupling constant. Including all the available theoretical input within our approach, we obtain {alpha}{sub s}{sup (5)}(M{sub Z})=0.1199{+-}0.0026 in the MS scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of ln(x) terms through the NNLL level and of ln Q{sup 2} terms by the renormalization group, in excellent agreement with the present world average.

  9. Higher-order threshold resummation for semi-inclusive e+e- annihilation

    International Nuclear Information System (INIS)

    Moch, S.; Vogt, A.

    2009-08-01

    The complete soft-enhanced and virtual-gluon contributions are derived for the quark coefficient functions in semi-inclusive e + e - annihilation to the third order in massless perturbative QCD. These terms enable us to extend the soft-gluon resummation for the fragmentation functions by two orders to the next-to-next-to-next-to-leading logarithmic (N 3 LL) accuracy. The resummation exponent is found to be the same as for the structure functions in inclusive deep-inelastic scattering. This finding, together with known results on the higher-order quark form factor, facilitates the determination of all soft and virtual contributions of the fourth-order difference of the coefficient functions for these two processes. Unlike the previous (N 2 LL) order in the exponentiation, the numerical effect of the N 3 LL contributions turns out to be negligible at LEP energies. (orig.)

  10. Effect of the nonlocal exchange on the performance of the orbital-dependent correlation functionals from second-order perturbation theory.

    Science.gov (United States)

    Schweigert, Igor V; Bartlett, Rodney J

    2008-09-28

    Adding a fraction of the nonlocal exchange operator to the local orbital-dependent exchange potential improves the many-body perturbation expansion based on the Kohn-Sham determinant. The effect of such a hybrid scheme on the performance of the orbital-dependent correlation functional from the second-order perturbation theory (PT2H) is investigated numerically. A small fraction of the nonlocal exchange is often sufficient to ensure the existence of the self-consistent solution for the PT2H potential. In the He and Be atoms, including 37% of the nonlocal exchange leads to the correlation energies and electronic densities that are very close to the exact ones. In molecules, varying the fraction of the nonlocal exchange may result in the PT2H energy closely reproducing the CCSD(T) value; however such a fraction depends on the system and does not always result in an accurate electronic density. We also numerically verify that the "semicanonical" perturbation series includes most of the beneficial effects of the nonlocal exchange without sacrificing the locality of the exchange potential.

  11. H+H- interaction up to higher orders of perturbation theory in the model with two Higgs doublets (self-energy and vertex diagrams)

    International Nuclear Information System (INIS)

    Dvoeglazov, V.V.; Skachkov, N.B.

    1991-01-01

    Self-energy and vertex blocks that enter into the amplitude of Higgs-Higgs-interaction are calculated up to the fourth order of perturbation theory in the framework of the model of electroweak interaction with two Higgs doublets and an arbitrary number of fermions. The renormalization is performed on the mass shell of the physical fields after a spontaneous symmetry breaking. The values of the coupling constants are, as a rule, not concretized in the paper. In the cases where it is needed to use them, their values obtained in the model with the minimal supersymmetric extension of the standard model (MSSM) are taken. 29 refs.; 1 tab

  12. Single hadron spectrum in γγ collisions: The QCD contribution to order αsub(s) and the non perturbative background

    International Nuclear Information System (INIS)

    Aurenche, P.; Douiri, A.; Baier, R.; Fontannaz, M.; Schiff, D.

    1985-01-01

    We calculate the corrections of order αsub(s) to the process γγ->HX where both initial photons are real. The analytic expressions are given and a detailed discussion of the variation of the corrections with psub(T) and rapidity is presented. The dependence on the factorization prescription and scale is also discussed. Using the equivalent photon approximation the cross-section for e + e - ->e + e - HX is calculated both in the PEP/PETRA and LEP energy range. Based on the vector meson dominance model the non perturbative background is estimated and its importance for present and future experiments is emphasized. (orig.)

  13. Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe(Astrophysics and Cosmology)

    OpenAIRE

    Ryuichi, TAKAHASHI; Department of Physics and Astrophysics, Nagoya University

    2008-01-01

    We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in a quasi-nonlinear regime (k≈0.1h/Mpc). Analytical solutions and simple fitting formulae are presented for the dark-energy model with the general time-varying equation of state w(a). It turns out that the power spectrum coincides with the approximate res...

  14. Large order asymptotics and convergent perturbation theory for critical indices of the φ4 model in 4 - ε expansion

    International Nuclear Information System (INIS)

    Honkonen, J.; Komarova, M.; Nalimov, M.

    2002-01-01

    Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the φ 4 (4 - ε) theory is discussed. Well-known results of the asymptotic 4 - ε expansion of critical indices are shown to be far from the large order asymptotic value. A convergent series for the model φ 4 (4 - ε) is then considered. Radius of convergence of the series for Green functions and for renormalisation group functions is studied. The results of the convergent expansion of critical indices in the 4 - ε scheme are revalued using the knowledge of large order asymptotics. Specific features of this procedure are discussed (Authors)

  15. Neutral pion electroproduction off light nuclei in chiral perturbation theory

    International Nuclear Information System (INIS)

    Lenkewitz, Mark

    2013-01-01

    Threshold pion electroproduction on tri-nucleon systems is investigated in the framework of baryon Chiral Perturbation Theory (ChPT) at next-to-leading one-loop order O(q 4 ) in the chiral expansion. To this order in small momenta, the production operator is a sum of one- and two-nucleon terms. While the one-nucleon terms resemble the impulse approximation, the two-nucleon contributions represent corrections due to the relevant nuclear interactions, e.g. pion-exchange interactions, which prove to be dominant, and due to recoil effects of the participating nucleons, which appear to be negligible. We calculate the expectation value of the production operator using chiral wave functions in a three-dimensional approach without partial wave expansion. The resulting integrals are evaluated using adaptive Monte Carlo integration, the VEGAS algorithm of Lepage. We obtain results for the threshold production multipoles E 0+ and L 0+ on 3 He and 3 H and comment on the sensitivity to the fundamental neutron amplitude E 0+ π 0 n . 3 He appears to be a particularly promising target to extract information about the neutron amplitude. This idea is usually invoked for spin-dependent quantities since the 3 He wave function is strongly dominated by the principal S-state component which suggests that its spin is largely driven by the one of the neutron.

  16. Generalized polarizabilities of the nucleon in baryon chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Lensky, Vadim [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany); Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Pascalutsa, Vladimir; Vanderhaeghen, Marc [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany)

    2017-02-15

    The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung (ep → epγ) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (BχPT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well known from elsewhere. Within the relatively large uncertainties of our calculation we find good agreement with the experimental observations of VCS and the empirical extractions of the GPs. We find large discrepancies with previous chiral calculations - all done in heavy-baryon χPT (HBχPT) - and discuss the differences between BχPT and HBχPT responsible for these discrepancies. (orig.)

  17. Remark on the higher order perturbative studies of flavor breaking in the standard SU(3) skyrmion quantum mechanics

    International Nuclear Information System (INIS)

    Li Jinping; Yan Mulin

    1997-01-01

    A quantitative criterion is proposed for testing the rationality of an effective QCD baryon theory. The higher order corrections of the standard SU(3) Skyrme model to the Gell-Mann-Okubo relations for baryons are studied according to the criterion, and some interesting results are presented. A possible prescription is recommended

  18. B-meson spectroscopy in HQET at order 1/m

    International Nuclear Information System (INIS)

    Bernardoni, Fabio; Fritsch, Patrick; Univ. Autonoma de Madrid; Gerardin, Antoine; Univ. Blaise Pascal CNRS/IN2P3, Aubiere; Heitger, Jochen; Hippel, Georg von; Simma, Hubert

    2015-05-01

    We present a study of the B spectrum performed in the framework of Heavy Quark Effective Theory expanded to next-to-leading order in 1/m b and non-perturbative in the strong coupling. Our analyses have been performed on N f =2 lattice gauge field ensembles corresponding to three different lattice spacings and a wide range of pion masses. We obtain the B s -meson mass and hyperfine splittings of the B- and B s -mesons that are in good agreement with the experimental values and examine the mass difference m B s -m B as a further cross-check of our previous estimate of the b-quark mass. We also report on the mass splitting between the first excited state and the ground state in the B and B s systems.

  19. Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA

    Energy Technology Data Exchange (ETDEWEB)

    Alioli, Simone; Bauer, Christian W.; Berggren, Calvin; Vermilion, Christopher K.; Walsh, Jonathan R.; Zuberi, Saba [California Univ., Berkeley, CA (United States). Ernest Orlando Lawrence Berkeley National Laboratory; Hornig, Andrew [Washington Univ., Seattle, WA (United States). Dept. of Physics; Tackmann, Frank J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie

    2012-11-15

    We extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in {alpha}{sub s} at both small and large jet resolutions, which has not been achieved so far. This requires the combination of the higher-order resummation of large Sudakov logarithms at small values of the jet resolution variable with the full next-to-leading order (NLO) matrix-element corrections at large values. As a by-product, this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. In this paper, we focus on the general construction of our method and discuss its application to e{sup +}e{sup -} and pp collisions. We present first results of the implementation in the GENEVA Monte Carlo framework. We employ N-jettiness as the jet resolution variable, combining its next-to-next-to-leading logarithmic resummation with fully exclusive NLO matrix elements, and PYTHIA 8 as the backend for further parton showering and hadronization. For hadronic collisions, we take Drell-Yan production as an example to apply our construction. For e{sup +}e{sup -} {yields} jets, taking {alpha}{sub s}(m{sub Z}) = 0.1135 from fits to LEP thrust data, together with the PYTHIA 8 hadronization model, we obtain good agreement with LEP data for a variety of 2-jet observables.

  20. Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme

    DEFF Research Database (Denmark)

    Kristensen, Kasper; Jørgensen, Poul; Jansik, Branislav

    2012-01-01

    We demonstrate that the divide-expand-consolidate (DEC) scheme – which has previously been used to determine the second-order Møller–Plesset (MP2) correlation energy – can be applied to evaluate the MP2 molecular gradient in a linear-scaling and embarrassingly parallel manner using a set of local......-box manner to ensure that the error in the DEC-MP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT). The FOT also implicitly controls the error in the DEC-MP2 molecular gradient as substantiated...... by a theoretical analysis and numerical results. The development of the DEC-MP2 molecular gradient is the initial step towards calculating higher order energy derivatives for large molecular systems using the DEC framework, both at the MP2 level of theory and for more accurate coupled-cluster methods....

  1. Nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems

    International Nuclear Information System (INIS)

    Afuwape, A.U.; Omari, P.

    1987-11-01

    This paper deals with the solvability of the nonlinear operator equations in normed spaces Lx=EGx+f, where L is a linear map with possible nontrivial kernel. Applications are given to the existence of periodic solutions for the third order scalar differential equation x'''+ax''+bx'+cx+g(t,x)=p(t), under various conditions on the interaction of g(t,x)/x with spectral configurations of a, b and c. (author). 48 refs

  2. Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

    Energy Technology Data Exchange (ETDEWEB)

    Yao, De-Liang [Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics,Forschungszentrum Jülich, D-52425 Jülich (Germany); Siemens, D. [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Bernard, V. [Groupe de Physique Théorique, Institut de Physique Nucléaire, UMR 8606,CNRS, University Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex (France); Epelbaum, E. [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Gasparyan, A.M. [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); SSC RF ITEP, Bolshaya Cheremushkinskaya 25, 117218 Moscow (Russian Federation); Gegelia, J. [Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics,Forschungszentrum Jülich, D-52425 Jülich (Germany); Tbilisi State University, 0186 Tbilisi (Georgia); Krebs, H. [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Meißner, Ulf-G. [Helmholtz Institut für Strahlen- und Kernphysik andBethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany); Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics,Forschungszentrum Jülich, D-52425 Jülich (Germany)

    2016-05-05

    We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S- and P-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

  3. Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling-Dennison resonance coefficients using the canonical Van Vleck perturbation theory

    International Nuclear Information System (INIS)

    Krasnoshchekov, Sergey V.; Isayeva, Elena V.; Stepanov, Nikolay F.

