WorldWideScience

Sample records for next-to-leading order perturbative

  1. Next-to-leading order improved perturbative QCD + saturation + hydrodynamics model for A+A collisions

    Energy Technology Data Exchange (ETDEWEB)

    Paatelainen, R.; Eskola, K.J. [Department of Physics, P.O.Box 35, FI-40014 University of Jyväskylä (Finland); Helsinki Institute of Physics, P.O.Box 64, FI-00014 University of Helsinki (Finland); Holopainen, H. [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany); Niemi, H. [Department of Physics, P.O.Box 35, FI-40014 University of Jyväskylä (Finland); Helsinki Institute of Physics, P.O.Box 64, FI-00014 University of Helsinki (Finland); Tuominen, K. [Department of Physics, P.O.Box 64, FI-00014 University of Helsinki (Finland); Helsinki Institute of Physics, P.O.Box 64, FI-00014 University of Helsinki (Finland)

    2014-06-15

    We calculate initial conditions for the hydrodynamical evolution in ultrarelativistic heavy-ion collisions at the LHC and RHIC in an improved next-to-leading order perturbative QCD + saturation framework. Using viscous relativistic hydrodynamics, we show that we obtain a good simultaneous description of the centrality dependence of charged particle multiplicities, transverse momentum spectra and elliptic flow at the LHC and at RHIC. In particular, we discuss how the temperature dependence of the shear viscosity is constrained by these data.

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

    International Nuclear Information System (INIS)

    Kilgore, W.B.

    1997-05-01

    I present results from a next-to-leading order event generator of purely gluonic jet production. 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

  3. 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.

  4. 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

    2018-03-01

    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.

  5. 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.

  6. 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

    We present theoretical predictions for five-jet production in proton-proton collisions at next-to-leading-order accuracy in QCD. Inclusive as well as differential observables are studied for collision energies of 7 and 8 TeV. In general the next-to-leading-order corrections stabilize the theoreti......We present theoretical predictions for five-jet production in proton-proton collisions at next-to-leading-order accuracy in QCD. Inclusive as well as differential observables are studied for collision energies of 7 and 8 TeV. In general the next-to-leading-order corrections stabilize...... the theoretical predictions with respect to scale variations. In the case of the inclusive jet cross sections, we compare with experimental data where possible and find reasonable agreement. We observe that the four-to-three and five-to-four jet ratios show better perturbative convergence than the known three......-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...

  7. 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.)

  8. 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.

  9. 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%.

  10. 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%.

  11. 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.)

  12. 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.

  13. The two-nucleon system at next-to-next-to-next-to-leading order

    Energy Technology Data Exchange (ETDEWEB)

    Evgeny Epelbaum; Walter Gloeckle; Ulf-G. Meissner

    2005-01-01

    We consider the two-nucleon system at next-to-next-to-next-to-leading order (N{sup 3}LO) in chiral effective field theory. The two--nucleon potential at N{sup 3}LO consists of one-, two- and three-pion exchanges and a set of contact interactions with zero, two and four derivatives. In addition, one has to take into account various isospin--breaking and relativistic corrections. We employ spectral function regularization for the multi--pion exchanges. Within this framework, it is shown that the three-pion exchange contribution is negligibly small. The low--energy constants (LECs) related to pion-nucleon vertices are taken consistently from studies of pion-nucleon scattering in chiral perturbation theory. The total of 26 four--nucleon LECs has been determined by a combined fit to some np and pp phase shifts from the Nijmegen analysis together with the nn scattering length.

  14. 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.

  15. 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

  16. 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

  17. 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

  18. 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

  19. Photoproduction of jets at HERA in next-to-leading order QCD

    International Nuclear Information System (INIS)

    Klasen, M.

    1996-09-01

    Photoproduction of jets is one of the most important processes investigated at the electron-proton collider HERA. It not only allows to test the theory of strong interactions, quantum chromodynamics (QCD), but it also permits to measure the proton and photon structure functions with high precision. This requires exact theoretical predictions for the observed one- and two-jet cross sections. These cross sections are given here for the first time for direct and resolved photoproduction in next-to-leading order of perturbation theory. We present the complete analytical results for the Born terms, the virtual, and the real corrections. Here, we use the phase space slicing method to separate singular and regular regions of phase space by an invariant mass cut. In this way, all soft and collinear singularities can be either cancelled, or absorbed into the structure functions. Using a flexible Monte Carlo program, we evaluate the cross sections numerically and compare them to data from the experiments H1 and ZEUS. (orig.)

  20. 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

  1. Zγ production in vector-boson scattering at next-to-leading order QCD

    Science.gov (United States)

    Campanario, Francisco; Kerner, Matthias; Zeppenfeld, Dieter

    2018-01-01

    Cross sections and differential distributions for Zγ production in association with two jets via vector boson fusion are presented at next-to-leading order in QCD. The leptonic decays of the Z boson with full off-shell effects and spin correlations are taken into account. The uncertainties due to different scale choices and pdf sets are studied. Furthermore, we analyze the effect of including anomalous quartic gauge couplings at NLO QCD.

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

    CERN Document Server

    Adeva, B; 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\\%.

  3. 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

  4. 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.

  5. 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.

  6. 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.)

  7. 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.

  8. Multi-Parton Loop Amplitudes and Next-to-Leading Order Jet Cross-Sections

    CERN Document Server

    Bern, Zvi; Kosower, David A.; Signer, Adrian

    1998-01-01

    We 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\\bar{q}ggg and q\\bar{q}q'\\bar{q}'g), and for an intermediate vector boson V \\equiv \\gamma^*,Z,W plus four external partons (Vq\\bar{q}gg and Vq\\bar{q}q'\\bar{q}'). Using these amplitudes, numerical programs have been constructed for the next-to-leading order corrections to the processes p\\bar{p} to 3 jets (ignoring quark contributions so far) and e^+e^- to 4 jets.

  9. Higgs boson production in bottom quark fusion at next-to-next-to-leading order

    International Nuclear Information System (INIS)

    Harlander, Robert V.; Kilgore, William B.

    2003-01-01

    The total cross section for Higgs boson production in bottom-quark annihilation is evaluated at next-to-next-to-leading order in QCD. This is the first time that all terms at order α s 2 are taken into account. We find a greatly reduced scale dependence with respect to lower order results, for both the factorization and the renormalization scales. The behavior of the result is consistent with earlier determinations of the appropriate factorization scale for this process of μ F ≅M H /4, and supports the validity of the bottom parton density approach for computing the total inclusive rate. We present precise predictions for the cross section at the Fermilab Tevatron and the CERN Large Hadron Collider

  10. 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

  11. 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

  12. 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.

  13. 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.

  14. Gluon-induced Higgs-strahlung at next-to-leading order QCD

    CERN Document Server

    Altenkamp, Lukas; Harlander, Robert V.; Rzehak, Heidi; Zirke, Tom J.E.

    2013-01-01

    Gluon-induced contributions to the associated production of a Higgs and a Z-boson are calculated with NLO accuracy in QCD. They constitute a significant contribution to the cross section for this process. The perturbative correction factor (K-factor) is calculated in the limit of infinite top-quark and vanishing bottom-quark masses. The qualitative similarity of the results to the well-known ones for the gluon-fusion process $gg\\to H$ allows to conclude that rescaling the LO prediction by this K-factor leads to a reliable NLO result and realistic error estimate due to missing higher-order perturbative effects. We consider the total inclusive cross section as well as a scenario with a boosted Higgs boson, where the Higgs boson's transverse momentum is restricted to values ptH>200GeV. In both cases, we find large correction factors $K\\approx 2$ in most of the parameter space.

  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. 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.

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

    Indian Academy of Sciences (India)

    In this section we present a general solution of the DGLAP gluon evolution equation at low x. .... evolution only. To solve this with a single boundary condition which can be any non-perturbative input distribution [16] of gluon at an initial scale Q2 = Q2. 0, viz.,. G(x, Q2 ... at any given point (x, t), the left-hand side of eq.

  19. 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.)

  20. 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.)

  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. 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...

  3. 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.

  4. Complete next-to-next-to-leading order calculation of NN → NNπ in chiral effective field theory

    Directory of Open Access Journals (Sweden)

    Filin A. A.

    2014-01-01

    Full Text Available We present the results of the pion production operator calculated up-to-and-including next-to-next-to-leading order (NNLO in chiral effective field theory. We include explicit Delta degrees of freedom and demonstrate that they provide essential contribution required to understand neutral pion production data. Analysis of chiral loops at NNLO reveals new mechanisms which are important, but haven’t been considered in phenomenological studies so far.

  5. 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 ($1-x)^{4.65 \\pm 0.68}$

  6. 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.

  7. 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.

  8. Uncertainties in next-to-leading order plus parton shower matched simulations of inclusive jet and dijet production

    Energy Technology Data Exchange (ETDEWEB)

    Höche, Stefan; Schönherr, Marek

    2012-11-01

    We quantify uncertainties in the Monte Carlo simulation of inclusive and dijet final states, which arise from using the MC@NLO technique for matching next-to-leading order parton-level calculations and parton showers. We analyse a large variety of data from early measurements at the LHC. In regions of phase space where Sudakov logarithms dominate over high-energy effects, we observe that the main uncertainty can be ascribed to the free parameters of the parton shower. In complementary regions, the main uncertainty stems from the considerable freedom in the simulation of underlying events.

  9. Next-to-leading order QCD predictions for W+2j and Z+2j production at the CERN LHC

    CERN Document Server

    Campbell, J; Rainwater, D L; Campbell, John

    2003-01-01

    We present cross sections and differential distributions for QCD radiative corrections to the QCD processes pp -> W+2j and pp -> Z+2j at the CERN LHC. Calculations are performed with the Monte Carlo program MCFM. Cross section dependence on the renormalization and factorization scales is greatly reduced, except for the heavy-flavor case of Wbb~, which has new features at next-to-leading order at the LHC. We also present cross sections for Wbb~ and Z+2j in kinematic configurations relevant for Higgs boson searches.

  10. 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.

  11. Beam Thrust Cross Section for Drell-Yan Production at Next-to-Next-to-Leading-Logarithmic Order

    International Nuclear Information System (INIS)

    Stewart, Iain W.; Tackmann, Frank J.; Waalewijn, Wouter J.

    2011-01-01

    At the LHC and Tevatron strong initial-state radiation (ISR) plays an important role. It can significantly affect the partonic luminosity available to the hard interaction or contaminate a signal with additional jets and soft radiation. An ideal process to study ISR is isolated Drell-Yan production, pp→Xl + l - without central jets, where the jet veto is provided by the hadronic event shape beam thrust τ B . Most hadron collider event shapes are designed to study central jets. In contrast, requiring τ B B s n ln m τ B corrections at next-to-next-to-leading-logarithmic order. This is the first resummation at this order for a hadron-hadron collider event shape. Measurements of τ B at the Tevatron and LHC can provide crucial tests of our understanding of ISR and of τ B 's utility as a central jet veto.

  12. Next-to-leading order QCD predictions for associated production of top squarks and charginos at the CERN LHC

    CERN Document Server

    Jin, L G

    2003-01-01

    We present the calculations of the complete next-to-leading order (NLO) inclusive total cross sections for the associated production processes pp->t sub i chi sub k sup - +X in the minimal supersymmetric standard model at the CERN Large Hadron Collider. Our calculations show that the total cross sections for the t sub 1 chi sub 1 sup - production for the lighter top squark masses in the region 100 GeV 500 GeV and the t sub 2 chi sub 2 sup - production channel. Moreover, we find that the NLO QCD corrections in general enhance the leading order total cross sections significantly, and vastly reduce the dependence of the total cross sections on the renormalization/factorization scale, which leads to increased confidence in predictions based on these results. (orig.)