    2014-01-01

    The second-order vibrational Hamiltonian of a semi-rigid polyatomic molecule when resonances are present can be reduced to a quasi-diagonal form using second-order vibrational perturbation theory. Obtaining exact vibrational energy levels requires subsequent numerical diagonalization of the Hamiltonian matrix including the first- and second-order resonance coupling coefficients. While the first-order Fermi resonance constants can be easily calculated, the evaluation of the second-order Darling-Dennison constants requires more complicated algebra for seven individual cases with different numbers of creation-annihilation vibrational quanta. The difficulty in precise evaluation of the Darling-Dennison coefficients is associated with the previously unrecognized interference with simultaneously present Fermi resonances that affect the form of the canonically transformed Hamiltonian. For the first time, we have presented the correct form of the general expression for the evaluation of the Darling-Dennison constants that accounts for the underlying effect of Fermi resonances. The physically meaningful criteria for selecting both Fermi and Darling-Dennison resonances are discussed and illustrated using numerical examples

  4. Higher-order radiative corrections for b b ¯→H-W+

    Science.gov (United States)

    Kidonakis, Nikolaos

    2018-02-01

    I present higher-order radiative corrections from collinear and soft-gluon emission for the associated production of a charged Higgs boson with a W boson. The calculation uses expressions from resummation at next-to-leading-logarithm accuracy. From the resummed cross section I derive analytical formulas at approximate next-to-next-to-leading order and next-to-next-to-next-to-leading order. Total cross sections are presented for the process b b ¯→H-W+ at various LHC energies. The transverse momentum and rapidity distributions of the charged Higgs boson are also calculated.

  5. A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

    Science.gov (United States)

    Hong, Youngjoon; Nicholls, David P.

    2017-09-01

    The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

  6. Perturbative corrections to Λ_b→Λ form factors from QCD light-cone sum rules

    International Nuclear Information System (INIS)

    Wang, Yu-Ming; Shen, Yue-Long

    2016-01-01

    We compute radiative corrections to Λ_b→Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ_b-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ_b-baryon correlation function is justified at leading power in Λ/m_b, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-B-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at O(α_s) shift the Λ_b→Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ_b→Λ from factors we further investigate several decay observables in the electro-weak penguin Λ_b→Λ ℓ"+ℓ"− transitions in the factorization limit (i.e., ignoring the “non-factorizable' hadronic effects which cannot be expressed in terms of the Λ_b→Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.

  7. Status of perturbative QCD

    International Nuclear Information System (INIS)

    Collins, J.C.

    1985-01-01

    Progress in quantum chromodynamics in the past year is reviewed in these specific areas: proof of factorization for hadron-hadron collisions, fast calculation of higher order graphs, perturbative Monte Carlo calculations for hadron-hadron scattering, applicability of perturbative methods to heavy quark production, and understanding of the small-x problem. 22 refs

  8. Linear perturbation of spherically symmetric flows: a first-order upwind scheme for the gas dynamics equations in Lagrangian coordinates; Perturbation lineaire d'ecoulements a symetrie spherique: schema decentre d'ordre 1 pour les equations de la dynamique des gaz en variables de Lagrange

    Energy Technology Data Exchange (ETDEWEB)

    Clarisse, J.M

    2007-07-01

    A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)

  9. HQET at order 1/m. Pt. 3. Decay constants in the quenched approximation

    Energy Technology Data Exchange (ETDEWEB)

    Blossier, Benoit [CNRS et Paris-Sud XI Univ., Orsay (France). Lab. de Physique Theorique; Della Morte, Michele [Mainz Univ. (Germany). Inst. fuer Kernphysik; Garron, Nicolas [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica e Inst. de Fisica Teorica IFT-UAM/CSIC; Edinburgh Univ. (United Kingdom). SUPA, School of Physics; Hippel, Georg von [Mainz Univ. (Germany). Inst. fuer Kernphysik; DESY, Zeuthen (Germany). NIC; Mendes, Tereza [DESY, Zeuthen (Germany). NIC; Sao Paulo Univ., Sao Carlos (Brazil). IFSC; Simma, Hubert; Sommer, Rainer [DESY, Zeuthen (Germany). NIC

    2010-06-15

    We report on the computation of the B{sub s} meson decay constant in Heavy Quark Effective Theory on the lattice. The next to leading order corrections in the HQET expansion are included non-perturbatively. We estimate higher order contributions to be very small. The results are extrapolated to the continuum limit, the main systematic error affecting the computation is therefore the quenched approximation used here. The Generalized Eigenvalue Problem and the use of all-to-all propagators are important technical ingredients of our approach that allow to keep statistical and systematic errors under control. We also report on the decay constant f{sub B{sub s}{sup '}} of the first radially excited state in the B{sub s} sector, computed in the static limit. (orig.)

  10. HQET at order 1/m. Pt. 3. Decay constants in the quenched approximation

    International Nuclear Information System (INIS)

    Blossier, Benoit; Della Morte, Michele; Garron, Nicolas; Edinburgh Univ.; Hippel, Georg von; DESY, Zeuthen; Mendes, Tereza; Sao Paulo Univ., Sao Carlos; Simma, Hubert; Sommer, Rainer

    2010-06-01

    We report on the computation of the B s meson decay constant in Heavy Quark Effective Theory on the lattice. The next to leading order corrections in the HQET expansion are included non-perturbatively. We estimate higher order contributions to be very small. The results are extrapolated to the continuum limit, the main systematic error affecting the computation is therefore the quenched approximation used here. The Generalized Eigenvalue Problem and the use of all-to-all propagators are important technical ingredients of our approach that allow to keep statistical and systematic errors under control. We also report on the decay constant f B s ' of the first radially excited state in the B s sector, computed in the static limit. (orig.)

  11. Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals

    International Nuclear Information System (INIS)

    Loibl, Stefan; Schütz, Martin

    2014-01-01

    In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation

  12. Oxygen ordering in the high-T$_c$ superconductor HgBa$_2$CaCu$_2$O$_{6+\\delta}$ as revealed by perturbed angular correlation

    CERN Document Server

    Mendonca, Tania Melo; Haas, Heinz; Odier, Philippe; Tavares, Pedro; Silva, Manuel Ribeiro; Lopes, Armandina; Pereira, Andre; Goncalves, Joao Nuno; Amaral, Joao; Darie, Celine; Araujo, Joao Pedro

    2011-01-01

    Lattice sites and collective ordering of oxygen atoms in HgBa$_2$CaCu$_2$O$_{6+\\delta}$ were studied using the perturbed angular correlation (PAC) technique at ISOLDE/CERN. The electric field gradients (EFG) at $^{199m}$Hg nuclei have been measured as functions of oxygen doping on the Hg planes, above and below T$_c$. In comparison with the results obtained for oxygen and fluorine doping in Hg-1201, the analysis shows a different oxygen ordering exhibited by Hg-1212. Moreover, for all studied cases, the experimental results show that at a local scale there is non-uniform oxygen distribution. A series of ab initio EFG calculations allowed to infer that at low concentrations, regions without oxygen coexist with regions where O$_{2\\delta}$ dumbbell molecules are located at the center of the Hg mesh. On the other side, at high concentrations, O$_{2\\delta}$ dumbbell molecules coexist with single O$_\\delta$ atoms occupying the center of the Hg mesh. The present results suggest that oxygen sits on the Hg planes in t...

  13. Factorization of exclusive processes in perturbative quantum-chromodynamics

    International Nuclear Information System (INIS)

    Segond, M.

    2007-12-01

    The work carried out in this thesis presents various theoretical and phenomenological studies of the exclusive production of longitudinally polarized neutral vector rho mesons in virtual photons collisions, within the framework of quantum-chromodynamics (QCD). The virtuality of the photons makes it possible to locate our approach in the perturbative area of the theory. The kinematical regimes considered allow the use of varied theoretical tools which reveal various properties of factorization of the scattering amplitude: two types of collinear factorization (at short distance) for this process are discussed in chapter 1, revealing - according to the polarization of the virtual photons and the kinematical limit considered- Generalized Distribution Amplitudes (GDA) or Transition Distribution Amplitudes (TDA), tools commonly used in the description of exclusive processes. We introduce into the Chapter 2 in a self-consistent way, the foundations of the BFKL (Balitskii, Fadin, Kuraev and Lipatov) formalism valid within the high energy limit (Regge limit) of QCD, for its phenomenological use detailed in Chapter 3: the scattering amplitude of the process is described in this formalism by exploiting the factorization in the two-dimensional transverse momentum space, or kT-factorization. We predict the value of the cross section of the process at Born order of the BFKL resummation and we discuss its possible observation at the future international linear collider (ILC). We consider also the differential cross sections of the process without momentum transfer with complete BFKL evolution at the order of the leading logarithms (Leading-Order) and also at the Next-to-Leading-Order to establish a fine test of this process with hard BFKL Pomeron exchange, observable at the future ILC. (author)

  14. Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT) and perturbation method

    Science.gov (United States)

    Khoshgoftar, M. J.; Mirzaali, M. J.; Rahimi, G. H.

    2015-11-01

    Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

  15. Perturbative and constructive renormalization

    International Nuclear Information System (INIS)

    Veiga, P.A. Faria da

    2000-01-01

    These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)

  16. Field transformations and the classical equation of motion in chiral perturbation theory

    International Nuclear Information System (INIS)

    Scherer, S.; Fearing, H.W.

    1995-01-01

    The construction of effective Lagrangians commonly involves the application of the ''classical equation of motion'' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory with particular emphasis on the new features which appear at O(p 6 ). The use of the ''classical equation of motion'' is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations leads to a modification of the coefficients of higher-order terms as well as eliminating structures, or what is equivalent, expressing certain structures in terms of already known different structures. This will become relevant once one considers the problem of expressing in canonical form a model effective interaction containing terms beyond next-to-leading order, i.e., beyond O(p 4 ). In such circumstances the naive application of the clasical equation of motion to simply drop terms, as is commonly done at lowest order, leads to subtle errors, which we discuss

  17. Non-perturbative Debye mass in finite-T QCD

    CERN Document Server

    Kajantie, Keijo; Peisa, J; Rajantie, A; Rummukainen, K; Shaposhnikov, Mikhail E

    1997-01-01

    Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD.

  18. Cosmological perturbation theory and quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)

    2016-08-04

    It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.

  19. Perturbative anyon gas

    International Nuclear Information System (INIS)

    Dasnieres de Veigy, A.; Ouvry, S.; Paris-6 Univ., 75

    1992-06-01

    The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant α is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a 3 , a 4 , a 5 and a 6 are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs

  20. Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach

    International Nuclear Information System (INIS)

    Del Ben, Mauro; Hutter, Jürg; VandeVondele, Joost

    2015-01-01

    The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU’s) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH 3 , CO 2 , formic acid, and benzene

  1. Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach

    Science.gov (United States)

    Del Ben, Mauro; Hutter, Jürg; VandeVondele, Joost

    2015-09-01

    The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU's) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH3, CO2, formic acid, and benzene.

  2. Perturbative corrections to Λ{sub b}→Λ form factors from QCD light-cone sum rules

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yu-Ming [Fakultät für Physik, Universität Wien,Boltzmanngasse 5, 1090 Vienna (Austria); Physik Department T31, Technische Universität München,James-Franck-Straße 1, D-85748 Garching (Germany); Shen, Yue-Long [College of Information Science and Engineering, Ocean University of China,Songling Road 238, Qingdao, Shandong 266100 (China)

    2016-02-29

    We compute radiative corrections to Λ{sub b}→Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ{sub b}-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ{sub b}-baryon correlation function is justified at leading power in Λ/m{sub b}, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-B-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at O(α{sub s}) shift the Λ{sub b}→Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ{sub b}→Λ from factors we further investigate several decay observables in the electro-weak penguin Λ{sub b}→Λ ℓ{sup +}ℓ{sup −} transitions in the factorization limit (i.e., ignoring the “non-factorizable' hadronic effects which cannot be expressed in terms of the Λ{sub b}→Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.

  3. Properties of three-body decay functions derived with time-like jet calculus beyond leading order

    International Nuclear Information System (INIS)

    Sugiura, Tetsuya

    2002-01-01

    Three-body decay functions in time-like parton branching are calculated using the jet calculus to the next-to-leading logarithmic (NLL) order in perturbative quantum chromodynamics (QCD). The phase space contributions from each of the ladder diagrams and interference diagrams are presented. We correct part of the results for the three-body decay functions calculated previously by two groups. Employing our new results, the properties of the three-body decay functions in the regions of soft partons are examined numerically. Furthermore, we examine the contribution of the three-body decay functions modified by the restriction resulting from the kinematical boundary of the phase space for two-body decay in the parton shower model. This restriction leads to some problems for the parton shower model. For this reason, we propose a new restriction introduced by the kinematical boundary of the phase space for two-body decay. (author)

  4. Traffic Perturbation

    CERN Multimedia

    C. Colloca TS/FM

    2004-01-01

    TS/FM group informs you that, for the progress of the works at the Prévessin site entrance, some perturbation of the traffic may occur during the week between the 14th and 18th of June for a short duration. Access will be assured at any time. For more information, please contact 160239. C. Colloca TS/FM

  5. Perturbative and non-perturbative approaches to string sigma-models in AdS/CFT

    Energy Technology Data Exchange (ETDEWEB)

    Vescovi, Edoardo

    2016-10-05

    This thesis discusses quantum aspects of type II superstring theories in AdS{sub 5} x S{sup 5} and AdS{sub 4} x CP{sup 3} backgrounds relevant for the AdS/CFT correspondence, using perturbative methods at large string tension and lattice field theory techniques inspired by a work of Roiban and McKeown. We review the construction of the supercoset sigma-model for strings in the AdS{sub 5} x S{sup 5} background, whereas the general quantum dynamics of the superstring in AdS{sub 4} x CP{sup 3} is described by a double dimensional reduction of the supermembrane action in AdS{sub 4} x S{sup 7}. We present a manifestly covariant formalism for semiclassical quantization of strings around arbitrary minimal-area surfaces in AdS{sub 5} x S{sup 5}, expressing the fluctuation operators in terms of intrinsic and extrinsic invariants of the background geometry. We exactly solve the spectral problem for a fourth-order generalization of the Lame differential equation with doubly periodic coefficients in a complex variable. This calculates the one-loop energy of the (J{sub 1},J{sub 2})-string in the SU(2) sector in the limit described by a quantum Landau-Lifshitz model and the bosonic contribution to the energy of the (S,J)-string rotating in AdS{sub 5} and S{sup 5}. Similar techniques calculate the 1/4-BPS latitude Wilson loops in N=4 SYM theory at one loop, normalized to the 1/2-BPS circular loop. Our regularization scheme reproduces the next-to-leading order predicted by supersymmetric localization, up to a remainder function that we discuss upon. We also study the AdS{sub 4} x CP{sup 3} string action expanded around the null cusp background and compute the cusp anomaly up to two loops. This agrees with an all-loop conjectured expression of the ABJM interpolating function. We finally discretize the AdS{sub 5} x S{sup 5} superstring theory in the AdS light-cone gauge and perform lattice simulations at finite coupling with a Monte Carlo algorithm. We measure the string action

  6. Non-perturbative versus perturbative renormalization of lattice operators

    International Nuclear Information System (INIS)

    Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.

    1995-09-01

    Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)

  7. Equivalence between the Arquès-Walsh sequence formula and the number of connected Feynman diagrams for every perturbation order in the fermionic many-body problem

    Science.gov (United States)

    Castro, E.

    2018-02-01

    From the perturbative expansion of the exact Green function, an exact counting formula is derived to determine the number of different types of connected Feynman diagrams. This formula coincides with the Arquès-Walsh sequence formula in the rooted map theory, supporting the topological connection between Feynman diagrams and rooted maps. A classificatory summing-terms approach is used, in connection to discrete mathematical theory.

  8. Penguin-dominated B→PV decays in NLO perturbative QCD

    International Nuclear Information System (INIS)

    Li Hsiangnan; Mishima, Satoshi

    2006-01-01

    We study the penguin-dominated B→PV decays, with P (V) representing a pseudoscalar (vector) meson, in the next-to-leading-order (NLO) perturbative QCD (PQCD) formalism, concentrating on the B→Kφ, πK*, ρK, and ωK modes. It is found that the NLO corrections dramatically enhance the B→ρK, ωK branching ratios, which were estimated to be small under the naive factorization assumption. The patterns of the direct CP asymmetries A CP (B 0 →ρ ± K ± )≅A CP (B ± →ρ 0 K ± ) and A CP (B 0 →π ± K* ± )>A CP (B ± →π 0 K* ± ) are predicted, differing from A CP (B 0 →π ± K ± )>>A CP (B ± →π 0 K ± ). The above patterns, if confirmed by data, will support the source of strong phases from the scalar penguin annihilation in PQCD. The results for the mixing-induced CP asymmetries S f are consistent with those obtained in the literature, except that our S ρ 0 K S is as low as 0.5

  9. Perturbed effects at radiation physics

    International Nuclear Information System (INIS)

    Külahcı, Fatih; Şen, Zekâi

    2013-01-01

    Perturbation methodology is applied in order to assess the linear attenuation coefficient, mass attenuation coefficient and cross-section behavior with random components in the basic variables such as the radiation amounts frequently used in the radiation physics and chemistry. Additionally, layer attenuation coefficient (LAC) and perturbed LAC (PLAC) are proposed for different contact materials. Perturbation methodology provides opportunity to obtain results with random deviations from the average behavior of each variable that enters the whole mathematical expression. The basic photon intensity variation expression as the inverse exponential power law (as Beer–Lambert's law) is adopted for perturbation method exposition. Perturbed results are presented not only in terms of the mean but additionally the standard deviation and the correlation coefficients. Such perturbation expressions provide one to assess small random variability in basic variables. - Highlights: • Perturbation methodology is applied to Radiation Physics. • Layer attenuation coefficient (LAC) and perturbed LAC are proposed for contact materials. • Perturbed linear attenuation coefficient is proposed. • Perturbed mass attenuation coefficient (PMAC) is proposed. • Perturbed cross-section is proposed

  10. Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering

    Science.gov (United States)

    Blümlein, Johannes; DeFreitas, Abilio; Schneider, Carsten

    2015-04-01

    The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities Q2. We also describe a series of mathematical, computer-algebraic and combinatorial methods and special function spaces, needed to perform these calculations. Finally, we briefly discuss the status of measuring αs (MZ), the charm quark mass mc, and the parton distribution functions at next-to-next-to-leading order from the world precision data on deep-inelastic scattering.

  11. Higher order heavy quark corrections to deep-inelastic scattering

    International Nuclear Information System (INIS)

    Bluemlein, J.; Freitas, A. de; Johannes Kepler Univ., Linz; Schneider, C.

    2014-11-01

    The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities Q 2 . We also describe a series of mathematical, computer-algebraic and combinatorial methods and special function spaces, needed to perform these calculations. Finally, we briefly discuss the status of measuring α s (M Z ), the charm quark mass m c , and the parton distribution functions at next-to-next-to-leading order from the world precision data on deep-inelastic scattering.

  12. Divergent Perturbation Series

    International Nuclear Information System (INIS)

    Suslov, I.M.

    2005-01-01

    Various perturbation series are factorially divergent. The behavior of their high-order terms can be determined by Lipatov's method, which involves the use of instanton configurations of appropriate functional integrals. When the Lipatov asymptotic form is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series, which can be resummed to solve various strong-coupling problems in a certain approximation. This approach is demonstrated by determining the Gell-Mann-Low functions in φ 4 theory, QED, and QCD with arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic form are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described both for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. Higher order corrections to the Lipatov asymptotic form are discussed

  13. Instantaneous stochastic perturbation theory

    International Nuclear Information System (INIS)

    Lüscher, Martin

    2015-01-01

    A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.

  14. Lattice QCD at the physical point meets S U (2 ) chiral perturbation theory

    Science.gov (United States)

    Dürr, Stephan; Fodor, Zoltán; Hoelbling, Christian; Krieg, Stefan; Kurth, Thorsten; Lellouch, Laurent; Lippert, Thomas; Malak, Rehan; Métivet, Thibaut; Portelli, Antonin; Sastre, Alfonso; Szabó, Kálmán; Budapest-Marseille-Wuppertal Collaboration

    2014-12-01

    We perform a detailed, fully correlated study of the chiral behavior of the pion mass and decay constant, based on 2 +1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O (a )-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of S U (2 ) chiral perturbation theory (χ PT ) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of next-to-leading order (NLO) S U (2 ) χ PT in two different expansions: the first in quark mass (x expansion), and the second in pion mass (ξ expansion). We find that these expansions begin showing signs of failure for Mπ≳300 MeV , for the typical percent-level precision of our Nf=2 +1 lattice results. We further determine the LO low energy constants (LECs), F =88.0 ±1.3 ±0.2 and BMS ¯(2 GeV )=2.61 (6 )(1 ) GeV , and the related quark condensate, ΣMS ¯(2 GeV )=(272 ±4 ±1 MeV )3 , as well as the NLO ones, ℓ¯3=2.6 (5 )(3 ) and ℓ¯4=3.7 (4 )(2 ), with fully controlled uncertainties. We also explore the next-to-next-to-leading order (NNLO) expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.

  15. Chiral perturbation theory

    International Nuclear Information System (INIS)

    Ecker, G.

    1996-06-01

    After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering. (author)

  16. The angular ordering in soft-gluon emission

    International Nuclear Information System (INIS)

    Tesima, K.

    1987-01-01

    The way to evaluate multi-parton cross-sections systematically is discussed. In the leading-double-log approximation in QCD, the successive emission of soft gluons is at successively smaller angles. The angular ordering, however, is violated in the next-to-leading order

  17. Nonperturbative perturbation theory

    International Nuclear Information System (INIS)

    Bender, C.M.

    1989-01-01

    In this talk we describe a recently proposed graphical perturbative calculational scheme for quantum field theory. The basic idea is to expand in the power of the interaction term. For example, to solve a λφ 4 theory in d-dimensional space-time, we introduce a small parameter δ and consider a λ(φ 2 ) 1+δ field theory. We show how to expand such a theory as a series in powers of δ. The resulting perturbation series appears to have a finite radius of convergence and numerical results for low-dimensional models are good. We have computed the two-point and four-point Green's functions to second order in powers of δ and the 2n-point Green's functions (n>2) to order δ. We explain how to renormalize the theory and show that, to first order in powers of δ, when δ>0 and d≥4 the theory is free. This conclusion remains valid to second order in powers of δ, and we believe that it remains valid to all orders in powers of δ. The new perturbative scheme is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

  18. Threshold resummation and higher order effects in QCD

    International Nuclear Information System (INIS)

    Ringer, Felix Maximilian

    2015-01-01

    Quantum chromodynamics (QCD) is a quantum field theory that describes the strong interactions between quarks and gluons, the building blocks of all hadrons. Thanks to the experimental progress over the past decades, there has been an ever-growing need for QCD precision calculations for scattering processes involving hadrons. For processes at large momentum transfer, perturbative QCD offers a systematic approach for obtaining precise predictions. This approach relies on two key concepts: the asymptotic freedom of QCD and factorization. In a perturbative calculation at higher orders, the infrared cancellation between virtual and real emission diagrams generally leaves behind logarithmic contributions. In many observables relevant for hadronic scattering these logarithms are associated with a kinematic threshold and are hence known as ''threshold logarithms''. They become large when the available phase space for real gluon emission shrinks. In order to obtain a reliable prediction from QCD, the threshold logarithms need to be taken into account to all orders in the strong coupling constant, a procedure known as ''threshold resummation''. The main focus of my PhD thesis is on studies of QCD threshold resummation effects beyond the next-to-leading logarithmic order. Here we primarily consider the production of hadron pairs in hadronic collisions as an example. In addition, we also consider hadronic jet production, which is particularly interesting for the phenomenology at the LHC. For both processes, we fully take into account the non-trivial QCD color structure of the underlying partonic hard- scattering cross sections. We find that threshold resummation leads to sizable numerical effects in the kinematic regimes relevant for comparisons to experimental data.

  19. Preheating curvaton perturbations

    International Nuclear Information System (INIS)

    Bastero-Gil, M.; Di Clemente, V.; King, S.F.