  13. 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}.

  14. 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.

  15. 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.

  16. 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...

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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

  2. 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.

  3. 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)

  4. 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.)

  5. 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.)

  6. W+n-jet predictions at the Large Hadron Collider at next-to-leading order matched with a parton shower.

    Science.gov (United States)

    Höche, Stefan; Krauss, Frank; Schönherr, Marek; Siegert, Frank

    2013-02-01

    For the first time, differential cross sections for the production of W bosons in conjunction with up to three jets, computed at next-to leading order in QCD and including parton shower corrections, are presented and compared to recent experimental data from the Large Hadron Collider.

  7. Differential distributions for t-channel single top-quark production and decay at next-to-next-to-leading order in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Berger, Edmond L.; Gao, Jun; Zhu, Hua Xing

    2017-11-01

    We present a detailed phenomenological study of the next-to-next-to-leading order (NNLO) QCD corrections for t-channel single top (anti-)quark production and its semi-leptonic decay at the CERN Large Hadron Collider (LHC). We find the NNLO corrections for the total inclusive rates at the LHC with different center of mass energies are generally smaller than the NLO corrections, indicative of improved convergence. However, they can be large for differential distributions, reaching a level of 10% or more in certain regions of the transverse momentum distributions of the top (anti-)quark and the pseudo-rapidity distributions of the leading jet in the event. In all cases the perturbative hard-scale uncertainties are greatly reduced after the NNLO corrections are included. We also show a comparison of the normalized parton-level distributions to recent data from the 8 TeV measurement of the ATLAS collaboration. The NNLO corrections tend to shift the theoretical predictions closer to the measured transverse momentum distribution of the top (anti)-quark. Importantly, for the LHC at 13 TeV, we present NNLO cross sections in a fiducial volume with decays of the top quark included.

  8. Decoupling of the DGLAP evolution equations at next-to-next-to-leading order (NNLO) at low-x

    Energy Technology Data Exchange (ETDEWEB)

    Boroun, G.R.; Rezaei, B. [Razi University, Physics Department, Kermanshah (Iran, Islamic Republic of)

    2013-05-15

    We present a set of formulas to extract two second-order independent differential equations for the gluon and singlet distribution functions. Our results extend from the LO up to NNLO DGLAP evolution equations with respect to the hard-Pomeron behavior at low-x. In this approach, both singlet quarks and gluons have the same high-energy behavior at low-x. We solve the independent DGLAP evolution equations for the functions F{sub 2}{sup s}(x,Q{sup 2}) and G(x,Q{sup 2}) as a function of their initial parameterization at the starting scale Q{sub 0}{sup 2}. The results not only give striking support to the hard-Pomeron description of the low-x behavior, but give a rather clean test of perturbative QCD showing an increase of the gluon distribution and singlet structure functions as x decreases. We compared our numerical results with the published BDM (Block et al. Phys. Rev. D 77:094003 (2008)) gluon and singlet distributions, starting from their initial values at Q{sub 0}{sup 2} = 1 GeV{sup 2}. (orig.)

  9. Short-distance QCD corrections to K{sup 0}K̄{sup 0} mixingat next-to-leading order in Left-Right models

    Energy Technology Data Exchange (ETDEWEB)

    Bernard, Véronique [Groupe de Physique Théorique, Institut de Physique Nucléaire, UMR 8608, CNRS,University Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex (France); Descotes-Genon, Sébastien [Laboratoire de Physique Théorique, UMR 8627, CNRS, University Paris-Sud, Université Paris-Saclay,91405 Orsay Cedex (France); Silva, Luiz Vale [Groupe de Physique Théorique, Institut de Physique Nucléaire, UMR 8608, CNRS,University Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex (France); Laboratoire de Physique Théorique, UMR 8627, CNRS, University Paris-Sud, Université Paris-Saclay,91405 Orsay Cedex (France)

    2016-08-23

    Left-Right (LR) models are extensions of the Standard Model where left-right symmetry is restored at high energies, and which are strongly constrained by kaon mixing described in the framework of the |ΔS|=2 effective Hamiltonian. We consider the short-distance QCD corrections to this Hamiltonian both in the Standard Model (SM) and in LR models. The leading logarithms occurring in these short-distance corrections can be resummed within a rigourous Effective Field Theory (EFT) approach integrating out heavy degrees of freedom progressively, or using an approximate simpler method of regions identifying the ranges of loop momentum generating large logarithms in the relevant two-loop diagrams. We compare the two approaches in the SM at next-to-leading order, finding a very good agreement when one scale dominates the problem, but only a fair agreement in the presence of a large logarithm at leading order. We compute the short-distance QCD corrections for LR models at next-to-leading order using the method of regions, and we compare the results with the EFT approach for the WW{sup ′} box with two charm quarks (together with additional diagrams forming a gauge-invariant combination), where a large logarithm occurs already at leading order. We conclude by providing next-to-leading-order estimates for cc, ct and tt boxes in LR models.

  10. Next-to-leading order QCD corrections to Higgs boson production in association with a photon via weak-boson fusion at the LHC

    CERN Document Server

    Arnold, Ken; Jager, Barbara; Zeppenfeld, Dieter

    2010-01-01

    Higgs boson production in association with a hard central photon and two forward tagging jets is expected to provide valuable information on Higgs boson couplings in a range where it is difficult to disentangle weak-boson fusion processes from large QCD backgrounds. We present next-to-leading order QCD corrections to Higgs production in association with a photon via weak-boson fusion at a hadron collider in the form of a flexible parton-level Monte Carlo program. The QCD corrections to integrated cross sections are found to be small for experimentally relevant selection cuts, while the shape of kinematic distributions can be distorted by up to 20% in some regions of phase space. Residual scale uncertainties at next-to-leading order are at the few-percent level.

  11. Full formula for heavy quarkonium energy levels at next-to-next-to-next-to-leading order

    Directory of Open Access Journals (Sweden)

    Y. Kiyo

    2014-12-01

    Full Text Available We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers n, ℓ, s and j, up to O(αs5m and O(αs5mlog⁡αs in perturbative QCD. The QCD Bethe logarithm is given in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers (π, ζ(3, ζ(5 and finite sums (besides the 3-loop constant a¯3 of the static potential whose full analytic form is still unknown. A derivation of the formula is given.

  12. 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

  13. 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.

  14. 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.)

  15. 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.)

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

    International Nuclear Information System (INIS)

    Levi, Michele; Steinhoff, Jan

    2014-01-01

    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

  17. The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

    CERN Document Server

    Alwall, J; Frixione, S; Hirschi, V; Maltoni, F; Mattelaer, O; Shao, H -S; Stelzer, T; Torrielli, P; Zaro, M

    2014-01-01

    We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5_aMC@NLO, capable of handling all these computations -- parton-level fixed order, shower-matched, merged -- in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV $e^+e^-$ collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well un...

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

    International Nuclear Information System (INIS)

    Levi, Michele; Steinhoff, Jan

    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

  19. 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.

  20. 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%.

  1. 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.

  2. 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.

  3. Next-to-leading order QCD predictions for tγ associated production via model-independent flavor-changing neutral-current couplings at hadron colliders

    International Nuclear Information System (INIS)

    Zhang Yue; Li Bohua; Li Chongsheng; Gao Jun; Zhu Huaxing

    2011-01-01

    We present the complete next-to-leading order (NLO) QCD predictions for the tγ associated production induced by model-independent tqγ and tqg flavor-changing neutral-current (FCNC) couplings at hadron colliders, respectively. We also consider the mixing effects between the tqγ and tqg FCNC couplings for this process. Our results show that, for the tqγ couplings, the NLO QCD corrections can enhance the total cross sections by about 50% and 40% at the Tevatron and LHC, respectively. Including the contributions from the tqγ, tqg FCNC couplings and their mixing effects, the NLO QCD corrections can enhance the total cross sections by about 50% for the tuγ and tug FCNC couplings, and by about 80% for the tcγ and tcg FCNC couplings at the LHC, respectively. Moreover, the NLO corrections reduce the dependence of the total cross section on the renormalization and factorization scale significantly. We also evaluate the NLO corrections for several important kinematic distributions.

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

    International Nuclear Information System (INIS)

    Levi, Michele; Steinhoff, Jan

    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

  5. 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.

  6. 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.)

  7. 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 ...

  8. 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

  9. 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.

  10. 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

    Directory of Open Access Journals (Sweden)

    Yu Feng

    2015-01-01

    Full Text Available 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 different NLO fit results of the NRQCD long-distance matrix elements, we evaluate a theoretical uncertainty which is certainly much larger than the projected experimental uncertainties with the expected 20 fb−1 to be collected per year with AFTER@LHC for pp collision at the center of mass energy s≃115 GeV.

  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. Diphoton production at hadron colliders: transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy

    Energy Technology Data Exchange (ETDEWEB)

    Cieri, Leandro [Dipartimento di Fisica, Università di Roma “La Sapienza” andINFN - Sezione di Roma, I-00185 Rome (Italy); Coradeschi, Francesco [INFN - Sezione di Firenze and Dipartimento di Fisica,Università di Firenze, I-50019 Sesto Fiorentino, Florence (Italy); Florian, Daniel de [Departamento de Física, FCEYN, Universidad de Buenos Aires (1428) Pabellón 1 Ciudad Universitaria, Capital Federal (Argentina)

    2015-06-26

    We consider the transverse-momentum (q{sub T}) distribution of a diphoton pair produced in hadron collisions. At small values of q{sub T}, we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next-to-leading logarithmic accuracy. At intermediate and large values of q{sub T}, we consistently combine resummation with the known next-to-leading order perturbative result. All perturbative terms up to order α{sub S}{sup 2} are included in our computation which, after integration over q{sub T}, reproduces the known next-to-next-to-leading order result for the diphoton pair production total cross section. We present a comparison with LHC data and an estimate of the perturbative accuracy of the theoretical calculation by performing the corresponding variation of scales. In general we observe that the effect of the resummation is not only to recover the predictivity of the calculation at small transverse momentum, but also to improve substantially the agreement with the experimental data.

  13. Next-to-Next-to-Next-to-Leading Order QCD Prediction for the Top Antitop S-Wave Pair Production Cross Section Near Threshold in e(+)e(-) Annihilation.

    Science.gov (United States)

    Beneke, Martin; Kiyo, Yuichiro; Marquard, Peter; Penin, Alexander; Piclum, Jan; Steinhauser, Matthias

    2015-11-06

    We present the third-order QCD prediction for the production of top antitop quark pairs in electron-positron collisions close to the threshold in the dominant S-wave state. We observe a significant reduction of the theoretical uncertainty and discuss the sensitivity to the top quark mass and width.

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

    Indian Academy of Sciences (India)

    Chandra Research Institute, Jhusi, Allahabad 211 019, India; C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, New York, USA; Instituut-Lorentz, University of Leiden, The Netherlands ...

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

    Indian Academy of Sciences (India)

    V RAVINDRAN, J sMITH and W L vAn NEERVEN. Harish-Chandra Research Institute, Jhusi, ... Instituut-Lorentz, University of Leiden, Leiden, The Netherlands. Abstract. We describe the calculation of ... total inclusive cross-section substantially. The NLO corrections along with NLO parton distributions yield a large Г factor.

  16. Meson structure in the next-to-leading order

    International Nuclear Information System (INIS)

    Khorramian, A.N.; Arash, F.

    2001-01-01

    We present here a general scheme for accessing informations about the meson structure. The idea is based on calculating the structure of a constituent quark, which is common to all hadrons. The method is applied to pion and kaon as an example. While there is only a scarce data on the ratio of up-quark valence distributions of the K + and π + mesons, our model calculation nicely agrees with the data. (orig.)