    2005-01-01

    We discuss the potentially important role played by preheating in certain variants of the curvaton mechanism in which isocurvature perturbations of a D-flat (and F-flat) direction become converted to curvature perturbations during reheating. We discover that parametric resonance of the isocurvature components amplifies the superhorizon fluctuations by a significant amount. As an example of these effects we develop a particle physics motivated model which involves hybrid inflation with the waterfall field N being responsible for generating the μ term, the right-handed neutrino mass scale, and the Peccei-Quinn symmetry breaking scale. The role of the curvaton field can be played either by usual Higgs field, or the lightest right-handed sneutrino. Our new results show that it is possible to achieve the correct curvature perturbations for initial values of the curvaton fields of order the weak scale. In this model we show that the prediction for the spectral index of the final curvature perturbation only depends on the mass of the curvaton during inflation, where consistency with current observational data requires the ratio of this mass to the Hubble constant to be 0.3

  20. Scalar cosmological perturbations

    International Nuclear Information System (INIS)

    Uggla, Claes; Wainwright, John

    2012-01-01

    Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly introducing a timelike reference congruence. The common ground is the use of gauge invariants derived from the metric tensor, the stress-energy tensor, or from vectors associated with a reference congruence, as basic variables. Although there is a complication in that there is no unique choice of gauge invariants, we will show that this can be used to advantage. With this in mind our first goal is to present an efficient way of constructing dimensionless gauge invariants associated with the tensors that are involved, and of determining their inter-relationships. Our second goal is to give a unified treatment of the various ways of writing the governing equations in dimensionless form using gauge-invariant variables, showing how simplicity can be achieved by a suitable choice of variables and normalization factors. Our third goal is to elucidate the connection between the metric-based approach and the so-called 1 + 3 gauge-invariant approach to cosmological perturbations. We restrict our considerations to linear perturbations, but our intent is to set the stage for the extension to second-order perturbations. (paper)

  1. Supersingular quantum perturbations

    International Nuclear Information System (INIS)

    Detwiler, L.C.; Klauder, J.R.

    1975-01-01

    A perturbation potential is called supersingular whenever generally every matrix element of the perturbation in the unperturbed eigenstates is infinite. It follows that supersingular perturbations do not have conventional perturbation expansions, say for energy eigenvalues. By invoking variational arguments, we determine the asymptotic behavior of the energy eigenvalues for asymptotically small values of the coupling constant of the supersingular perturbation

  2. Scrutinizing the top quark at lepton colliders with higher orders. From fixed order to resummation and matching

    Energy Technology Data Exchange (ETDEWEB)

    Nejad, Bijan Chokoufe

    2017-07-12

    In this thesis, we present detailed studies of top-pair production with (t anti tH) and without association of a Higgs boson (t anti t) in e{sup +}e{sup -} collisions. These processes are of utmost interest for the top physics program of future lepton colliders. They allow in particular a precise measurement of the top quark mass and the Yukawa coupling. For this purpose, we present predictions for off-shell t anti t and t anti tH production including non-resonant and interference contributions up to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD). This allows for top-quark phenomenology in the continuum at an unprecedented level of accuracy. We show that off-shell effects and NLO QCD corrections for these processes do not factorize in general. In particular, we present the Yukawa coupling dependence of the cross section, which receives negative corrections due to sizable interference terms. We also add a discussion of p{sub T} resummation in the form of combining the NLO prediction via POWHEG matching with the parton shower and the associated uncertainties. To handle large Coulomb singularities at threshold, we include the next-to-leading log (NLL) threshold resummation derived in nonrelativistic QCD (NRQCD) for t anti t production. This results in a form factor that we incorporate in a fully relativistic cross section, which is factorized within an extended double-pole approximation. Fixed-order QCD corrections are included, hereby, for the top decay. We combine this calculation with the full fixed-order QCD results at NLO for W{sup +}W{sup -}b anti b production to obtain a computation that is not only valid at threshold but smoothly interpolates to the continuum. This allows us to present the first prediction for exclusive W{sup +}W{sup -}b anti b production at a lepton collider with a consistent matching between the top-antitop threshold and continuum regions. This computation is not only required to describe the intermediate energy

  3. Scrutinizing the top quark at lepton colliders with higher orders. From fixed order to resummation and matching

    International Nuclear Information System (INIS)

    Nejad, Bijan Chokoufe

    2017-01-01

    In this thesis, we present detailed studies of top-pair production with (t anti tH) and without association of a Higgs boson (t anti t) in e"+e"- collisions. These processes are of utmost interest for the top physics program of future lepton colliders. They allow in particular a precise measurement of the top quark mass and the Yukawa coupling. For this purpose, we present predictions for off-shell t anti t and t anti tH production including non-resonant and interference contributions up to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD). This allows for top-quark phenomenology in the continuum at an unprecedented level of accuracy. We show that off-shell effects and NLO QCD corrections for these processes do not factorize in general. In particular, we present the Yukawa coupling dependence of the cross section, which receives negative corrections due to sizable interference terms. We also add a discussion of p_T resummation in the form of combining the NLO prediction via POWHEG matching with the parton shower and the associated uncertainties. To handle large Coulomb singularities at threshold, we include the next-to-leading log (NLL) threshold resummation derived in nonrelativistic QCD (NRQCD) for t anti t production. This results in a form factor that we incorporate in a fully relativistic cross section, which is factorized within an extended double-pole approximation. Fixed-order QCD corrections are included, hereby, for the top decay. We combine this calculation with the full fixed-order QCD results at NLO for W"+W"-b anti b production to obtain a computation that is not only valid at threshold but smoothly interpolates to the continuum. This allows us to present the first prediction for exclusive W"+W"-b anti b production at a lepton collider with a consistent matching between the top-antitop threshold and continuum regions. This computation is not only required to describe the intermediate energy region but also allows to study

  4. Renormalized Lie perturbation theory

    International Nuclear Information System (INIS)

    Rosengaus, E.; Dewar, R.L.

    1981-07-01

    A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another

  5. Functional perturbative RG and CFT data in the ε-expansion

    Energy Technology Data Exchange (ETDEWEB)

    Codello, A. [Southern Denmark Univ., Odense (Denmark). CP3-Origins; INFN-Sezione di Bologna, Bologna (Italy); Safari, M. [INFN-Sezione di Bologna, Bologna (Italy); Bologna Univ. (Italy). Dipt di Fisica e Astronomia; Vacca, G.P. [INFN-Sezione di Bologna, Bologna (Italy); Zanusso, O. [INFN-Sezione di Bologna, Bologna (Italy); Jena Univ. (Germany). Theoretisch-Physikalisches Inst.

    2018-01-15

    We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the ε-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multi-critical models φ{sup 2n}. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks. (orig.)

  6. Perturbation-based moment equation approach for flow in heterogeneous porous media: applicability range and analysis of high-order terms

    International Nuclear Information System (INIS)

    Li Liyong; Tchelepi, Hamdi A.; Zhang Dongxiao

    2003-01-01

    We present detailed comparisons between high-resolution Monte Carlo simulation (MCS) and low-order numerical solutions of stochastic moment equations (SMEs) for the first and second statistical moments of pressure. The objective is to quantify the difference between the predictions obtained from MCS and SME. Natural formations with high permeability variability and large spatial correlation scales are of special interest for underground resources (e.g. oil and water). Consequently, we focus on such formations. We investigated fields with variance of log-permeability, σ Y 2 , from 0.1 to 3.0 and correlation scales (normalized by domain length) of 0.05 to 0.5. In order to avoid issues related to statistical convergence and resolution level, we used 9000 highly resolved realizations of permeability for MCS. We derive exact discrete forms of the statistical moment equations. Formulations based on equations written explicitly in terms of permeability (K-based) and log-transformed permeability (Y-based) are considered. The discrete forms are applicable to systems of arbitrary variance and correlation scales. However, equations governing a particular statistical moment depend on higher moments. Thus, while the moment equations are exact, they are not closed. In particular, the discrete form of the second moment of pressure includes two triplet terms that involve log-permeability (or permeability) and pressure. We combined MCS computations with full discrete SME equations to quantify the importance of the various terms that make up the moment equations. We show that second-moment solutions obtained using a low-order Y-based SME formulation are significantly better than those from K-based formulations, especially when σ Y 2 >1. As a result, Y-based formulations are preferred. The two triplet terms are complex functions of the variance level and correlation length. The importance (contribution) of these triplet terms increases dramatically as σ Y 2 increases above one. We

  7. Third-order QCD corrections to the charged-current structure function F3

    International Nuclear Information System (INIS)

    Moch, S.; Vermaseren, J.A.M.; Vogt, A.

    2008-12-01

    We compute the coefficient function for the charge-averaged W ± -exchange structure function F 3 in deep-inelastic scattering (DIS) to the third order in massless perturbative QCD. Our new three-loop contribution to this quantity forms, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-to-next-to-leading order corrections. It thus facilitates improved determinations of the strong coupling α s and of 1/Q 2 power corrections from scaling violations measured in neutrino-nucleon DIS. The expansion of F 3 in powers of α s is stable at all values of x relevant to measurements at high scales Q 2 . At small x the third-order coefficient function is dominated by diagrams with the colour structure d abc d abc not present at lower orders. At large x the coefficient function for F 3 is identical to that of F 1 up to terms vanishing for x→1. (orig.)

  8. Third-order QCD corrections to the charged-current structure function F{sub 3}

    Energy Technology Data Exchange (ETDEWEB)

    Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Vermaseren, J.A.M. [NIKHEF, Amsterdam (Netherlands); Vogt, A. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences

    2008-12-15

    We compute the coefficient function for the charge-averaged W{sup {+-}}-exchange structure function F{sub 3} in deep-inelastic scattering (DIS) to the third order in massless perturbative QCD. Our new three-loop contribution to this quantity forms, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-to-next-to-leading order corrections. It thus facilitates improved determinations of the strong coupling {alpha}{sub s} and of 1/Q{sup 2} power corrections from scaling violations measured in neutrino-nucleon DIS. The expansion of F{sub 3} in powers of {alpha}{sub s} is stable at all values of x relevant to measurements at high scales Q{sup 2}. At small x the third-order coefficient function is dominated by diagrams with the colour structure d{sup abc}d{sub abc} not present at lower orders. At large x the coefficient function for F{sub 3} is identical to that of F{sub 1} up to terms vanishing for x{yields}1. (orig.)

  9. Seven topics in perturbative QCD

    International Nuclear Information System (INIS)

    Buras, A.J.

    1980-09-01

    The following topics of perturbative QCD are discussed: (1) deep inelastic scattering; (2) higher order corrections to e + e - annihilation, to photon structure functions and to quarkonia decays; (3) higher order corrections to fragmentation functions and to various semi-inclusive processes; (4) higher twist contributions; (5) exclusive processes; (6) transverse momentum effects; (7) jet and photon physics

  10. Kato expansion in quantum canonical perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)

    2016-06-15

    This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

  11. Kato expansion in quantum canonical perturbation theory

    International Nuclear Information System (INIS)

    Nikolaev, Andrey

    2016-01-01

    This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

  12. Masses and sigma terms of doubly charmed baryons up to O (p4) in manifestly Lorentz-invariant baryon chiral perturbation theory

    Science.gov (United States)

    Yao, De-Liang

    2018-02-01

    We calculate the masses and sigma terms of the doubly charmed baryons up to next-to-next-to-next-to-leading order [i.e., O (p4) ] in a covariant baryon chiral perturbation theory by using the extended-on-mass-shell renormalization scheme. Their expressions both in infinite and finite volumes are provided for chiral extrapolation in lattice QCD. As a first application, our chiral results of the masses are confronted with the existing lattice QCD data in the presence of finite-volume corrections. Up to O (p3) , all relevant low-energy constants can be well determined. As a consequence, we obtain the physical values for the masses of Ξc c and Ωc c baryons by extrapolating to the physical limit. Our determination of the Ξc c mass is consistent with the recent experimental value by LHCb Collaboration, however, larger than the one by SELEX Collaboration. In addition, we predict the pion-baryon and strangeness-baryon sigma terms, as well as the mass splitting between the Ξc c and Ωc c states. Their quark mass dependences are also discussed. The numerical procedure can be applied to the chiral results of O (p4) order, where more unknown constants are involved, when more data are available for unphysical pion masses.

  13. Perturbation Theory of Embedded Eigenvalues

    DEFF Research Database (Denmark)

    Engelmann, Matthias

    project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...

  14. de Sitter limit of inflation and nonlinear perturbation theory

    DEFF Research Database (Denmark)

    R. Jarnhus, Philip; Sloth, Martin Snoager

    2007-01-01

    We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...

  15. Primordial spectra of slow-roll inflation at second-order with the Gauss-Bonnet correction

    Science.gov (United States)

    Wu, Qiang; Zhu, Tao; Wang, Anzhong

    2018-05-01

    The slow-roll inflation for a single scalar field that couples to the Gauss-Bonnet (GB) term represents an important higher-order curvature correction inspired by string theory. With the arrival of the era of precision cosmology, it is expected that the high-order corrections become more and more important. In this paper we study the observational predictions of the slow-roll inflation with the GB term by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble and GB coupling flow parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. In addition, by studying the theoretical predictions of the scalar spectral index and the tensor-to-scalar ratio with the Planck 2015 constraints in a model with power-law potential and GB coupling, we show that the second-order corrections are important in the future measurements. We expect that the understanding of the GB corrections in the primordial spectra and their constraints by forthcoming observational data will provide clues for the UV complete theory of quantum gravity, such as the string/M-theory.