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

    Indian Academy of Sciences (India)

    To obtain the proton structure function in valon model with respect to the Laguerre polynomials one needs to use an elegant and fast numerical method at LO up to NLO. Therefore, we concentrate on the Laguerre polynomials in our determinations. In the. Laguerre method [13,14], the Laguerre polynomials are defined as.

  18. 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.

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

    Indian Academy of Sciences (India)

    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. DOI: 10.1007/s12043-015-0980-1; ePublication: 25 July 2015. Abstract.

  20. 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

  1. Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation

    CERN Document Server

    Cacciari, Matteo; Mangano, Michelangelo L; Mitov, Alexander; Nason, Paolo

    2012-01-01

    Incorporating all recent theoretical advances, we resum soft-gluon corrections to the total $t\\bar t$ cross-section at hadron colliders at the next-to-next-to-leading logarithmic (NNLL) order. We perform the resummation in the well established framework of Mellin $N$-space resummation. We exhaustively study the sources of systematic uncertainty like renormalization and factorization scale variation, power suppressed effects and missing two- and higher-loop corrections. The inclusion of soft-gluon resummation at NNLL brings only a minor decrease in the perturbative uncertainty with respect to the NLL approximation, and a small shift in the central value, consistent with the quoted uncertainties. These numerical predictions agree with the currently available measurements from the Tevatron and LHC and have uncertainty of similar size. We conclude that significant improvements in the $t\\bar t$ cross-sections can potentially be expected only upon inclusion of the complete NNLO corrections.

  2. 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.

  3. 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.

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

    Science.gov (United States)

    Del Duca, V.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C. D.

    2017-11-01

    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 relies on a recently derived factorisation formula for NLP threshold effects at amplitude level, and therefore applies both if the leading-order process is tree-level and if it is loop-induced. It holds for differential distributions as well. The results can furthermore be seen as applications of recently derived next-to-soft theorems for gauge theory amplitudes. We use our universal expression to re-derive known results for the production of up to three Higgs bosons at NLO in the large top mass limit, and for the hadro-production of a pair of electroweak gauge bosons. Finally, we present new analytic results for Higgs boson pair production at NLO and NLP, with exact top-mass dependence.

  5. Higher order corrections in perturbative quantum chromodynamics

    Indian Academy of Sciences (India)

    to compute Feynman graphs beyond one-loop order. These techniques are useful to compute the three-loop splitting functions in QCD and to obtain the complete second order QED corrections to. Bhabha scattering. Keywords. Quantum chromodynamics; perturbation theory; higher order. PACS Nos 12.38.-t; 12.38.

  6. 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.

  7. 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)

  8. 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.

  9. 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.

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

    Indian Academy of Sciences (India)

    Therefore, it is of paramount importance to measure this parameter to the best possible ... the experimental uncer- tainty, one need to take into account the theoretical uncertainty on such a fundamental ... to the higher moments of 1 − T. the scale uncertainty as the dominant theoretical error on the precise determination of αs.

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

    Directory of Open Access Journals (Sweden)

    M. Hentschinski

    2014-10-01

    Full Text Available 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.

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

    Indian Academy of Sciences (India)

    QCD) correc- tion to the first three moments of the four event-shape variables in electron–positron annihilation, the thrust, heavy jet mass, wide, and total jet broadening, is computed. It is observed that the NNLO correction gives a better ...

  13. 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 ...

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. Pyflation: Second Order Perturbations During Inflation Beyond Slow-roll

    Science.gov (United States)

    Huston, Ian

    2011-03-01

    Pyflation calculates cosmological perturbations during an inflationary expansion of the universe. The modules in the pyflation Python package can be used to run simulations of different scalar field models of the early universe. The main classes are contained in the cosmomodels module and include simulations of background fields and first order and second order perturbations. The sourceterm package contains modules required for the computation of the term required for the evolution of second order perturbations. Alongside the Python package, the bin directory contains Python scripts which can run first and second order simulations. A helper script called pyflation-qsubstart.py sets up a full second order run (including background, first order and source calculations) to be used on queueing system which contains the qsub executable (e.g. a Rocks cluster).

  19. 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.

  20. 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.

  1. Stochastic systems with delay: Perturbation theory for second order statistics

    Energy Technology Data Exchange (ETDEWEB)

    Frank, T.D., E-mail: till.frank@uconn.edu

    2016-03-24

    Within the framework of delay Fokker–Planck equations, a perturbation theoretical method is developed to determine second-order statistical quantities such as autocorrelation functions for stochastic systems with delay. Two variants of the perturbation theoretical approach are presented. The first variant is based on a non-local Fokker–Planck operator. The second variant requires to solve a Fokker–Planck equation with source term. It is shown that the two variants yield consistent results. The perturbation theoretical approaches are applied to study negative autocorrelations that are induced by feedback delays and mediated by the strength of the fluctuating forces that act on the feedback systems. - Highlights: • A perturbation theory for stochastic delay systems is presented. • The perturbation theory yields second order statistical quantities. • The theory is developed within the framework of delay Fokker–Planck equations. • The effective Fokker–Planck operator is a non-local operator in space. • Negative autocorrelations can be induced by time-delayed feedback.

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

    Science.gov (United States)

    Ghobadi, Ahmadreza F; Elliott, J Richard

    2015-09-21

    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., A3/A2, 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).

  3. 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.

  4. Cosmological perturbation theory at three-loop order

    CERN Document Server

    Blas, Diego; Konstandin, Thomas

    2014-01-01

    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.

  5. 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.

  6. Higher orders of the perturbation theory and summation of perturbational series in quantum mechanics

    International Nuclear Information System (INIS)

    Popov, V.S.; Weinberg, V.M.

    1982-01-01

    Calculation of higher orders of the perturbation theory is considered for screened Coulomb potentials. Particular cases of such potentials are the Yukawa potential, a familiar object of nuclear physics, and the funnel-shaped potential, applied to analysis of heavy quark-antiquark systems. The calculation of higher perturbational orders is reduced to recursive relations, quite appropriate for computer. The Pade approximants and a modified Pade-Borel summation method are applied for calculation of sums of diverging PT series. It is shown that in the considered problems higher orders of the PT determine the behaviour of E(g) in the region of strong coupling (Esub(g)-the energy of eigen-value)

  7. Symbolic summation and higher orders in perturbation theory

    International Nuclear Information System (INIS)

    Moch, S.

    2005-08-01

    Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms. Examples such as the non-planar vertex at two loops, or integrals from the recent calculation of the three-loop QCD corrections to structure functions in deep-inelastic scattering are given. (orig.)

  8. 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

  9. 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.

  10. 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.

  11. Jet-veto in bottom-quark induced Higgs production at next-to-next-to-leading order

    CERN Document Server

    Harlander, Robert

    2012-01-01

    We present results for associated Higgs+n-jet production in bottom quark annihilation, for n=0 and n>=1 at NNLO and NLO accuracy, respectively. We consider both the cases with and without b-tagging. Numerical results are presented for parameters relevant for experiments at the LHC.

  12. 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).

  13. Linear sigma model at finite density in the 1/N expansion to next-to-leading order

    Czech Academy of Sciences Publication Activity Database

    Andersen, J. O.; Brauner, Tomáš

    2008-01-01

    Roč. 78, č. 1 (2008), 014030/1-014030/12 ISSN 0167-2789 R&D Projects: GA ČR GA202/06/0734 Institutional research plan: CEZ:AV0Z10480505 Keywords : 1/N expansion * Bose -Einstein condensation * Linear sigma model Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.926, year: 2008

  14. 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)

  15. CMB anisotropies at second order III: bispectrum from products of the first-order perturbations

    CERN Document Server

    Nitta, Daisuke; Bartolo, Nicola; Matarrese, Sabino; Riotto, Antonio

    2009-01-01

    We calculate the bispectrum of the Cosmic Microwave Background (CMB) temperature anisotropies induced by the second-order fluctuations in the Boltzmann equation. In this paper, which is one of a series of papers on the numerical calculation of the bispectrum from the second-order fluctuations, we consider the terms that are products of the first-order perturbations, and leave intrinsically second-order terms and perturbations in the recombination history to the subsequent papers. We show that the bispectrum has the maximum signal in the squeezed triangles, similar to the local-type primordial bispectrum, as both types generate non-linearities via products of the first-order terms in position space. However, detailed calculations show that their shapes are sufficiently different: the cross-correlation coefficient reaches 0.5 at the maximum multipole of l_{max}~ 200, and then weakens to 0.3 at l_{max}~ 2000. The differences in shape arise from (i) the way the acoustic oscillations affect the bispectrum, and (ii...

  16. 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.)

  17. High order singular rank one perturbations of a positive operator

    NARCIS (Netherlands)

    Dijksma, A.; Kurasov, P.; Shondin, Yu.

    2005-01-01

    In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression Lα = L + α〈·, φ〉φ are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space H with inner product 〈· ,·〉, α is a real parameter, and φ in the rank one perturbation is a

  18. 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

  19. 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)

  20. Perturbative calculations with the first order form of gauge theories

    Science.gov (United States)

    Brandt, F. T.; McKeon, D. G. C.

    2015-05-01

    The first- and second-order forms of gauge theories are classically equivalent; we consider the consequence of quantizing the first-order form using the Faddeev-Popov approach. Both the Yang-Mills and the Einstein-Hilbert actions are considered. An advantage of this approach is that the interaction vertices are quite simple, being independent of momenta. However, it is necessary to consider the propagator for two fields (including a mixed propagator). We derive the Feynman rules for both models and consider the one-loop correction for the thermal energy momentum tensor.

  1. 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.

  2. Protein-induced bilayer perturbations: Lipid ordering and hydrophobic coupling

    International Nuclear Information System (INIS)

    Petersen, Frederic N.R.; Laursen, Ib; Bohr, Henrik; Nielsen, Claus Helix

    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 A results in up to 10-fold increased exchange rates as compared to the 'optimal' match situation pointing to the regulatory role of hydrophobic coupling in lipid-protein interactions.

  3. Determination of the QCD scale parameter. Lambda. sub MS with QCD cascade on the basis of the next-to-leading logarithmic approximation

    Energy Technology Data Exchange (ETDEWEB)

    Abe, K. (Tohoku Univ., Sendai (Japan). Dept. of Physics); Amako, K.; Arai, Y.; Fukawa, M.; Fukushima, Y.; Haidt, D.; Ishihara, N.; Kamitani, T.; Kanzaki, J.; Kondo, T.; Matsui, T.; Odaka, S.; Ogawa, K.; Ohama, T.; Sakamoto, H.; Sakuda, M.; Shirai, J.; Sumiyoshi, T.; Takasaki, F.; Tsuboyama, T.; Uehara, S.; Unno, Y.; Watase, Y.; Yamada, Y. (National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan)); Asano, Y.; Koseki, T.; Mori, S.; Sakano, M.; Shirakata, M.; Takada, Y.; Yonezawa, Y. (Tsukuba Univ., Sakura, Ibaraki (Japan). Inst. of Applied Physics); Chiba, M.; Fukui, T.; Hirose, T.; Minami, M.; Narita, Y.; Oyama, T.; Saito, H.; Utsumi, M.; Wakai, M.; Watanabe, T.; Yabuki, F.; Yamagata, T. (Tokyo Metropolitan Univ. (Japan). Dept. of Physics); Chiba, Y.; Hayashibara, I.; Ohsugi, T.; Taketani, A.; Tanaka, R.; Terunuma, N. (Hiroshima Univ. (Japan)); Daigo, M. (Wakayama Medical Coll. (Japan)); Emura, T. (Tokyo Univ. of Agriculture and Technology, Koganei (Japan)); Haba, J.; Kane; VENUS Collaboration

    1990-04-19

    The relative production ratio of 3-jet events to the total number of hadronic events was studied in e{sup +}e{sup -} annihilations at centre-of-mass energies between 54 and 61.4 GeV. The QCD scale parameter has been determined to be {Lambda}{sub MS}=254{sub -47}{sup +55}{plus minus}56 MeV on the basis of a QCD cascade with the next-to-leading logarithmic approximation. (orig.).