  16. Perturbation methods for power and reactivity reconstruction

    International Nuclear Information System (INIS)

    Palmiotti, G.; Salvatores, M.; Estiot, J.C.; Broccoli, U.; Bruna, G.; Gomit, J.M.

    1987-01-01

    This paper deals with recent developments and applications in perturbation methods. Two types of methods are used. The first one is an explicit method, which allows the explicit reconstruction of a perturbed flux using a linear combination of a library of functions. In our application, these functions are the harmonics (i.e. the high order eigenfunctions of the system). The second type is based on the Generalized Perturbation Theory GPT and needs the calculation of an importance function for each integral parameter of interest. Recent developments of a particularly useful high order formulation allows to obtain satisfactory results also for very large perturbations

  17. Perturbation theory with instantons

    International Nuclear Information System (INIS)

    Carruthers, P.; Pinsky, S.S.; Zachariasen, F.

    1977-05-01

    ''Perturbation theory'' rules are developed for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the ''dilute gas'' approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form (μ 2 /q 2 )/sup -8π 2 b/ where b is the coefficient in the expansion of the β function: β = bg 3 +...

  18. Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory

    Science.gov (United States)

    Bozkaya, Uǧur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David

    2011-09-01

    Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Møller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O_4^+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O_4^+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that

  19. Renormalization group improved bottom mass from {Upsilon} sum rules at NNLL order

    Energy Technology Data Exchange (ETDEWEB)

    Hoang, Andre H.; Stahlhofen, Maximilian [Wien Univ. (Austria). Fakultaet fuer Physik; Ruiz-Femenia, Pedro [Wien Univ. (Austria). Fakultaet fuer Physik; Valencia Univ. - CSIC (Spain). IFIC

    2012-09-15

    We determine the bottom quark mass from non-relativistic large-n {Upsilon} sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of {alpha}{sub s} ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic {alpha}{sub s} ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling ({alpha}{sub s}(M{sub Z})=0.1183{+-}0.0010) we obtain M{sub b}{sup 1S}=4.755{+-}0.057{sub pert} {+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.

  20. On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x

    International Nuclear Information System (INIS)

    Soar, G.; Vogt, A.; Vermaseren, J.A.M.

    2009-12-01

    We present the coefficient functions for deep-inelastic scattering (DIS) via the exchange of a scalar φ directly coupling only to gluons, such as the Higgs boson in the limit of a very heavy top quark and n f effectively massless light flavours, to the third order in perturbative QCD. The two-loop results are employed to construct the next-to-next-to-leading order physical evolution kernels for the system (F 2 ,F φ ) of flavour-singlet structure functions. The practical relevance of these kernels as an alternative to MS factorization is bedevilled by artificial double logarithms at small values of the scaling variable x, where the large top-mass limit ceases to be appropriate. However, they show an only single-logarithmic enhancement at large x. Conjecturing that this feature persists to the next order also in the present singlet case, the three-loop coefficient functions facilitate exact predictions (backed up by their particular colour structure) of the double-logarithmic contributions to the fourth-order singlet splitting functions, i.e., of the terms (1-x) a ln k (1-x) with k=4,5,6 and k=3,4,5, respectively, for the off-diagonal and diagonal quantities to all powers a in (1-x). (orig.)

  1. Chiral symmetry in perturbative QCD

    International Nuclear Information System (INIS)

    Trueman, T.L.

    1979-04-01

    The chiral symmetry of quantum chromodynamics with massless quarks is unbroken in perturbation theory. Dimensional regularization is used. The ratio of the vector and axial vector renormalization constante is shown to be independent of the renormalization mass. The general results are explicitly verified to fourth order in g, the QCD coupling constant

  2. Recoil velocity at second post-Newtonian order for spinning black hole binaries

    International Nuclear Information System (INIS)

    Racine, Etienne; Buonanno, Alessandra; Kidder, Larry

    2009-01-01

    We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at second post-Newtonian (2PN) order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely, next-to-leading order spin-orbit terms at 1.5 post-Newtonian (1.5PN) order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasicircular orbits, we integrate the linear-momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to a factor ∼3 with respect to the leading-order PN prediction. Whereas the recoil velocity computed in PN theory within the adiabatic approximation can accurately describe the early inspiral phase, we find that its fast increase during the late inspiral and plunge, and the arbitrariness in determining until when it should be trusted, makes the PN predictions for the total recoil not very accurate and robust. Nevertheless, the linear-momentum flux at higher PN orders can be employed to build more reliable resummed expressions aimed at capturing the nonperturbative effects until merger. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasicircular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mikoczi, Vasuth, and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka, and Sasaki obtained in the context of black hole perturbation theory.

  3. Developments in perturbation theory

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators

  4. Complete active space second order perturbation theory (CASPT2) study of N({sup 2}D) + H{sub 2}O reaction paths on D{sub 1} and D{sub 0} potential energy surfaces: Direct and roaming pathways

    Energy Technology Data Exchange (ETDEWEB)

    Isegawa, Miho; Liu, Fengyi [Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Kyoto 606-8103 (Japan); Maeda, Satoshi [Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan); Morokuma, Keiji, E-mail: morokuma@fukui.kyoto-u.ac.jp [Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Kyoto 606-8103 (Japan); Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia 30322 (United States)

    2014-10-21

    We report reaction paths starting from N({sup 2}D) + H{sub 2}O for doublet spin states, D{sub 0} and D{sub 1}. The potential energy surfaces are explored in an automated fashion using the global reaction route mapping strategy. The critical points and reaction paths have been fully optimized at the complete active space second order perturbation theory level taking all valence electrons in the active space. In addition to direct dissociation pathways that would be dominant, three roaming processes, two roaming dissociation, and one roaming isomerization: (1) H{sub 2}ON → H–O(H)N → H–HON → NO({sup 2}Π) + H{sub 2}, (2) cis-HNOH → HNO–H → H–HNO → NO + H{sub 2}, (3) H{sub 2}NO → H–HNO → HNO–H → trans-HNOH, are confirmed on the D{sub 0} surface.

  5. The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

    Energy Technology Data Exchange (ETDEWEB)

    Bykov, Dmytro; Kristensen, Kasper; Kjærgaard, Thomas [Department of Chemistry, qLeap Center for Theoretical Chemistry, University of Aarhus, DK-8000 Århus C (Denmark)

    2016-07-14

    We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 method and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.

  6. The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

    International Nuclear Information System (INIS)

    Bykov, Dmytro; Kristensen, Kasper; Kjærgaard, Thomas

    2016-01-01

    We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 method and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.

  7. Finite-temperature second-order many-body perturbation and Hartree–Fock theories for one-dimensional solids: An application to Peierls and charge-density-wave transitions in conjugated polymers

    International Nuclear Information System (INIS)

    He, Xiao; Ryu, Shinsei; Hirata, So

    2014-01-01

    Finite-temperature extensions of ab initio Gaussian-basis-set spin-restricted Hartree–Fock (HF) and second-order many-body perturbation (MP2) theories are implemented for infinitely extended, periodic, one-dimensional solids and applied to the Peierls and charge-density-wave (CDW) transitions in polyyne and all-trans polyacetylene. The HF theory predicts insulating CDW ground states for both systems in their equidistant structures at low temperatures. In the same structures, they turn metallic at high temperatures. Starting from the “dimerized” low-temperature equilibrium structures, the systems need even higher temperatures to undergo a Peierls transition, which is accompanied by geometric as well as electronic distortions from dimerized to non-dimerized forms. The conventional finite-temperature MP2 theory shows a sign of divergence in any phase at any nonzero temperature and is useless. The renormalized finite-temperature MP2 (MP2R) theory is divergent only near metallic electronic structures, but is well behaved elsewhere. MP2R also predicts CDW and Peierls transitions occurring at two different temperatures. The effect of electron correlation is primarily to lower the Peierls transition temperature

  8. Perturbations of the Friedmann universe

    International Nuclear Information System (INIS)

    Novello, M.; Salim, J.M.; Heintzmann, H.

    1982-01-01

    Correcting and extending previous work by Hawking (1966) and Olson (1976) the complete set of perturbation equations of a Friedmann Universe in the quasi-Maxwellian form is derived and analized. The formalism is then applied to scalar, vector and tensor perturbations of a phenomenological fluid, which is modelled such as to comprise shear and heat flux. Depending on the equation of state of the background it is found that there exist unstable (growing) modes of purely rotational character. It is further found that (to linear order at least) any vortex perturbation is equivalent to a certain heat flux vector. The equation for the gravitational waves are derived in a completely equivalent method as in case of the propagation, in a curved space-time, of electromagnetic waves in a plasma endowed with some definite constitutive relations. (Author) [pt

  9. Difference scheme for a singularly perturbed parabolic convection-diffusion equation in the presence of perturbations

    Science.gov (United States)

    Shishkin, G. I.

    2015-11-01

    An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.

  10. Non-leading contributions in QCD: Summing the perturbative series

    International Nuclear Information System (INIS)

    Trentadue, L.

    1984-01-01

    This paper presents the results of a systematic analysis of the leading and non-leading contributions in perturbative QCD and addresses the question of logarithmic contributions to all orders of the perturbative series

  11. New Methods in Non-Perturbative QCD

    Energy Technology Data Exchange (ETDEWEB)

    Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)

    2017-01-31

    In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.

  12. Complete-active-space second-order perturbation theory (CASPT2//CASSCF) study of the dissociative electron attachment in canonical DNA nucleobases caused by low-energy electrons (0-3 eV)

    Energy Technology Data Exchange (ETDEWEB)

    Francés-Monerris, Antonio; Segarra-Martí, Javier; Merchán, Manuela; Roca-Sanjuán, Daniel, E-mail: Daniel.Roca@uv.es [Instituto de Ciencia Molecular, Universitat de València, P.O. Box 22085, 46071 València (Spain)

    2015-12-07

    Low-energy (0-3 eV) ballistic electrons originated during the irradiation of biological material can interact with DNA/RNA nucleobases yielding transient-anion species which undergo decompositions. Since the discovery that these reactions can eventually lead to strand breaking of the DNA chains, great efforts have been dedicated to their study. The main fragmentation at the 0-3 eV energy range is the ejection of a hydrogen atom from the specific nitrogen positions. In the present study, the methodological approach introduced in a previous work on uracil [I. González-Ramírez et al., J. Chem. Theory Comput. 8, 2769-2776 (2012)] is employed to study the DNA canonical nucleobases fragmentations of N–H bonds induced by low-energy electrons. The approach is based on minimum energy path and linear interpolation of internal coordinates computations along the N–H dissociation channels carried out at the complete-active-space self-consistent field//complete-active-space second-order perturbation theory level. On the basis of the calculated theoretical quantities, new assignations for the adenine and cytosine anion yield curves are provided. In addition, the π{sub 1}{sup −} and π{sub 2}{sup −} states of the pyrimidine nucleobases are expected to produce the temporary anions at electron energies close to 1 and 2 eV, respectively. Finally, the present theoretical results do not allow to discard neither the dipole-bound nor the valence-bound mechanisms in the range of energies explored, suggesting that both possibilities may coexist in the experiments carried out with the isolated nucleobases.

  13. Revisiting the pion's scalar form factor in chiral perturbation theory

    CERN Document Server

    Juttner, Andreas

    2012-01-01

    The quark-connected and the quark-disconnected Wick contractions contributing to the pion's scalar form factor are computed in the two and in the three flavour chiral effective theory at next-to-leading order. While the quark-disconnected contribution to the form factor itself turns out to be power-counting suppressed its contribution to the scalar radius is of the same order of magnitude as the one of the quark-connected contribution. This result underlines that neglecting quark-disconnected contributions in simulations of lattice QCD can cause significant systematic effects. The technique used to derive these predictions can be applied to a large class of observables relevant for QCD-phenomenology.

  14. Mass generation in perturbed massless integrable models

    International Nuclear Information System (INIS)

    Controzzi, D.; Mussardo, G.

    2005-01-01

    We extend form-factor perturbation theory to non-integrable deformations of massless integrable models, in order to address the problem of mass generation in such systems. With respect to the standard renormalisation group analysis this approach is more suitable for studying the particle content of the perturbed theory. Analogously to the massive case, interesting information can be obtained already at first order, such as the identification of the operators which create a mass gap and those which induce the confinement of the massless particles in the perturbed theory

  15. Perturbation calculations with Wilson loop

    International Nuclear Information System (INIS)

    Peixoto Junior, L.B.

    1984-01-01

    We present perturbative calculations with the Wilson loop (WL). The dimensional regularization method is used with a special attention concerning to the problem of divergences in the WL expansion in second and fourth orders, in three and four dimensions. We show that the residue in the pole, in 4d, of the fourth order graphs contribution sum is important for the charge renormalization. We compute up to second order the exact expression of the WL, in three-dimensional gauge theories with topological mass as well as its assimptotic behaviour for small and large distances. the author [pt

  16. Perturbative QCD and exclusive processes

    International Nuclear Information System (INIS)

    Bennett, J.; Hawes, F.; Zhao, M.; Zyla, P.

    1991-01-01

    The authors discuss perturbation theory as applied to particle physics calculations. In particle physics one is generally interested in the scattering amplitude for a system going from some initial state to a final state. The intermediate state or states are unknown. To get the scattering amplitude it is necessary to sum the contributions from processes which pass through all possible intermediate states. Intermediate states involve the exchange of intermediate vector bosons between the particles, and with this interaction is associated a coupling constant α. Each additional boson exchange involves an additional contribution of α to the coupling. If α is less than 1, one can see that the relative contribution of higher order processes is less and less important as α falls. In QCD the gluons serve as the intermediate vector bosons exchanged by quarks and gluons, and the interaction constant is not really a constant, but depends upon the distance between the particles. At short distances the coupling is small, and one can assume perturbative expansions may converge rapidly. Exclusive scattering processes, as opposed to inclusive, are those in which all of the final state products are detected. The authors then discuss the application of perturbative QCD to the deuteron. The issues of chiral conservation and color transparancy are also discussed, in the scheme of large Q 2 interations, where perturbative QCD should be applicable

  17. The development of the light cone in the quantum chromodynamics up to the first non-leading order

    International Nuclear Information System (INIS)

    Kaschluhn, L.

    1986-01-01

    For the product of two electromagnetic currents in QCD there is derived in a systematic way a nonlocal light-cone expansion up to next-to-leading order. Thereby the gauge-invariance of the underlying theory has been taken into acccount by using the known general solutions of the Ward identities in axial gauge. (author)

  18. Secondary isocurvature perturbations from acoustic reheating

    Science.gov (United States)

    Ota, Atsuhisa; Yamaguchi, Masahide

    2018-06-01

    The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the convolutions which may pick products of short wavelength perturbations up. We then introduce second order conserved quantities on superhorizon scales under the conditions (i) and (iii) even in the presence of the gradient terms by employing the full second order cosmological perturbation theory. We also discuss the violation of the condition (iii), that is, the energy momentum tensor is conserved for the total system but not for each component fluid. As an example, we explicitly evaluate second order heat conduction between baryons and photons due to the weak Compton scattering, which dominates during the period just before recombination. We show that such secondary effects can be recast into the isocurvature perturbations on superhorizon scales if the local type primordial non Gaussianity exists a priori.

  19. Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr [Department of Chemistry, Atatürk University, Erzurum 25240, Turkey and Department of Chemistry, Middle East Technical University, Ankara 06800 (Turkey)

    2014-09-28

    General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.

  20. Second-order Hydrodynamics in QCD at NLO arXiv

    CERN Document Server

    Ghiglieri, Jacopo; Teaney, Derek

    We compute the hydrodynamic relaxation times $\\tau_\\pi$ and $\\tau_j$ for hot QCD at next-to-leading order in the coupling by using kinetic theory. We show that certain dimensionless ratios of second-order to first-order transport coefficients obey bounds which apply whenever a kinetic theory description is possible; the computed values lie somewhat above these bounds. Strongly coupled theories with holographic duals strongly violate these bounds, highlighting their distance from a quasiparticle description.

  1. Dihadron production at the LHC: full next-to-leading BFKL calculation

    Energy Technology Data Exchange (ETDEWEB)

    Celiberto, Francesco G.; Papa, Alessandro [Dipartimento di Fisica dell' Universita della Calabria, Arcavacata di Rende, Cosenza (Italy); INFN-Gruppo collegato di Cosenza, Arcavacata di Rende, Cosenza (Italy); Ivanov, Dmitry Yu. [Sobolev Institute of Mathematics, Novosibirsk (Russian Federation); Novosibirsk State University, Novosibirsk (Russian Federation); Murdaca, Beatrice [INFN-Gruppo collegato di Cosenza, Arcavacata di Rende, Cosenza (Italy)

    2017-06-15

    The study of the inclusive production of a pair of charged light hadrons (a ''dihadron'' system) featuring high transverse momenta and well separated in rapidity represents a clear channel for the test of the BFKL dynamics at the Large Hadron Collider (LHC). This process has much in common with the well-known Mueller-Navelet jet production; however, hadrons can be detected at much smaller values of the transverse momentum than jets, thus allowing to explore an additional kinematic range, supplementary to the one studied with Mueller-Navelet jets. Furthermore, it makes it possible to constrain not only the parton densities (PDFs) for the initial proton, but also the parton fragmentation functions (FFs) describing the detected hadron in the final state. Here, we present the first full NLA BFKL analysis for cross sections and azimuthal angle correlations for dihadrons produced in the LHC kinematic ranges. We make use of the Brodsky-Lapage-Mackenzie optimization method to set the values of the renormalization scale and study the effect of choosing different values for the factorization scale. We also gauge the uncertainty coming from the use of different PDF and FF parametrizations. (orig.)

  2. Dihadron production at the LHC: full next-to-leading BFKL calculation

    Science.gov (United States)

    Celiberto, Francesco G.; Ivanov, Dmitry Yu.; Murdaca, Beatrice; Papa, Alessandro

    2017-06-01

    The study of the inclusive production of a pair of charged light hadrons (a "dihadron" system) featuring high transverse momenta and well separated in rapidity represents a clear channel for the test of the BFKL dynamics at the Large Hadron Collider (LHC). This process has much in common with the well-known Mueller-Navelet jet production; however, hadrons can be detected at much smaller values of the transverse momentum than jets, thus allowing to explore an additional kinematic range, supplementary to the one studied with Mueller-Navelet jets. Furthermore, it makes it possible to constrain not only the parton densities (PDFs) for the initial proton, but also the parton fragmentation functions (FFs) describing the detected hadron in the final state. Here, we present the first full NLA BFKL analysis for cross sections and azimuthal angle correlations for dihadrons produced in the LHC kinematic ranges. We make use of the Brodsky-Lapage-Mackenzie optimization method to set the values of the renormalization scale and study the effect of choosing different values for the factorization scale. We also gauge the uncertainty coming from the use of different PDF and FF parametrizations.

  3. Extra dimension searches at hadron colliders to next-to-leading ...

    Indian Academy of Sciences (India)

    The quantitative impact of NLO-QCD corrections for searches of large and warped extra dimensions at hadron colliders are investigated for the Drell-Yan process. The K-factor for various observables at hadron colliders are presented. Factorisation, renormalisation scale dependence and uncertainties due to various parton ...

  4. Kerr-CFT and gravitational perturbations

    International Nuclear Information System (INIS)

    Dias, Oscar J.C.; Reall, Harvey S.; Santos, Jorge E.

    2009-01-01

    Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and traveling waves. Imposing suitable (outgoing) boundary conditions, we find that there are no unstable modes. The explicit form of metric perturbations is obtained using the Hertz potential formalism, and compared with the Kerr-CFT boundary conditions. The energy and angular momentum associated with scalar field and gravitational normal modes are calculated. The energy is positive in all cases. The behaviour of second order perturbations is discussed.

  5. On perturbation theory for distance dependent statistics.

    Energy Technology Data Exchange (ETDEWEB)

    Mashkevich, S V

    1994-12-31

    It is known that perturbation theory for anyons has to be modified near Bose statistics in order to get correct finite results. For ``distance dependent statistics`` or anyons with smeared flux tubes, perturbation theory is in principle applicable directly but gives results which hold for too small values of the statistical parameter and, in particular, are not valid as the flux tube radius tends to zero. In this paper we discuss the way to modify perturbation theory for this situation, which allows to obtain the appropriate results. (author). 6 refs.

  6. Perturbative QCD and jets

    International Nuclear Information System (INIS)

    Mueller, A.H.

    1986-03-01

    A brief review of some of the recent progress in perturbative QCD is given (heavy quark production, small-x physics, minijets and related topics, classical simulations in high energy reactions, coherence and the string effect)

  7. Generalized chiral perturbation theory

    International Nuclear Information System (INIS)

    Knecht, M.; Stern, J.

    1994-01-01

    The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs

  8. PerturbationAnalyzer: a tool for investigating the effects of concentration perturbation on protein interaction networks.

    Science.gov (United States)

    Li, Fei; Li, Peng; Xu, Wenjian; Peng, Yuxing; Bo, Xiaochen; Wang, Shengqi

    2010-01-15

    The propagation of perturbations in protein concentration through a protein interaction network (PIN) can shed light on network dynamics and function. In order to facilitate this type of study, PerturbationAnalyzer, which is an open source plugin for Cytoscape, has been developed. PerturbationAnalyzer can be used in manual mode for simulating user-defined perturbations, as well as in batch mode for evaluating network robustness and identifying significant proteins that cause large propagation effects in the PINs when their concentrations are perturbed. Results from PerturbationAnalyzer can be represented in an intuitive and customizable way and can also be exported for further exploration. PerturbationAnalyzer has great potential in mining the design principles of protein networks, and may be a useful tool for identifying drug targets. PerturbationAnalyzer can be accessed from the Cytoscape web site http://www.cytoscape.org/plugins/index.php or http://biotech.bmi.ac.cn/PerturbationAnalyzer. Supplementary data are available at Bioinformatics online.

  9. Even order snake resonances

    International Nuclear Information System (INIS)

    Lee, S.Y.

    1993-01-01

    We found that the perturbed spin tune due to the imperfection resonance plays an important role in beam depolarization at snake resonances. We also found that even order snake resonances exist in the overlapping intrinsic and imperfection resonances. Due to the perturbed spin tune shift of imperfection resonances, each snake resonance splits into two

  10. Strings as perturbations of evolving spin networks

    International Nuclear Information System (INIS)

    Smolin, Lee

    2000-01-01

    One step in the construction of a background independent formulation of string theory is detailed, in which it is shown how perturbative strings may arise as small fluctuations around histories in a formulation of non-perturbative dynamics of spin networks due to Markopoulou. In this formulation the dynamics of spin network states and their generalizations is described in terms of histories which have discrete analogues of the causal structure and many fingered time of Lorentzian spacetimes. Perturbations of these histories turn out to be described in terms of spin systems defined on 2-dimensional timelike surfaces embedded in the discrete spacetime. When the history has a classical limit which is Minkowski spacetime, the action of the perturbation theory is given to leading order by the spacetime area of the surface, as in bosonic string theory. This map between a non-perturbative formulation of quantum gravity and a 1+1 dimensional theory generalizes to a large class of theories in which the group SU(2) i s extended to any quantum group or supergroup. It is argued that a necessary condition for the non-perturbative theory to have a good classical limit is that the resulting 1+1 dimensional theory defines a consistent and stable perturbative string theory

  11. The cosmological perturbation theory in loop cosmology with holonomy corrections

    International Nuclear Information System (INIS)

    Wu, Jian-Pin; Ling, Yi

    2010-01-01

    In this paper we investigate the scalar mode of first-order metric perturbations over spatially flat FRW spacetime when the holonomy correction is taken into account in the semi-classical framework of loop quantum cosmology. By means of the Hamiltonian derivation, the cosmological perturbation equations is obtained in longitudinal gauge. It turns out that in the presence of metric perturbation the holonomy effects influence both background and perturbations, and contribute the non-trivial terms S h1 and S h2 in the cosmological perturbation equations

  12. Hadronic Structure from Perturbative Dressing

    Energy Technology Data Exchange (ETDEWEB)

    Arash, Firooz [Physics Department, Tafresh University, Tafresh, Iran and Center for theoretical physics and Mathematics, AEOI, P.O. Box 11365-8486, Tehran (Iran, Islamic Republic of)]. E-mail: farash@cic.aut.ac.ir

    2005-09-15

    Perturbative dressing of a valence quark in QCD produces the internal structure of an extended object, the so-called Valon. The valon structure is universal and independent of the hosting hadron. Polarized and unpolarized proton and pion structure functions are calculated in the valon representation. One finds that although all the available data on g{sub 1}{sup p,n,d} are easily reproduced, a sizable orbital angular momentum associated with the partonic structure of the valon is required in order to have a spin 1/2 valon.