  4. 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

  5. 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.)

  6. Existence of Infinitely Many Periodic Solutions for Perturbed Semilinear Fourth-Order Impulsive Differential Inclusions

    Directory of Open Access Journals (Sweden)

    Massimiliano Ferrara

    2016-01-01

    Full Text Available This paper discusses the existence of infinitely many periodic solutions for a semilinear fourth-order impulsive differential inclusion with a perturbed nonlinearity and two parameters. The approach is based on a critical point theorem for nonsmooth functionals.

  7. Calculation of molecular response properties with the second-order coupled perturbed electron propagator

    Energy Technology Data Exchange (ETDEWEB)

    Deleuze, M.S.; Pickup, B.T.; Wilton, D.J.

    2000-04-05

    The authors present the theory of the electron propagator perturbed by an external electric field and show how it can be used to calculate a variety of one-electron linear response properties that are accurate through second order in electron correlation. Some illustrative calculations are discussed.

  8. Large-order estimates in perturbative QCD and non-borel summable series

    International Nuclear Information System (INIS)

    Fischer, J.

    1994-01-01

    Basic facts about the summation of divergent power series are reviewed, both for series with non vanishing and for series with vanishing convergence radius. Particular attention is paid to the recent development that makes it possible, in the former case, to define summation in the whole Mittag-Leffler star and, in the latter case, to define summation when the point of expansion lies at the tip of a horn-shaped analyticity domain with zero opening angle. Relevance of these results to perturbative QCD is stressed in relation to current discussions concerning large-order estimates of perturbative QCD expansion coefficients. (orig.)

  9. Symmetric Wilson Loops beyond leading order

    Directory of Open Access Journals (Sweden)

    Xinyi Chen-Lin

    2016-12-01

    Full Text Available We study the circular Wilson loop in the symmetric representation of U(N in $\\mathcal{N} = 4$ super-Yang-Mills (SYM. In the large N limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests non-perturbative physics in the dual holographic theory. We also computed the next-to-leading order term in 1/N, and the result matches with the exact result from the k-fundamental representation.

  10. 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

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

    Directory of Open Access Journals (Sweden)

    Davies Christine

    2018-01-01

    Full Text Available 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.

  12. 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.)

  13. 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.

  14. Convergence analysis of homotopy perturbation method for Volterra integro-differential equations of fractional order

    Directory of Open Access Journals (Sweden)

    K. Sayevand

    2013-12-01

    Full Text Available Based on the homotopy perturbation method (HPM, a general analytical approach for obtaining approximate series solutions to Volterra integro-differential equations of fractional order is proposed. The approximate solutions are calculated in the form of a convergent series with easily computable components. In this paper, the uniqueness of the obtained solution and the convergence properties of the approach are studied. Some examples are presented, to verify convergence, and illustrating the efficiency and simplicity of the approach.

  15. Uniform ergodicities and perturbation bounds of Markov chains on ordered Banach spaces

    Science.gov (United States)

    Erkursun Özcan, Nazife; Mukhamedov, Farrukh

    2017-03-01

    In this paper, we consider uniformly mean ergodic and uniformly asymptotical stable Markov operators on ordered Banach spaces. In terms of the ergodicity coefficient, we show the equivalence of uniform and weak mean ergodicities of Markov operators. This result allowed us to establish a category theorem for uniformly mean ergodic Markov operators. Furthermore, using properties of the ergodicity coefficient, we develop the perturbation theory for uniformly asymptotical stable Markov chains in the abstract scheme.

  16. Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

    Science.gov (United States)

    Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

    2017-09-01

    In this paper, we investigate two stochastic SIR epidemic models with higher order perturbation. For the nonautonomous periodic case of the model, by using Has'minskii's theory of periodic solution, we show that the system has at least one nontrivial positive T-periodic solution. For the system disturbed by both the white noise and telephone noise, we establish sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the positive solution.

  17. 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.)

  18. 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

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. Kaon-nucleon scattering to one-loop order in heavy baryon chiral perturbation theory

    Science.gov (United States)

    Huang, Bo-Lin; Li, Yun-De

    2015-12-01

    We calculate the T matrices of kaon-nucleon (K N ) and antikaon-nucleon (K ¯N ) scattering to one-loop order in SU(3) heavy baryon chiral perturbation theory (HB χ PT ). The low-energy constants (LECs) and their combinations are then determined by fitting the phase shifts of K N scattering and the corresponding data. This leads to a good description of the phase shifts below 200 MeV kaon laboratory momentum. We obtain the LEC uncertainties through statistical regression analysis and successfully reduce one parameter. We also determine the LECs through the use of scattering lengths in order to check the consistency of the HB χ PT framework for different observables and obtain a consistent result. By using these LECs, we predict the K ¯N elastic scattering phase shifts and obtain reasonable results. The scattering lengths are also predicted, which turn out to be in good agreement with the empirical values except for the isospin-0 K ¯N scattering length that is strongly affected by the Λ (1405 ) resonance. As most calculations in the chiral perturbation theory, the convergence issue is discussed in detail. Our calculations provide a possibility to investigate the baryon-baryon interaction in HB χ PT .

  5. Higher-order perturbative corrections to b --> c transitions at zero recoil

    CERN Document Server

    Neubert, M

    1995-01-01

    We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currents \\bar c\\,\\gamma^\\mu b and \\bar c\\,\\gamma^\\mu\\gamma_5\\,b by calculating the terms of order n_f\\,\\alpha_s^2 and substituting the dependence on the number of flavours by the first coefficient of the \\beta-function. Both for vector and axial vector currents, we find moderate two-loop corrections below 1\\% in magnitude. Using the Brodsky--Lepage--Mack enzie prescription to set the scale in the order-\\alpha_s corrections in the \\overline{\\rm MS} scheme, we obtain \\mu_V\\simeq 0.92\\sqrt{m_b m_c} and \\mu_A\\simeq 0.51\\sqrt{m_b m_c} in the two cases. These scales are sufficiently large for perturbation theory to be well-behaved. The implications of our results to the extraction of |\\, V_{cb}| are briefly discussed.

  6. 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.

  7. 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

  8. A path crossing lemma and applications to nonlinear second order equations under slowly varyng perturbations

    Directory of Open Access Journals (Sweden)

    Anna Pascoletti

    2010-12-01

    Full Text Available We present some recent results on the existence of periodic solutions and chaotic like dynamics for second order scalar nonlinear ODEs. The equations under consideration belong to a simple class of perturbed planar Hamiltonian systems with slowly varying periodic coefficients, a typical example being given by the pendulum equation with moving support. Although there is already a broad literature on this subject, our approach, based on the concept of stretching along the paths, appears new in this context. In particular, our method is global in nature and stable with respect to small perturbations of the coefficients. Thus it applies even when some small friction terms are inserted into the equations. The main tool on which all our results are based is a topological lemma (that we call path crossing lemma which was already implicitly used by Poincaré (1883-1884 [51], as well as by Butler (1976 [8] and Conley (1975 [12] and subsequently “rediscovered” and applied in many different contexts. For this reason, the first part of this paper is devoted to a detailed exposition of the Crossing Lemma and its connections with other topological results.

  9. 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.

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

    Science.gov (United States)

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

    2012-11-01

    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 mEh of the correct values after 108 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.

  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. Azimuthal decorrelations between QCD jets at all orders

    Energy Technology Data Exchange (ETDEWEB)

    Banfi, A. [Universita degli studi di Milano-Bicocca and INFN, Sezione di Milano-Bicocca (Italy)], E-mail: andrea.banfi@mib.infn.it; Dasgupta, M. [School of Physics and Astronomy, University of Manchester, Manchester M13 9PL (United Kingdom); Delenda, Y. [Department de Physique, Faculte des Sciences, Universite de Batna (Algeria)

    2008-07-17

    A quantity that promises to reveal important information on perturbative and non-perturbative QCD dynamics is the azimuthal decorrelation between jets in different hard processes. In order to access this information fixed-order NLO predictions need to be supplemented by resummation of logarithmic terms which are large in the region where the jets are nearly back-to-back in azimuth. In the present Letter we carry out this resummation to next-to-leading logarithmic accuracy explaining the important role played by the recombination scheme in general resummations for such jet observables.

  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. 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.)

  16. 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.

  17. 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.

  18. 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

  19. Dhage Iteration Method for Nonlinear First Order Hybrid Differential Equations with a Linear Perturbation of Second Type

    Directory of Open Access Journals (Sweden)

    B.C. Dhage

    2016-08-01

    Full Text Available In this paper the authors prove algorithms for the existence and approximation of the solutions for an initial and a periodic boundary value problem of nonlinear first order ordinary hybrid differential equations with a linear perturbation of second type via Dhage iteration method. Examples are furnished to illustrate the hypotheses and main abstract results of this paper.

  20. Dhage Iteration Method for Nonlinear First Order Hybrid Differential Equations with a Linear Perturbation of Second Type

    OpenAIRE

    B.C. Dhage

    2016-01-01

    In this paper the authors prove algorithms for the existence and approximation of the solutions for an initial and a periodic boundary value problem of nonlinear first order ordinary hybrid differential equations with a linear perturbation of second type via Dhage iteration method. Examples are furnished to illustrate the hypotheses and main abstract results of this paper.

  1. Second-order many-body perturbation study of solid hydrogen fluoride under pressure.

    Science.gov (United States)

    Sode, Olaseni; Hirata, So

    2012-06-07

    A linear-scaling, embedded-fragment, second-order many-body perturbation (MP2) method with basis sets up to aug-cc-pVTZ is applied to the antiparallel structure of solid hydrogen fluoride and deuterium fluoride under 0-20 GPa of ambient pressure. The optimized structures, including the lattice parameters and molar volume, and phonon dispersion as well as phonon density of states (DOS), are determined as a function of pressure. The basis-set superposition errors are removed by the counterpoise correction. The structural parameters at 0 GPa calculated by MP2 agree accurately with the observed, making the predicted values at higher pressures a useful pilot for future experiments. The corresponding values obtained by the Hartree-Fock method have large, systematic errors. The MP2/aug-cc-pVDZ frequencies of the infrared- and Raman-active vibrations of the three-dimensional solids are in good agreement with the observed and also justify previous vibrational analyses based on one-dimensional chain models; the non-coincidence of the infrared and Raman mode pairs can be explained as factor-group (Davydov) splitting. The exceptions are one pair of modes in the librational region, for which band assignments based on a one-dimensional chain model need to be revised, as well as the five pseudo-translational modes that exist only in a three-dimensional treatment. The observed pressure dependence of Raman bands in the stretching region, which red-shift with pressure, is accounted for by theory only qualitatively, while that in the pseudo-translational region is reproduced with quantitative accuracy. The present calculation proves to be limited in explaining the complex pressure dependence of the librational modes. The hydrogen-amplitude-weighted phonon DOS at 0 GPa is much less structured than the DOS obtained from one-dimensional models and may be more realistic in view of the also broad, structureless observed inelastic neutron scattering spectra. All major observed peaks can be

  2. Thermodynamic Perturbation Theory of the Second-Order: Implementation for Models with Double-Bonded Sites

    Czech Academy of Sciences Publication Activity Database

    Vlček, Lukáš; Slovák, Jan; Nezbeda, Ivo

    2003-01-01

    Roč. 101, č. 18 (2003), s. 2921-2927 ISSN 0026-8976 R&D Projects: GA AV ČR IAA4072303 Institutional research plan: CEZ:AV0Z4072921 Keywords : perturbation theory * methanol * water Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.591, year: 2003

  3. Optimization of QCD perturbation theory: Results for R{sub e{sup +}e{sup -}} at fourth order

    Energy Technology Data Exchange (ETDEWEB)

    Stevenson, P.M., E-mail: stevenson@physics.rice.edu [T.W. Bonner Laboratory, Department of Physics and Astronomy, Rice University, Houston, TX 77251 (United States)

    2013-03-01

    Physical quantities in QCD are independent of renormalization scheme (RS), but that exact invariance is spoiled by truncations of the perturbation series. 'Optimization' corresponds to making the perturbative approximant, at any given order, locally invariant under small RS changes. A solution of the resulting optimization equations is presented. It allows an efficient algorithm for finding the optimized result. Example results for R{sub e{sup +}e{sup -}}=3 N-Ary-Summation q{sub i}{sup 2}(1+R) to fourth order (NNNLO) are given that show nice convergence, even down to arbitrarily low energies. The Q=0 'freezing' behavior, R=0.3{+-}0.3, found at third order is confirmed and made more precise; R=0.2{+-}0.1. Low-energy results in the MS{sup Macron} scheme, by contrast, show the typical pathologies of a non-convergent asymptotic series.