  13. Mode coupling of Schwarzschild perturbations: Ringdown frequencies

    International Nuclear Information System (INIS)

    Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel

    2010-01-01

    Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.

  14. Second-order QCD effects in Higgs boson production through vector boson fusion

    Science.gov (United States)

    Cruz-Martinez, J.; Gehrmann, T.; Glover, E. W. N.; Huss, A.

    2018-06-01

    We compute the factorising second-order QCD corrections to the electroweak production of a Higgs boson through vector boson fusion. Our calculation is fully differential in the kinematics of the Higgs boson and of the final state jets, and uses the antenna subtraction method to handle infrared singular configurations in the different parton-level contributions. Our results allow us to reassess the impact of the next-to-leading order (NLO) QCD corrections to electroweak Higgs-plus-three-jet production and of the next-to-next-to-leading order (NNLO) QCD corrections to electroweak Higgs-plus-two-jet production. The NNLO corrections are found to be limited in magnitude to around ± 5% and are uniform in several of the kinematical variables, displaying a kinematical dependence only in the transverse momenta and rapidity separation of the two tagging jets.

  15. Perturbative corrections to B → D form factors in QCD

    Science.gov (United States)

    Wang, Yu-Ming; Wei, Yan-Bing; Shen, Yue-Long; Lü, Cai-Dian

    2017-06-01

    We compute perturbative QCD corrections to B → D form factors at leading power in Λ/ m b , at large hadronic recoil, from the light-cone sum rules (LCSR) with B-meson distribution amplitudes in HQET. QCD factorization for the vacuum-to- B-meson correlation function with an interpolating current for the D-meson is demonstrated explicitly at one loop with the power counting scheme {m}_c˜ O(√{Λ {m}_b}) . The jet functions encoding information of the hard-collinear dynamics in the above-mentioned correlation function are complicated by the appearance of an additional hard-collinear scale m c , compared to the counterparts entering the factorization formula of the vacuum-to- B-meson correction function for the construction of B → π from factors. Inspecting the next-to-leading-logarithmic sum rules for the form factors of B → Dℓν indicates that perturbative corrections to the hard-collinear functions are more profound than that for the hard functions, with the default theory inputs, in the physical kinematic region. We further compute the subleading power correction induced by the three-particle quark-gluon distribution amplitudes of the B-meson at tree level employing the background gluon field approach. The LCSR predictions for the semileptonic B → Dℓν form factors are then extrapolated to the entire kinematic region with the z-series parametrization. Phenomenological implications of our determinations for the form factors f BD +,0 ( q 2) are explored by investigating the (differential) branching fractions and the R( D) ratio of B → Dℓν and by determining the CKM matrix element |V cb | from the total decay rate of B → Dμν μ .

  16. Supersymmetry restoration in superstring perturbation theory

    International Nuclear Information System (INIS)

    Sen, Ashoke

    2015-01-01

    Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

  17. Supersymmetry restoration in superstring perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India)

    2015-12-14

    Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

  18. String perturbation theory diverges

    International Nuclear Information System (INIS)

    Gross, D.J.; Periwal, V.

    1988-01-01

    We prove that perturbation theory for the bosonic string diverges for arbitrary values of the coupling constant and is not Borel summable. This divergence is independent of the existence of the infinities that occur in the theory due to the presence of tachyons and dilaton tadpoles. We discuss the physical implications of such a divergence

  19. Cosmological perturbations in antigravity

    Science.gov (United States)

    Oltean, Marius; Brandenberger, Robert

    2014-10-01

    We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.

  20. Perturbed Markov chains

    OpenAIRE

    Solan, Eilon; Vieille, Nicolas

    2015-01-01

    We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

  1. Generalized perturbation series

    International Nuclear Information System (INIS)

    Baird, L.C.; Stinchcomb, G.

    1973-01-01

    An approximate solution of the Green's function equation may be used to generate an exact solution of the Schroedinger equation. This is accomplished through an iterative procedure. The procedure is equivalent to a perturbation expansion if the approximate Green's function is exact with respect to some reference potential

  2. Perturbed S3 neutrinos

    DEFF Research Database (Denmark)

    jora, Renata; Schechter, Joseph; Naeem Shahid, M.

    2009-01-01

    We study the effects of the perturbation which violates the permutation symmetry of three Majorana neutrinos but preserves the well known (23) interchange symmetry. This is done in the presenceof an arbitrary Majorana phase which serves to insure the degeneracy of the three neutrinos at the unper...... at the unperturbed level....

  3. Output synchronization of chaotic systems under nonvanishing perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-Mancilla, Didier [Departamento de Ciencias Exactas y Tecnologicas, Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG), Enrique Diaz de Leon s/n, 47460 Lagos de Moreno, Jal. (Mexico)], E-mail: didier@uabc.mx; Cruz-Hernandez, Cesar [Electronics and Telecommunications Department, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107, Carretera Tijuana-Ensenada, 22860 Ensenada, B.C. (Mexico)], E-mail: ccruz@cicese.mx

    2008-08-15

    In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included.

  4. Output synchronization of chaotic systems under nonvanishing perturbations

    International Nuclear Information System (INIS)

    Lopez-Mancilla, Didier; Cruz-Hernandez, Cesar

    2008-01-01

    In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included

  5. Heavy quark threshold dynamics in higher order

    Energy Technology Data Exchange (ETDEWEB)

    Piclum, J.H.

    2007-05-15

    In this work we discuss an important building block for the next-to-next-to-next-to leading order corrections to the pair production of top quarks at threshold. Specifically, we explain the calculation of the third order strong corrections to the matching coefficient of the vector current in non-relativistic Quantum Chromodynamics and provide the result for the fermionic part, containing at least one loop of massless quarks. As a byproduct, we obtain the matching coefficients of the axial-vector, pseudo-scalar and scalar current at the same order. Furthermore, we calculate the three-loop corrections to the quark renormalisation constants in the on-shell scheme in the framework of dimensional regularisation and dimensional reduction. Finally, we compute the third order strong corrections to the chromomagnetic interaction in Heavy Quark Effective Theory. The calculational methods are discussed in detail and results for the master integrals are given. (orig.)

  6. Quark mass relations to four-loop order

    International Nuclear Information System (INIS)

    Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias

    2015-02-01

    We present results for the relation between a heavy quark mass defined in the on-shell and MS scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS heavy quark masses.

  7. Perturbations of ultralight vector field dark matter

    Energy Technology Data Exchange (ETDEWEB)

    Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)

    2017-02-13

    We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with k{sup 2}≪Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with k{sup 2}≫Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c{sub s}{sup 2}≃k{sup 2}/m{sup 2}a{sup 2}. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ−Ψ)/Φ∼c{sub s}{sup 2}. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ∼c{sub s}{sup 2}. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.

  8. The heavy quarkonium spectrum at order $m\\alpha_{s}^{5}\\ln\\alpha_{s}$

    CERN Document Server

    Brambilla, Nora; Soto, Joan; Vairo, Antonio

    1999-01-01

    We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at $O(m\\alpha_s^5)$ in the heavy quarkonium spectrum. These leading logs, when $\\Lambda_{QCD} \\ll m\\alpha_s^2$, give the complete $O(m\\alpha_s^5 \\ln \\alpha_s)$ corrections to the heavy quarkonium spectrum.

  9. Studying the perturbative Reggeon

    International Nuclear Information System (INIS)

    Griffiths, S.; Ross, D.A.

    2000-01-01

    We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ''reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q 2 dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel. (orig.)

  10. Perturbed asymptotically linear problems

    OpenAIRE

    Bartolo, R.; Candela, A. M.; Salvatore, A.

    2012-01-01

    The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...

  11. Twisting perturbed parafermions

    Directory of Open Access Journals (Sweden)

    A.V. Belitsky

    2017-07-01

    Full Text Available The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang–Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6 nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current–current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3 sigma model which is reformulated as perturbed parafermions.

  12. Quenched Chiral Perturbation Theory to one loop

    NARCIS (Netherlands)

    Colangelo, G.; Pallante, E.

    The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the B0 parameter of the leading order Lagrangian. Finally, we do the chiral

  13. Schroedinger operators with singular perturbation potentials

    International Nuclear Information System (INIS)

    Harrell, E.M. II.

    1976-01-01

    This is a perturbative analysis of the eigenvalues and eigenfunctions of Schroedinger operators of the form -Δ + A + lambda V, defined on the Hilbert space L 2 (R/sup n/). A is a potential function (a smooth, real multiplication operator), and V is a ''spikelike'' perturbation, i.e., a perturbative potential function which diverges at some finite point. Lambda is a small real or complex parameter. The emphasis is on one-dimensional problems, and in particular the typical example is the ''spiked harmonic oscillator'' Hamiltonian, -d 2 /dx 2 + x 2 + lambda x/sup -α/, where α is a positive constant. An earlier study by L. Detwiler and J. R. Klauder [Phys. Rev. D 11 (1975) 1436] indicated that the lowest-order corrections to the ground-state eigenvalue of the spiked harmonic oscillator with lambda greater than 0 were proportional to lambda ln lambda when α = 3, and to lambda/sup 1/(α-2) when α is greater than 3. These and analogous results for a large class of operators and arbitrary eigenvalues are proved. Explicit constants in a modified perturbation series with a complicated dependence on lambda are determined and exhibited. Higher-order corrections for real lambda and lowest-order corrections for complex lambda are also discussed. While the substance of the dissertation is mathematical, its main applications are to quantum physics. The immediate cause of interest in such problems was the use of their peculiar convergence properties by J. R. Klauder as models for the behavior of nonrenormalizable quantum field theories. However, the results of this study are likely to be of greater importance in chemical or nuclear physics, as positive spikelike perturbations represent repulsive core interactions for quantum mechanical particles. The modified perturbation series are a new calculation technique for this situation

  14. Perturbative evaluation of the Thermal Wilson Loop

    International Nuclear Information System (INIS)

    Gava, E.; Jengo, R.

    1981-06-01

    The Thermal Wilson Loop 0 sup(β) dtauA 0 (tau, x-vector)>, representing an order parameter for the gauge theory and expected to be zero in the confining phase, is perturbatively evaluated up to the O(g 4 ) included for an SU(N) pure Yang-Mills theory. This evaluation should be meaningful at high temperature, β → 0. Its behaviour is discussed and a possible need for non-perturbative instanton-like contributions is pointed out. (author)

  15. On the level order for Dirac operators

    International Nuclear Information System (INIS)

    Grosse, H.

    1987-01-01

    We start from the Dirac operator for the Coulomb potential and prove within first order perturbation theory that degenerate levels split in a definite way depending on the sign of the Laplacian of the perturbing potential. 9 refs. (Author)

  16. Non-hard sphere thermodynamic perturbation theory.

    Science.gov (United States)

    Zhou, Shiqi

    2011-08-21

    A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. © 2011 American Institute of Physics

  17. Acoustic anisotropic wavefields through perturbation theory

    KAUST Repository

    Alkhalifah, Tariq Ali

    2013-09-01

    Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.

  18. Solitary wave solution to a singularly perturbed generalized Gardner ...

    Indian Academy of Sciences (India)

    2017-03-24

    Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...

  19. Scalar perturbations in p-nflation: the 3-form case

    Energy Technology Data Exchange (ETDEWEB)

    Germani, Cristiano [LUTH, Observatoire de Paris, CNRS UMR 8102, Université Paris Diderot, 5 Place Jules Janssen, 92195 Meudon Cedex (France); Kehagias, Alex, E-mail: cristiano.germani@obspm.fr, E-mail: kehagias@central.ntua.gr [Department of Physics, National Technical University of Athens, Hroon Polytechniou 9, 15780 Zogrtafou, Athens (Greece)

    2009-11-01

    We calculate the primordial spectrum of scalar perturbations of the 3-form inflation and we find that the curvature perturbations decay at late times. As as result, although a non-minimally coupled massive 3-form field may drive inflation at early times, it should be assisted by other fields in order to reproduce the observed temperature fluctuations of the CMB sky.

  20. Where does cosmological perturbation theory break down?

    International Nuclear Information System (INIS)

    Armendariz-Picon, Cristian; Fontanini, Michele; Penco, Riccardo; Trodden, Mark

    2009-01-01

    It is often assumed that initial conditions for the evolution of a cosmological mode should be set at the time its physical wavelength reaches a cut-off of the order of the Planck length. Beyond that scale, trans-Planckian corrections to the dispersion relation are supposed to become dominant, leading to the breakdown of cosmological perturbation theory. In this paper, we apply the effective field theory approach to the coupled metric-inflaton system in order to calculate the corrections to the power spectrum of scalar and tensor perturbations induced by higher-dimension operators at short wavelengths. These corrections can be interpreted as modifications of the dispersion relation, and thus open a window to probe the validity of cosmological perturbation theory. Both for scalars and tensors, the modifications become important when the Hubble parameter is of the order of the Planck mass, or when the physical wave number of a cosmological perturbation mode approaches the square of the Planck mass divided by the Hubble constant. Thus, the cut-off length at which such a breakdown occurs is finite, but much smaller than the Planck length.

  1. On the singular perturbations for fractional differential equation.

    Science.gov (United States)

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  2. On the Singular Perturbations for Fractional Differential Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  3. Perturbation measurement of waveguides for acoustic thermometry

    Science.gov (United States)

    Lin, H.; Feng, X. J.; Zhang, J. T.

    2013-09-01

    Acoustic thermometers normally embed small acoustic transducers in the wall bounding a gas-filled cavity resonator. At high temperature, insulators of transducers loss electrical insulation and degrade the signal-to-noise ratio. One essential solution to this technical trouble is to couple sound by acoustic waveguides between resonator and transducers. But waveguide will break the ideal acoustic surface and bring perturbations(Δf+ig) to the ideal resonance frequency. The perturbation model for waveguides was developed based on the first-order acoustic theory in this paper. The frequency shift Δf and half-width change g caused by the position, length and radius of waveguides were analyzed using this model. Six different length of waveguides (52˜1763 mm) were settled on the cylinder resonator and the perturbation (Δf+ig) were measured at T=332 K and p=250˜500 kPa. The experiment results agreed with the theoretical prediction very well.

  4. On the domain of string perturbation theory

    International Nuclear Information System (INIS)

    Davis, S.

    1989-06-01

    For a large class of effectively closed surfaces, it is shown that the only divergences in string scattering amplitudes at each order in perturbation theory are those associated with the coincidence of vertex operators and the boundary of moduli space. This class includes all closed surfaces of finite genus, and infinite-genus surfaces which can be uniformized by a group of Schottky type. While the computation is done explicitly for bosonic strings in their ground states, it can also be extended to excited states and to superstrings. The properties of these amplitudes lead to a definition of the domain of perturbation theory as the set of effectively closed surfaces. The implications of the restriction to effectively closed surfaces on the behavior of the perturbation series are discussed. (author). 20 refs, 6 figs

  5. MCNP perturbation technique for criticality analysis

    International Nuclear Information System (INIS)

    McKinney, G.W.; Iverson, J.L.

    1995-01-01

    The differential operator perturbation technique has been incorporated into the Monte Carlo N-Particle transport code MCNP and will become a standard feature of future releases. This feature includes first and/or second order terms of the Taylor Series expansion for response perturbations related to cross-section data (i.e., density, composition, etc.). Criticality analyses can benefit from this technique in that predicted changes in the track-length tally estimator of K eff may be obtained for multiple perturbations in a single run. A key advantage of this method is that a precise estimate of a small change in response (i.e., < 1%) is easily obtained. This technique can also offer acceptable accuracy, to within a few percent, for up to 20-30% changes in a response

  6. Non-Perturbative Renormalization

    CERN Document Server

    Mastropietro, Vieri

    2008-01-01

    The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi

  7. Perturbative quantum chromodynamics

    CERN Document Server

    1989-01-01

    This book will be of great interest to advanced students and researchers in the area of high energy theoretical physics. Being the most complete and updated review volume on Perturbative QCD, it serves as an extremely useful textbook or reference book. Some of the reviews in this volume are the best that have been written on the subject anywhere. Contents: Factorization of Hard Processes in QCD (J C Collins, D E Soper & G Sterman); Exclusive Processes in Quantum Chromodynamics (S J Brodsky & G P Lepage); Coherence and Physics of QCD Jets (Yu L Dokshitzer, V A Khoze & S I Troyan); Pomeron in Qu

  8. Perturbative quantum chromodynamics

    International Nuclear Information System (INIS)

    Radyushkin, A.V.

    1987-01-01

    The latest achievements in perturbative quantum chromodynamics (QCD) relating to the progress in factorization of small and large distances are presented. The following problems are concerned: Development of the theory of Sudakov effects on the basis of mean contour formalism. Development of nonlocal condensate formalism. Calculation of hadron wave functions and hadron distribution functions using QCD method of sum rules. Development of the theory of Regge behaviour in QCD, behaviour of structure functions at small x. Study of polarization effects in hadron processes with high momentum transfer

  9. Local perturbations perturb—exponentially–locally

    International Nuclear Information System (INIS)

    De Roeck, W.; Schütz, M.

    2015-01-01

    We elaborate on the principle that for gapped quantum spin systems with local interaction, “local perturbations [in the Hamiltonian] perturb locally [the groundstate].” This principle was established by Bachmann et al. [Commun. Math. Phys. 309, 835–871 (2012)], relying on the “spectral flow technique” or “quasi-adiabatic continuation” [M. B. Hastings, Phys. Rev. B 69, 104431 (2004)] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of Hamza et al. [J. Math. Phys. 50, 095213 (2009)] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. This allows to improve locality bounds on the effect of perturbations on the low lying states in certain gapped models with a unique “bulk ground state” or “topological quantum order.” We also give some estimate on the exponential decay of correlations in models with impurities where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with a localized groundstate

  10. Operator Decomposition Framework for Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Abdel-Khalik, Hany S.; Wang, Congjian; Bang, Young Suk [North Carolina State University, Raleigh (United States)

    2012-05-15

    This summary describes a new framework for perturbation theory intended to improve its performance, in terms of the associated computational cost and the complexity of implementation, for routine reactor calculations in support of design, analysis, and regulation. Since its first introduction in reactor analysis by Winger, perturbation theory has assumed an aura of sophistication with regard to its implementation and its capabilities. Only few reactor physicists, typically mathematically proficient, have contributed to its development, with the general body of the nuclear engineering community remaining unaware of its current status, capabilities, and challenges. Given its perceived sophistication and the small body of community users, the application of perturbation theory has been limited to investigatory analyses only. It is safe to say that the nuclear community is split into two groups, a small one which understands the theory and, and a much bigger group with the perceived notion that perturbation theory is nothing but a fancy mathematical approach that has very little use in practice. Over the past three years, research has demonstrated two goals. First, reduce the computational cost of perturbation theory in order to enable its use for routine reactor calculations. Second, expose some of the myth about perturbation theory and present it in a form that is simple and relatable in order to stimulate the interest of nuclear practitioners, especially those who are currently working on the development of next generation reactor design and analysis tools. The operator decomposition approach has its roots in linear algebra and can be easily understood by code developers, especially those involved in the design of iterative numerical solution strategies

  11. Quark mass effects in quark number susceptibilities

    International Nuclear Information System (INIS)

    Graf, Thorben; Petreczky, Peter

    2017-01-01

    The quark degrees of freedom of the QGP with special focus on mass effects are investigated. A next-to-leading-order perturbation theory approach with quark mass dependence is applied and compared to lattice QCD results. (paper)

  12. Non-linear perturbations of a spherically collapsing star

    International Nuclear Information System (INIS)

    Brizuela, David

    2009-01-01

    Linear perturbation theory has been a successful tool in General Relativity, and can be considered as complementary to full nonlinear simulations. Going to second and higher perturbative orders improves the approximation and offers a controlled way to analyze the nonlinearities of the theory, though the problem becomes much harder computationally. We present a systematic approach to the treatment of high order metric perturbations, focusing on the scenario of nonspherical perturbations of a dynamical spherical background. It is based on the combination of adapted geometrical variables and the use of efficient computer algebra techniques. After dealing with a number of theoretical issues, like the construction of gauge invariants, we apply the formalism to the particular case of a perfect fluid star surrounded by a vacuum exterior. We describe the regularization of the divergences of the perturbations at null infinity and the matching conditions through the surface of the star.

  13. Perturbation studies on KAHTER

    Energy Technology Data Exchange (ETDEWEB)

    Rueckert, M.; Jonas, H.; Neef, R. D.

    1974-10-15

    The paper describes experimental and analytical results by both transport theory and diffusion theory calculations of perturbation tests in the KAHTER pebble bed critical experiment. The fission-weighted adjoint flux is measured from in-core detector responses by introducing a Cf-source into the core. Adjoint-weighted reactivities are calculated and compared to reactivity measurements for the introduction of a fuel and graphite pebble onto the top of the critical pile, the central rod worth, and the effect of replacing B4C with varying amounts of HfC in the central rod. In addition, analytical studies were made of the sensitivity of criticality to the fuel to graphite pebble ratio as measured in tests and of the effect of the upper void cavity as simulated in tests by placing cadmium layer across the top of the pebble pile to force a zero flux boundary condition.

  14. Introduction to perturbation methods

    CERN Document Server

    Holmes, M

    1995-01-01

    This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas.

  15. Perturbation theory around the Wess-Zumino-Witten model

    International Nuclear Information System (INIS)

    Hasseln, H. v.

    1991-05-01

    We consider a perturbation of the Wess-Zumino-Witten model in 2D by a current-current interaction. The β-function is computed to third order in the coupling constant and a nontrivial fixedpoint is found. By non-abelian bosonization, this perturbed WZW-model is shown to have the same β-function (at least to order g 2 ) as the fermionic theory with a four-fermion interaction. (orig.) [de

  16. Singular perturbation of simple eigenvalues

    International Nuclear Information System (INIS)

    Greenlee, W.M.

    1976-01-01

    Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem

  17. Unique Fock quantization of scalar cosmological perturbations

    Science.gov (United States)

    Fernández-Méndez, Mikel; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.

    2012-05-01

    We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter-field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.

  18. Baryon form factors in chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Kubis, B.; Meissner, U.G. [Forschungszentrum Juelich GmbH (Germany). Inst. fuer Kernphysik

    2001-01-01

    We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the {sigma}{sup -} charge radius and the {lambda}-{sigma}{sup 0} transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory. (orig.)

  19. Privacy Is Become with, Data Perturbation

    Science.gov (United States)

    Singh, Er. Niranjan; Singhai, Niky

    2011-06-01

    Privacy is becoming an increasingly important issue in many data mining applications that deal with health care, security, finance, behavior and other types of sensitive data. Is particularly becoming important in counterterrorism and homeland security-related applications. We touch upon several techniques of masking the data, namely random distortion, including the uniform and Gaussian noise, applied to the data in order to protect it. These perturbation schemes are equivalent to additive perturbation after the logarithmic Transformation. Due to the large volume of research in deriving private information from the additive noise perturbed data, the security of these perturbation schemes is questionable Many artificial intelligence and statistical methods exist for data analysis interpretation, Identifying and measuring the interestingness of patterns and rules discovered, or to be discovered is essential for the evaluation of the mined knowledge and the KDD process as a whole. While some concrete measurements exist, assessing the interestingness of discovered knowledge is still an important research issue. As the tool for the algorithm implementations we chose the language of choice in industrial world MATLAB.

  20. Chiral perturbation theory

    International Nuclear Information System (INIS)

    Harada, Masayasu

    2009-01-01

    Chiral perturbation theory has been used for great number of phenomenological analyses in low energy QCD as well as the lattice QCD analyses since the creation of the theory by Weinberg in 1979 followed by its consolidation by Gasser and Leutwyler in 1984 and 85. The theory is now the highly established one as the approach based on the effective field theory to search for Green function including quantum correlations in the frame of the systematic expansion technique using Lagrangian which includes all of the terms allowed by the symmetry. This review has been intended to describe how systematically physical quantities are calculated in the framework of the chiral symmetry. Consequently many of the various phenomenological analyses are not taken up here for which other reports are to be referred. Further views are foreseen to be developed based on the theory in addition to numbers of results reported up to the present. Finally π-π scattering is taken up to discuss to what energy scale the theory is available. (S. Funahashi)