  4. 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.

  5. 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

  6. An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Hannon, Kevin P.; Li, Chenyang; Evangelista, Francesco A., E-mail: francesco.evangelista@emory.edu [Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322 (United States)

    2016-05-28

    We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller–Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (Δ{sub ST}) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the Δ{sub ST} values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.

  7. 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

  8. 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.

  9. All order I.R. finite expansion for short distance behavior of massless theories perturbed by a relevant operator

    Energy Technology Data Exchange (ETDEWEB)

    Guida, R. [Genova Univ. (Italy). Dipartimento di Fisica; Magnoli, N. [Genova Univ. (Italy). Dipartimento di Fisica]|[Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Via Dodecaneso 33, 16146 Genoa (Italy)

    1996-07-08

    We consider here renormalizable theories without relevant couplings and present an I.R. consistent technique to study corrections to short distance behavior (Wilson O.P.E. coefficients) due to a relevant perturbation. Our method is the result of a complete reformulation of recent works on the field, and is characterized by a more orthodox treatment of U.V. divergences that allows for simpler formulae and consequently an explicit all order (regularization invariant) I.R. finiteness proof. Underlying hypotheses are discussed in detail and found to be satisfied in conformal theories that constitute a natural field of application of this approach. (orig.).

  10. 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.)

  11. On periodic boundary value problems of first-order perturbed impulsive differential inclusions

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2004-06-01

    Full Text Available In this paper we present an existence result for a first order impulsive differential inclusion with periodic boundary conditions and impulses at the fixed times under the convex condition of multi-functions.

  12. 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

  13. The chaos and order in human ECG under the influence of the external perturbations

    Science.gov (United States)

    Ragulskaya, Maria; Valeriy, Pipin

    The results of the many-year telecommunication heliomedical monitoring "Heliomed" show, that space weather and geophysical factor variations serve as a training factor for the adaptation-resistant member of the human population. Here we discuss the specific properties of the human ECG discovered in our experiment. The program "Heliomed" is carried out simultaneously at the different geographical areas that cover the different latitudes. The daily registered param-eters include: the psycho-emotional tests and the 1-st lead ECG, the arterial pressure, the variability cardiac contraction, the electric conduction of bioactive points on skin. The results time series compared with daily values of space weather and geomagnetic parameters. The analysis of ECG signal proceeds as follows. At first step we construct the ECG embedding into 3D phase space using the first 3 Principal Components of the ECG time series. Next, we divide ECG on the separate cycles using the maxima of the ECG's QRS complex. Then, we filter out the non-typical ECG beats by means of the Housdorff distance. Finally, we average the example of the ECG time series along the reference trajectory and study of the dynamical characteristics of the averaged ECG beat. It is found, that the ECG signal embeded in 3D phase space can be considered as a mix of a few states. At the rest, the occurrence of the primary ECG state compare to additional ones is about 8:2. The occurrence of the primary state increases after the stress. The main effect of the external perturbation is observed in structural change of the cardio-cycle and not in the variability of the R-R interval. The num-ber of none-typical cycles increase during an isolated magnetic storm. At the all monitoring centers participating experiment the same type of changes in the cardiac activity parameters is detected to go nearly simultaneously during an isolated magnetic storm. To understand the origin of the standard cardio-cycle changes we use the dynamical

  14. 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

  15. 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.

  16. 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

  17. 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.

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

    Energy Technology Data Exchange (ETDEWEB)

    Mereghetti, E., E-mail: emanuele@physics.arizona.ed [Department of Physics, University of Arizona, Tucson, AZ 85721 (United States); Vries, J. de [KVI, Theory Group, University of Groningen 9747 AA Groningen (Netherlands); Hockings, W.H. [Department of Mathematics and Natural Sciences, Blue Mountain College, Blue Mountain, MS 38610 (United States); Maekawa, C.M. [Instituto de Matematica, Estatistica e Fisica, Universidade Federal do Rio Grande, Campus Carreiros, PO Box 474, 96201-900 Rio Grande, RS (Brazil); Kolck, U. van [Department of Physics, University of Arizona, Tucson, AZ 85721 (United States)

    2011-01-24

    The electric dipole form factor (EDFF) of the nucleon stemming from the QCD {theta}-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, non-analytic contribution from the pion cloud. In the case of the {theta}-bar term, the expected lower bound on the deuteron electric dipole moment is |d{sub d}|{>=}1.4.10{sup -4{theta}}-bar 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.

  19. A Possible Generalization of Acoustic Wave Equation Using the Concept of Perturbed Derivative Order

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2013-01-01

    Full Text Available The standard version of acoustic wave equation is modified using the concept of the generalized Riemann-Liouville fractional order derivative. Some properties of the generalized Riemann-Liouville fractional derivative approximation are presented. Some theorems are generalized. The modified equation is approximately solved by using the variational iteration method and the Green function technique. The numerical simulation of solution of the modified equation gives a better prediction than the standard one.

  20. On the Aubin Property of Critical Points to Perturbed Second-Order Cone Programs

    Czech Academy of Sciences Publication Activity Database

    Outrata, Jiří; Ramírez, H. C.

    2011-01-01

    Roč. 21, č. 3 (2011), s. 798-823 ISSN 1052-6234 R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : second-order cone programming * strong regularity * Aubin property Subject RIV: BA - General Mathematics Impact factor: 1.629, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/outrata-0364167.pdf

  1. 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

  2. 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.

  3. 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

    2017-12-07

    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.

  4. 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.

  5. Quarkonium spectroscopy and perturbative QCD massive quark-loop effects

    CERN Document Server

    Brambilla, Nora; Vairo, Antonio

    2002-01-01

    We study the spectra of the bottomonium and B_c states within perturbative QCD up to order alpha_s^4. The O(Lambda_QCD) renormalon cancellation between the static potential and the pole mass is performed in the epsilon-expansion scheme. We extend our previous analysis by including the effects of non-zero charm-quark mass in loops up to the next-to-leading non-vanishing order epsilon^3. An extensive quantitative analysis is provided. Qualitatively the effect of the charm mass is to widen the level spacings and the effect becomes larger among higher levels. The size of non-perturbative and higher order contributions is discussed by comparing the obtained predictions with the experimental data. An agreement of the perturbative predictions and the experimental data depends crucially on the precise value (inside the present error) of alpha_s(M_Z). For the b-quark MSbar mass we obtain $m_b^{\\overline{MS}}(m_b^{\\overline{MS}}) = 4190 \\pm 20 \\pm 25 \\pm 4 ~ {MeV}$.

  6. Self-consistent second-order Green’s function perturbation theory for periodic systems

    International Nuclear Information System (INIS)

    Rusakov, Alexander A.; Zgid, Dominika

    2016-01-01

    Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green’s function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear as promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green’s function (GF2) method, where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in k-space are the key components of a computationally feasible algorithm. We apply this technique to the one-dimensional hydrogen lattice — a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases

  7. 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.

  8. Quantum mechanical/molecular mechanical/continuum style solvation model: Second order Møller-Plesset perturbation theory

    International Nuclear Information System (INIS)

    Thellamurege, Nandun M.; Si, Dejun; Cui, Fengchao; Li, Hui

    2014-01-01

    A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant

  9. Exact third-order density perturbation and one-loop power spectrum in general dark energy models

    Directory of Open Access Journals (Sweden)

    Seokcheon Lee

    2014-09-01

    Full Text Available Under the standard perturbation theory (SPT, we obtain the fully consistent third-order density fluctuation and kernels for the general dark energy models without using the Einstein–de Sitter (EdS universe assumption for the first time. We also show that even though the temporal and spatial components of the SPT solutions cannot be separable, one can find the exact solutions to any order in general dark energy models. With these exact solutions, we obtain the less than % error correction of one-loop matter power spectrum compared to that obtained from the EdS assumption for k=0.1 hMpc−1 mode at z=0(1,1.5. Thus, the EdS assumption works very well at this scale. However, if one considers the correction for P13, the error is about 6 (9, 11% for the same mode at z=0(1,1.5. One absorbs P13 into the linear power spectrum in the renormalized perturbation theory (RPT and thus one should use the exact solution instead of the approximation one. The error on the resummed propagator N of RPT is about 14 (8, 6% at z=0(1,1.5 for k=0.4 hMpc−1. For k=1 hMpc−1, the error correction of the total matter power spectrum is about 3.6 (4.6, 4.5% at z=0(1,1.5. Upcoming observation is required to archive the sub-percent accuracy to provide the strong constraint on the dark energy and this consistent solution is prerequisite for the model comparison.

  10. Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of nonrelativistic fermions in one dimension

    Science.gov (United States)

    Loheac, Andrew C.; Drut, Joaquín E.

    2017-05-01

    We analyze the pressure and density equations of state of unpolarized nonrelativistic fermions at finite temperature in one spatial dimension with contact interactions. For attractively interacting regimes, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo results (there is no sign problem in this regime), and demonstrate agreement with real Langevin calculations. For repulsive interactions, we present lattice perturbation theory results as well as complex Langevin calculations, with a modified action to prevent uncontrolled excursions in the complex plane. Although perturbation theory is a common tool, our implementation of it is unconventional; we use a Hubbard-Stratonovich transformation to decouple the system and automate the application of Wick's theorem, thus generating the diagrammatic expansion, including symmetry factors, at any desired order. We also present an efficient technique to tackle nested Matsubara frequency sums without relying on contour integration, which is independent of dimension and applies to both relativistic and nonrelativistic systems, as well as all energy-independent interactions. We find exceptional agreement between perturbative and nonperturbative results at weak couplings, and furnish predictions based on complex Langevin at strong couplings. We additionally present perturbative calculations of up to the fifth-order virial coefficient for repulsive and attractive couplings. Both the lattice perturbation theory and complex Langevin formalisms can easily be extended to a variety of situations including polarized systems, bosons, and higher dimension.

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

    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, Berkely, CA (United States); Hornig, Andrew [Washington Univ., Seattle, WA (United States). Dept. of Physics; Tackmann, Frank J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie

    2013-05-15

    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 {alpha}{sub s} at both small and large jet resolution scales. Results for e{sup +}e{sup -}{yields}jets compared to LEP data and pp{yields}(Z/{gamma}{sup *}{yields}l{sup +}l{sup -})+jets are presented.

  12. 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.

  13. 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.

  14. 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.

  15. Variational collapse of the optimized effective potential method with an orbital-dependent exchange-correlation functional based on second order perturbation theory

    NARCIS (Netherlands)

    Rohr, D.; Gritsenko, O.V.; Baerends, E.J.

    2006-01-01

    It is well known, that second-order perturbation theory (PT2) breaks down when the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied MO (LUMO) becomes too low. It is demonstrated that when the local Kohn-Sham (KS) potential v

  16. 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

  17. 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...

  18. 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.

  19. 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.)

  20. Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks

    DEFF Research Database (Denmark)

    Bernardoni, F.; Blossier, B.; Bulava, J.

    2014-01-01

    We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on Nf=2 gauge field ensembles, covering three l...... limits. Our final results read fB=186(13)MeV, fBs=224(14)MeV and fBs/fB=1.203(65). A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible....

  1. H+H- interaction up to higher orders of perturbation theory in the model with two Higgs doublets (Lagrangian and one-loop amplitudes)

    International Nuclear Information System (INIS)

    Dvoeglazov, V.V.; Skachkov, N.B.

    1991-01-01

    The one-loop amplitude of the Higgs-Higgs interaction is calculated in the fourth order of perturbation theory in the framework of the model with two Higgs doublets and an arbitrary number of fermions. The Lagrangian of this interaction is taken without any approximations. The vertex coupling constants like f 3H , f HHV , etc., are taken as given by the minimal SUSY extension of the Standard Model. 7 refs.; 1 fig

  2. Canard solution and its asymptotic approximation in a second-order nonlinear singularly perturbed boundary value problem with a turning point

    Science.gov (United States)

    Shen, Jianhe; Han, Maoan

    2014-08-01

    This paper considers the existence and uniformly valid asymptotic approximation of canard solutions in a second-order nonlinear singularly perturbed boundary value problem with a turning point. We get the main results by constructing the asymptotic solution first and then defining a couple of upper and lower solutions suitably on the basis of the asymptotic solution. Two examples are carried out to illustrate and verify the theoretical results.

  3. 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

  4. Conformal invariance of curvature perturbation

    CERN Document Server

    Gong, Jinn-Ouk; Park, Wan Il; Sasaki, Misao; Song, Yong-Seon

    2011-01-01

    We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation slicing, where all perturbations are again conformally invariant to all perturbation orders. We apply this result to the delta N formalism, and show its conformal invariance.

  5. Generalizing the bra state in the symmetry-adapted cluster singles and doubles method and the second-order perturbation correction

    Science.gov (United States)

    Hasegawa, Jun-ya; Obata, Akihiro; Matsuda, Kenji

    2010-02-01

    We present a procedure to overcome the quasi-degeneracy problem in the CCSD and SACSD methods. A multi-configuration bra state in the SACSD equations (MRbra-SACSD equation) together with a second-order perturbation correction gives quantitatively correct potential curves for bond dissociations. The benchmark results for HF, F 2, and H 2O show that the perturbative triple correction reduces the deviations from Full-CI energies to within 3 mHartree (1.9 kcal/mol). Within the benchmark calculations, the results of the present method are comparable with the recent post-CCSD corrections, the CR-CCSD(T) and CCSD(2) T methods, and are slightly less accurate than the CR-CC(2,3) method.

  6. 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.

  7. 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.)

  8. 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.

  9. 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

  10. 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.

  11. Higher-order QCD effects for associated WH production and decay at the LHC

    Energy Technology Data Exchange (ETDEWEB)

    Ferrera, Giancarlo [Dipartimento di Fisica, Università di Milano and INFN - Sezione di Milano,via Celoria 16, I-20133 Milan (Italy); Grazzini, Massimiliano [Institut für Theoretische Physik, Universität Zürich,Winterthurerstrasse 190, CH-8057 Zürich (Switzerland); Tramontano, Francesco [Dipartimento di Fisica, Università di Napoli “Federico II”and INFN - Sezione di Napoli,Complesso di Monte Sant’Angelo, via Cintia, I-80125 Naples (Italy)

    2014-04-07

    We consider Standard Model Higgs boson production in association with a W boson in hadron collisions. We supplement the fully exclusive perturbative computation of QCD radiative effects up to next-to-next-to-leading order (NNLO) with the computation of the decay of the Higgs boson into a bb-macron pair at next-to-leading order (NLO). We consider the selection cuts that are typically applied in the LHC experimental analysis, and we compare our fixed-order predictions with the results obtained with the MC@NLO event generator. We find that NLO corrections to the H→bb-macron decay can be important to obtain a reliable p{sub T} spectrum of the Higgs boson, but that, in the cases of interest, their effect is well accounted for by the parton shower Monte Carlo. NNLO corrections to the production process typically decrease the cross section by an amount which depends on the detail of the applied cuts, but they have a mild effect on the shape of the Higgs p{sub T} spectrum. We also discuss the effect of QCD radiative corrections on the invariant mass distribution of the Higgs candidate.

  12. Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA

    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.

    2012-11-01

    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 α 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 + e - 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 + e - → jets, taking α s (m 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.

  13. 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.

  14. Multiconfiguration Pair-Density Functional Theory Predicts Spin-State Ordering in Iron Complexes with the Same Accuracy as Complete Active Space Second-Order Perturbation Theory at a Significantly Reduced Computational Cost.

    Science.gov (United States)

    Wilbraham, Liam; Verma, Pragya; Truhlar, Donald G; Gagliardi, Laura; Ciofini, Ilaria

    2017-05-04

    The spin-state orderings in nine Fe(II) and Fe(III) complexes with ligands of diverse ligand-field strength were investigated with multiconfiguration pair-density functional theory (MC-PDFT). The performance of this method was compared to that of complete active space second-order perturbation theory (CASPT2) and Kohn-Sham density functional theory. We also investigated the dependence of CASPT2 and MC-PDFT results on the size of the active-space. MC-PDFT reproduces the CASPT2 spin-state ordering, the dependence on the ligand field strength, and the dependence on active space at a computational cost that is significantly reduced as compared to CASPT2.

  15. 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.

  16. Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory

    International Nuclear Information System (INIS)

    Phillips, Jordan J.; Zgid, Dominika

    2014-01-01

    We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and self-energy are built on the imaginary frequency and imaginary time domain, respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H 32 finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases, GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spin-symmetry breaking. Our results show that self-consistent Green's function many-body theory offers a viable route to describing strong correlations while remaining within a computationally tractable single-particle formalism

  17. 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)

  18. 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.)

  19. 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

  20. 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...

  1. The Perturbed Puma Model

    International Nuclear Information System (INIS)

    Rong Shu-Jun; Liu Qiu-Yu

    2012-01-01

    The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element U e3 is always zero. The nonzero mixing matrix element U e3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry. (the physics of elementary particles and fields)

  2. The Perturbed Puma Model

    Science.gov (United States)

    Rong, Shu-Jun; Liu, Qiu-Yu

    2012-04-01

    The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.

  3. 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)

  4. Frame independent cosmological perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)

    2013-09-01

    We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and n-point functions.

  5. Massively parallel and linear-scaling algorithm for second-order Møller-Plesset perturbation theory applied to the study of supramolecular wires

    Science.gov (United States)

    Kjærgaard, Thomas; Baudin, Pablo; Bykov, Dmytro; Eriksen, Janus Juul; Ettenhuber, Patrick; Kristensen, Kasper; Larkin, Jeff; Liakh, Dmitry; Pawłowski, Filip; Vose, Aaron; Wang, Yang Min; Jørgensen, Poul

    2017-03-01

    We present a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide-Expand-Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide-Expand-Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI +X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalability of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the "resolution of the identity second-order Møller-Plesset perturbation theory" (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24 440 basis functions and 91 280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

  6. Cosmological perturbation theory and quantum gravity

    International Nuclear Information System (INIS)

    Brunetti, Romeo; Fredenhagen, Klaus; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna

    2016-01-01

    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.

  7. 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.

  8. 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

  9. 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

  10. 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

  11. 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.

  12. Functional perturbative RG and CFT data in the ɛ -expansion

    Science.gov (United States)

    Codello, A.; Safari, M.; Vacca, G. P.; Zanusso, O.

    2018-01-01

    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 ɛ -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 ^{2n}. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks.

  13. 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)

  14. 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

  15. 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.

  16. Higher-order soft corrections to squark hadro-production

    Energy Technology Data Exchange (ETDEWEB)

    Langenfeld, U.; Moch, S.

    2009-01-15

    We present new predictions for the total cross section of squark pair-production at Tevatron and LHC through next-to-next-to-leading order within the Minimal Supersymmetric Standard Model. The results are based on the numerically dominant soft corrections. They are exact in all logarithmically enhanced terms near threshold, include the Coulomb corrections at two loops and exact scale dependence. We translate the increased total cross section at next-to-next-to-leading order into improved exclusion limits for squark masses and we investigate the scale dependence as well as the sensitivity on the parton luminosity. (orig.)

  17. 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)

  18. Cosmological perturbations in massive bigravity

    International Nuclear Information System (INIS)

    Lagos, Macarena; Ferreira, Pedro G.

    2014-01-01

    We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and tensor perturbations have growing solutions. We argue that special initial conditions are needed for tensor modes in order to have a viable model

  19. 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

  20. 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.

  1. Variational nodal transport perturbation theory

    International Nuclear Information System (INIS)

    Laurin-Kovitz, K.F.; Lewis, E.E.

    1996-01-01

    A perturbation method based on the variational nodal method for solving the neutron transport equation is developed for multidimensional geometries. The method utilizes the solution of the corresponding adjoint transport equation to calculate changes in the critical eigenvalue due to cross-section changes. Both first-order and exact perturbation theory expressions are derived. The adjoint solution algorithm has been formulated and incorporated into the variational nodal option of the Argonne National Laboratory DIF3D production code. To demonstrate the efficacy of the methods, perturbation calculations are performed on the three-dimensional Takeda benchmark problems in both Cartesian and hexagonal geometries. The resulting changes in eigenvalue are also obtained by direct calculation with the variational nodal method and compared with the change approximated by the first-order and exact theory expressions from the perturbation method. Exact perturbation results are in excellent agreement with the actual eigenvalue differences calculated in VARIANT. First-order theory holds well for sufficiently small perturbations. The times required for the perturbation calculations are small compared with those expended for the base-forward and adjoint calculations

  2. Soliton Perturbations, Revisited.

    Science.gov (United States)

    Herman, Russell Leland

    Starting with an 'integrable' nonlinear evolution equation, we are investigating perturbations about a one soliton solution, through the inversion of a linear equation for the first order correction. This differs from the methods based on the perturbation of certain 'scattering data', as the proposed method takes place in coordinate space, and not spectral space. The method is tested on several perturbed Korteweg -DeVries equations. The damped KdV equation is studied in detail, resulting in the resolution of the controversy over the shift in the center of the soliton in favor of the results of Karpman and Maslov. Using a finite difference scheme, a numerically induced shift in the damped soliton's position is predicted through the use of perturbation theory. We extend the results of Ott and Sudan for other damped KdV equations, giving expressions for the shift in soliton position and the asymptotic form of the first order correction to the solution. Next we investigate Menyuk's case of a solution consisting of a soliton plus arbitrary initial radiation, which is subject to a Hamiltonian perturbation; and we show that the radiation must start out small. After these preliminary investigations, we turn to the stochastic KdV equation with external Gaussian white noise, zeta(x,t). For the cases of damping and no damping, the averaged soliton asymptotically becomes a Gaussian wave packet, which decays and broadens according to the same power laws as found by Wadati and Akutsu for the noise zeta(t). Next, we investigate the propagation of a modulated KP soliton and compare our results to the work of Chang. We find that singular perturbation theory cannot explain the evolution of this profile, but we can obtain good qualitative results from the solution of the Cauchy problem for the linearized KP equation. The modulations travel away from the soliton peak and decay in time, leaving a stable planar soliton behind. Finally, we discuss the application of the method to the

  3. 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

  4. 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

  5. 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

  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. 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.

  8. Leading order relativistic hyperon-nucleon interactions in chiral effective field theory

    Science.gov (United States)

    Li, Kai-Wen; Ren, Xiu-Lei; Geng, Li-Sheng; Long, Bing-Wei

    2018-01-01

    We apply a recently proposed covariant power counting in nucleon-nucleon interactions to study strangeness S=‑1 {{\\varLambda }}N-{{\\varSigma }}N interactions in chiral effective field theory. At leading order, Lorentz invariance introduces 12 low energy constants, in contrast to the heavy baryon approach, where only five appear. The Kadyshevsky equation is adopted to resum the potential in order to account for the non-perturbative nature of hyperon-nucleon interactions. A fit to the 36 hyperon-nucleon scattering data points yields {χ }2≃ 16, which is comparable with the sophisticated phenomenological models and the next-to-leading order heavy baryon approach. However, one cannot achieve a simultaneous description of the nucleon-nucleon phase shifts and strangeness S=‑1 hyperon-nucleon scattering data at leading order. Supported by the National Natural Science Foundation of China (11375024, 11522539, 11375120), the China Postdoctoral Science Foundation (2016M600845, 2017T100008) and the Fundamental Research Funds for the Central Universities

  9. 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.

  10. Perturbation Theory of Embedded Eigenvalues

    DEFF Research Database (Denmark)

    Engelmann, Matthias

    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...... 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....

  11. 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...

  12. 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 +...

  13. Review of chiral perturbation theory

    Indian Academy of Sciences (India)

    A review of chiral perturbation theory and recent developments on the comparison of its predictions with .... terms of the effective Lagrangian at two-loop or O(p6) order is now available [12]. The formidable task of ... and straightforward manner for the system and are of great importance for the analysis of experimental ...

  14. 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

  15. 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.

  16. Multiconfiguration Pair-Density Functional Theory and Complete Active Space Second Order Perturbation Theory. Bond Dissociation Energies of FeC, NiC, FeS, NiS, FeSe, and NiSe.

    Science.gov (United States)

    Sharkas, Kamal; Gagliardi, Laura; Truhlar, Donald G

    2017-12-07

    We investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) and complete active space second-order perturbation theory for computing the bond dissociation energies of the diatomic molecules FeC, NiC, FeS, NiS, FeSe, and NiSe, for which accurate experimental data have become recently available [Matthew, D. J.; Tieu, E.; Morse, M. D. J. Chem. Phys. 2017, 146, 144310-144320]. We use three correlated participating orbital (CPO) schemes (nominal, moderate, and extended) to define the active spaces, and we consider both the complete active space (CAS) and the separated-pair (SP) schemes to specify the configurations included for a given active space. We found that the moderate SP-PDFT scheme with the tPBE on-top density functional has the smallest mean unsigned error (MUE) of the methods considered. This level of theory provides a balanced treatment of the static and dynamic correlation energies for the studied systems. This is encouraging because the method is low in cost even for much more complicated systems.

  17. 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.

  18. 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

  19. 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

  20. Probing higher-order corrections in dijet production at the LHC

    DEFF Research Database (Denmark)

    Alioli, S.; Andersen, J. R.; Oleari, C.

    2012-01-01

    -angle, hard emissions. In this paper, we identify regions of phase space in dijet production where some observables receive large corrections beyond next-to-leading order and study their theoretical description with two tools that perform these two different resummations: the POWHEG BOX and HEJ. Furthermore...

  1. 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.

  2. 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.

  3. Perturbation theory in light-cone quantization

    Energy Technology Data Exchange (ETDEWEB)

    Langnau, Alex [Stanford Univ., CA (United States)

    1992-01-01

    A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.

  4. 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.

  5. Non Borel summable series and perturbative QCD

    International Nuclear Information System (INIS)

    Fischer, J.

    1994-01-01

    I report a generalization of the Borel method of summation of divergent power series that permits one to define the sum when the analyticity domain has a horn with zero opening angle and the function is expanded around the tip of the horn. The summation is unique only if the expansion coefficients satisfy severe restrictions at large orders. Relevance to perturbative QCD is stressed in relation to current discussions about large-order behaviour of perturbation expansion coefficients. (orig.)

  6. Automated Lattice Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Monahan, Christopher

    2014-11-01

    I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.

  7. 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

  8. Variational principle for boundary perturbation in transport theory

    International Nuclear Information System (INIS)

    Gheorghiu, H.N.M.; Rahnema, F.

    1996-01-01

    A new variational principle is presented for estimating the eigenvalue of the monoenergetic neutron transport equation when the external boundary of the system is slightly perturbed. It is shown that the principle reduces to the first-order perturbation result for small boundary perturbations. (author)

  9. Extra dimension searches at hadron colliders to next-to-leading ...

    Indian Academy of Sciences (India)

    functions are studied. Uncertainties arising from the error on experimental data ... The gauge hierarchy problem has been one of the main motivations for physics beyond the standard model (SM). .... We have studied the impact of various parton density sets at NLO in QCD on the. Drell-Yan production of dileptons at hadron ...

  10. 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.)

  11. 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)

  12. Zircons reveal ancient perturbations

    Science.gov (United States)

    McKenzie, N. Ryan

    2017-12-01

    A link between CO2 outgassing from carbonatite volcanoes during the Ediacaran and one of the most prominent carbon cycle perturbations in Earth's history is suggested by an analysis of the trace-element composition of detrital zircons.

  13. Introduction to perturbation techniques

    CERN Document Server

    Nayfeh, Ali H

    2011-01-01

    Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.

  14. 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.

  15. Combining fixed-order helicity amplitudes with resummation using SCET

    Energy Technology Data Exchange (ETDEWEB)

    Stewart, Ian W. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics; Tackmann, Frank J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Waalewijn, Wouter J. [California Univ., San Diego, La Jolla, CA (United States). Dept. of Physics

    2012-11-15

    We discuss how to construct a simple and easy-to-use helicity operator basis in Soft-Collinear Effective Theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of the color-ordered QCD helicity amplitudes. This provides an interface to seamlessly combine fixed-order helicity amplitudes, which are the basic building blocks of state-of-the-art next-to-leading order calculations for multileg processes, with a resummation of higher-order logarithmic corrections using SCET.

  16. 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

  17. 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

  18. Perturbing macroscopic magnetohydrodynamic stability for toroidal plasmas

    Science.gov (United States)

    Comer, Kathryn J.

    convergence. The unexpected sensitivity to equilibrium (rather than wall) perturbations in the toroidal calculations is traced to the compressional Alfven wave energy contribution to the stability. Beyond a very small range of perturbations, second order terms in the expansion of compressional Alfven wave energy become large. We explored several methods of ameliorating these second order terms, but none improve results consistently or in a meaningful way.

  19. Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

    Science.gov (United States)

    Sakamoto, Hiroki; Yamamoto, Toshihiro

    2017-09-01

    This paper presents improvement and performance evaluation of the "perturbation source method", which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an "on-the-fly" technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

  20. Cosmological perturbations in teleparallel Loop Quantum Cosmology

    International Nuclear Information System (INIS)

    Haro, Jaime

    2013-01-01

    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator. In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation. In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum

  1. Mode coupling of Schwarzschild perturbations: Ringdown frequencies

    Science.gov (United States)

    Pazos, Enrique; Brizuela, David; Martín-García, José M.; Tiglio, Manuel

    2010-11-01

    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.

  2. Predicting Bond Dissociation Energies of Transition-Metal Compounds by Multiconfiguration Pair-Density Functional Theory and Second-Order Perturbation Theory Based on Correlated Participating Orbitals and Separated Pairs.

    Science.gov (United States)

    Bao, Junwei Lucas; Odoh, Samuel O; Gagliardi, Laura; Truhlar, Donald G

    2017-02-14

    We study the performance of multiconfiguration pair-density functional theory (MC-PDFT) and multireference perturbation theory for the computation of the bond dissociation energies in 12 transition-metal-containing diatomic molecules and three small transition-metal-containing polyatomic molecules and in two transition-metal dimers. The first step is a multiconfiguration self-consistent-field calculation, for which two choices must be made: (i) the active space and (ii) its partition into subspaces, if the generalized active space formulation is used. In the present work, the active space is chosen systematically by using three correlated-participating-orbitals (CPO) schemes, and the partition is chosen by using the separated-pair (SP) approximation. Our calculations show that MC-PDFT generally has similar accuracy to CASPT2, and the active-space dependence of MC-PDFT is not very great for transition-metal-ligand bond dissociation energies. We also find that the SP approximation works very well, and in particular SP with the fully translated BLYP functional SP-ftBLYP is more accurate than CASPT2. SP greatly reduces the number of configuration state functions relative to CASSCF. For the cases of FeO and NiO with extended-CPO active space, for which complete active space calculations are unaffordable, SP calculations are not only affordable but also of satisfactory accuracy. All of the MC-PDFT results are significantly better than the corresponding results with broken-symmetry spin-unrestricted Kohn-Sham density functional theory. Finally we test a perturbation theory method based on the SP reference and find that it performs slightly worse than CASPT2 calculations, and for most cases of the nominal-CPO active space, the approximate SP perturbation theory calculations are less accurate than the much less expensive SP-PDFT calculations.

  3. Dressed-state perturbation theory for multiphoton ionization of atoms

    International Nuclear Information System (INIS)

    Pan, L.; Sundaram, B.; Armstrong, L. Jr.

    1987-01-01

    We introduce a perturbation theory using dressed bound states to include higher-order transition processes in the calculation of atomic multiphoton ionization. We calculate the ionization probability of hydrogen atoms using this theory and compare the results with the lowest-order perturbation result. We also calculate the shift of the hydrogen atom's ground state that is due to the external field

  4. Second-order QCD effects in Higgs boson production through vector boson fusion arXiv

    CERN Document Server

    Cruz-Martinez, J.; Glover, E.W.N.; Huss, A.

    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 $\\pm 5\\%$ 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.

  5. Understanding Theoretical Uncertainties in Perturbative QCD Computations

    DEFF Research Database (Denmark)

    Jenniches, Laura Katharina

    Abstract To compare theoretical predictions and experimental results, we require not only a precise knowledge of the observables themselves, but also a good understanding of the uncertainty introduced by missing higher orders in perturbative QCD. In this work, we present a method which combines....... The second project focuses on theoretical uncertainties in perturbative QCD. We perform a study of theoretical uncertainties obtained using the traditional scale-variation and the Cacciari-Houdeau approach [1], which uses Bayesian statistics to estimate missing-higher-order uncertainties. In addition, we...

  6. 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...

  7. 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.

  8. 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

  9. 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.)

  10. Degenerate asymptotic perturbation theory

    International Nuclear Information System (INIS)

    Hunziker, W.; Pillet, C.A.

    1983-01-01

    Asymptotic Rayleigh-Schroedinger perturbation theory for discrete eigenvalues is developed systematically in the general degenerate case. For this purpose we study the spectral properties of mxm - matrix functions A(kappa) of a complex variable kappa which have an asymptotic expansion ΣAsub(k)kappasup(k) as kappa->0. We show that asymptotic expansions for groups of eigenvalues and for the corresponding spectral projections of A(kappa) can be obtained from the set [Asub(k)] by analytic perturbation theory. Special attention is given to the case where A(kappa) is Borel-summable in some sector originating from kappa=0 with opening angle >π. Here we prove that the asymptotic series describe individual eigenvalues and eigenprojections of A(kappa) which are shown to be holomorphic in S near kappa=0 and Borel summable if Asub(k)sup(*)=Asub(k) for all k. We then fit these results into the scheme of Rayleigh-Schroedinger perturbation theory and we give some examples of asymptotic estimates for Schroedinger operators. (orig.)

  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. Perturbative Chern-Simons theory revisited

    DEFF Research Database (Denmark)

    McLellan, Brendan Donald Kenneth

    2013-01-01

    We reconsider perturbative Chern-Simons theory on a closed and oriented three-manifold with a choice of contact structure following C. Beasley and E. Witten. Closed three manifolds that admit a Sasakian structure are explicitly computed to first order in perturbation in terms of their Seifert data....... The general problem of extending this work to arbitrary three-manifolds is presented and some initial observations are made. Mathematically, this article is closely related to the work of Rumin and Seshadri and an index type theorem in the contact geometric setting....

  13. 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.

  14. 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.

  15. The perturbation method to solve subdiffusion-reaction equations

    OpenAIRE

    Lewandowska, Katarzyna D.; Kosztołowicz, Tadeusz; Piwnik, Mateusz

    2012-01-01

    We use the perturbation method to approximately solve subdiffusion-reaction equations. Within this method we obtain the solutions of the zeroth and the first order. The comparison our analytical solutions with the numerical results shown that the perturbation method can be useful to find approximate solutions of nonlinear subdiffusion--reaction equations.

  16. MPI/OpenMP hybrid parallel algorithm for resolution of identity second-order Møller-Plesset perturbation calculation of analytical energy gradient for massively parallel multicore supercomputers.

    Science.gov (United States)

    Katouda, Michio; Nakajima, Takahito

    2017-03-30

    A massively parallel algorithm of the analytical energy gradient calculations based the resolution of identity Møller-Plesset perturbation (RI-MP2) method from the restricted Hartree-Fock reference is presented for geometry optimization calculations and one-electron property calculations of large molecules. This algorithm is designed for massively parallel computation on multicore supercomputers applying the Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) hybrid parallel programming model. In this algorithm, the two-dimensional hierarchical MP2 parallelization scheme is applied using a huge number of MPI processes (more than 1000 MPI processes) for acceleration of the computationally demanding O(N 5 ) step such as calculations of occupied-occupied and virtual-virtual blocks of MP2 one-particle density matrix and MP2 two-particle density matrices. The new parallel algorithm performance is assessed using test calculations of several large molecules such as buckycatcher C 60 @C 60 H 28 (144 atoms, 1820 atomic orbitals (AOs) for def2-SVP basis set, and 3888 AOs for def2-TZVP), nanographene dimer (C 96 H 24 ) 2 (240 atoms, 2928 AOs for def2-SVP, and 6432 AOs for cc-pVTZ), and trp-cage protein 1L2Y (304 atoms and 2906 AOs for def2-SVP) using up to 32,768 nodes and 262,144 central processing unit (CPU) cores of the K computer. The results of geometry optimization calculations of trp-cage protein 1L2Y at the RI-MP2/def2-SVP level using the 3072 nodes and 24,576 cores of the K computer are presented and discussed to assess the efficiency of the proposed algorithm. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  17. Inhomogeneous Broadening in Perturbed Angular Correlation Spectroscopy

    Science.gov (United States)

    Bunker, Austin; Adams, Mike; Hodges, Jeffery; Park, Tyler; Stufflebeam, Michael; Evenson, William; Matheson, Phil; Zacate, Matthew

    2009-10-01

    Our research concerns the effect of a static distribution of defects on the net electric field gradient (EFG) within crystal structures. Defects and vacancies perturb the distribution of gamma rays emitted from radioactive probe nuclei within the crystal. These defects and vacancies produce a net EFG at the site of the probe which causes the magnetic quadrupole moment of the nucleus of the probe to precess about the EFG. The net EFG, which is strongly dependent upon the defect concentration, perturbs the angular correlation (PAC) of the gamma rays, and is seen in the damping of the perturbation function, G2(t), in time and broadening of the spectral peaks in the Fourier transform. We have used computer simulations to study the probability distribution of EFG tensor components in order to uncover the concentration dependence of G2(t). This in turn can be used to analyze experimental PAC data and quantitatively describe properties of the crystal.

  18. 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

  19. Perturbative 2-body parent Hamiltonians for projected entangled pair states

    Science.gov (United States)

    Brell, Courtney G.; Bartlett, Stephen D.; Doherty, Andrew C.

    2014-12-01

    We construct parent Hamiltonians involving only local 2-body interactions for a broad class of projected entangled pair states (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual PEPS space with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. An encoded parent Hamiltonian for the double semion string net ground state is explicitly constructed as a concrete example.

  20. 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

  1. Perturbative and Non-Perturbative Aspects of N=8 Supergravity

    CERN Document Server

    Ferrara, Sergio

    2011-01-01

    Some aspects of quantum properties of N=8 supergravity in four dimensions are discussed for non-practitioners. At perturbative level, they include the Weyl trace anomaly as well as composite duality anomalies, the latter being relevant for perturbative finiteness. At non-perturbative level, we briefly review some facts about extremal black holes, their Bekenstein-Hawking entropy and attractor flows for single- and two-centered solutions.

  2. Perturbative Noncommutative Regularization

    CERN Document Server

    Hawkins, E J

    1999-01-01

    I propose a nonperturbative regularization of quantum field theories with contact interactions (primarily, scalar field theories). This is given by the geometric quantization of compact Kähler manifolds and generalizes what has already been proposed by Madore, Grosse, Klimčík, and Prešnajder for the two-sphere. I discuss the perturbation theory derived from this regularized model and propose an approximation technique for evaluating the Feynman diagrams. This amounts to a momentum cutoff combined with phase factors at vertices. To illustrate the exact and approximate calculations, I present, as examples, the simplest diagrams for the lf4 model on the spaces S2,S 2×S2 , and CP2 . This regularization fails for noncompact spaces. I give a brief dimensional analysis argument as to why this is so. I also discuss the relevance of the topology of Feynman diagrams to their ultra-violet and infra-red divergence behavior in this model.

  3. 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

  4. Perturbative Semiclassical Trace Formulae for Harmonic Oscillators

    DEFF Research Database (Denmark)

    Møller-Andersen, Jakob; Ögren, Magnus

    2015-01-01

    U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...... the conclusion that the gross structure of the quantum spectrum is determined from only classical circular and diameter orbits for this class of systems....

  5. 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.

  6. Constructing higher-order hydrodynamics: The third order

    Science.gov (United States)

    Grozdanov, Sašo; Kaplis, Nikolaos

    2016-03-01

    Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematization of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list 20 new transport coefficient candidates in the conformal case and 68 in the nonconformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-2) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a nonlinear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the N =4 supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and an infinite number of colors to find the values of five new linear combinations of the conformal transport coefficients.

  7. Application of a perturbation method for realistic dynamic simulation of industrial robots

    NARCIS (Netherlands)

    Waiboer, R.R.; Aarts, Ronald G.K.M.; Jonker, Jan B.

    2005-01-01

    This paper presents the application of a perturbation method for the closed-loop dynamic simulation of a rigid-link manipulator with joint friction. In this method the perturbed motion of the manipulator is modelled as a first-order perturbation of the nominal manipulator motion. A non-linear finite

  8. Perturbative quantum chromodynamics

    International Nuclear Information System (INIS)

    Brodsky, S.J.

    1979-12-01

    The application of QCD to hadron dynamics at short distances, where asymptotic freedom allows a systematic perturbative approach, is addressed. The main theme of the approach is to incorporate systematically the effects of the hadronic wave function in large momentum transfer exclusive and inclusive reactions. Although it is conventional to treat the hadron as a classical source of on-shell quarks, there are important dynamical effects due to hadronic constituent structure which lead to a broader testing ground for QCD. QCD predictions are discussed for exclusive processes and form factors at large momentum transfer in which the short-distance behavior and the finite compositeness of the hadronic wave functions play crucial roles. Many of the standard tests of QCD are reviewed including the predictions for R = sigma/sub e + e - →had//sigma/sub e + e - →μ + μ - /, the structure functions of hadrons and photons, jet phenomena, and the QCD corrections to deep inelastic processes. The exclusive-inclusive connection in QCD, the effects of power-law scale-breaking contributions, and the important role of the available energy in controlling logarithmic scale violations are also discussed. 150 references, 44 figures

  9. Perturbative quantum chromodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, S.J.

    1979-12-01

    The application of QCD to hadron dynamics at short distances, where asymptotic freedom allows a systematic perturbative approach, is addressed. The main theme of the approach is to incorporate systematically the effects of the hadronic wave function in large momentum transfer exclusive and inclusive reactions. Although it is conventional to treat the hadron as a classical source of on-shell quarks, there are important dynamical effects due to hadronic constituent structure which lead to a broader testing ground for QCD. QCD predictions are discussed for exclusive processes and form factors at large momentum transfer in which the short-distance behavior and the finite compositeness of the hadronic wave functions play crucial roles. Many of the standard tests of QCD are reviewed including the predictions for R = sigma/sub e/sup +/e/sup -/..-->..had//sigma/sub e/sup +/e/sup -/..--> mu../sup +/..mu../sup -//, the structure functions of hadrons and photons, jet phenomena, and the QCD corrections to deep inelastic processes. The exclusive-inclusive connection in QCD, the effects of power-law scale-breaking contributions, and the important role of the available energy in controlling logarithmic scale violations are also discussed. 150 references, 44 figures. (RWR)

  10. Perturbation analysis of octupoles in circular accelerators

    International Nuclear Information System (INIS)

    Moohyun Yoon

    1998-01-01

    The octupole effects in a circular accelerator are analyzed using a first-order canonical perturbation theory. It is shown that, to the first order, the nonlinear amplitude-dependent tune shifts due to an octupole are composed of two types: terms of second order and terms of fourth order in betatron-oscillation amplitudes. The fourth-order part of tune shifts is expressed in terms of distortion functions. Distortion functions are also expanded in harmonics to express the higher-order tune shifts in harmonically expanded form. Finally, the results are applied to an accelerator and compared with the results of numerical tracking of particles. Laskar's algorithm for numerical analysis of the fundamental frequency is used to determine tunes from the tracking data, in which the error becomes inversely proportional to the cube of the number of data points. (author)

  11. Degenerate R-S perturbation theory

    Science.gov (United States)

    Hirschfelder, J. O.; Certain, P. R.

    1973-01-01

    A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.

  12. Propagation of Ion Acoustic Perturbations

    DEFF Research Database (Denmark)

    Pécseli, Hans

    1975-01-01

    Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered.......Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered....

  13. Review of chiral perturbation theory

    Indian Academy of Sciences (India)

    41] which will be measured to high accuracy at Jefferson Laboratory at the experiment PrimEx. 4. Baryon chiral perturbation theory. Baryon chiral perturbation theory in the modern era was first formulated in [6]. This was a relativistic formulation ...

  14. On summation of perturbation expansions

    International Nuclear Information System (INIS)

    Horzela, A.

    1985-04-01

    The problem of the restoration of physical quantities defined by divergent perturbation expansions is analysed. The Pad'e and Borel summability is proved for alternating perturbation expansions with factorially growing coefficients. The proof is based on the methods of the classical moments theory. 17 refs. (author)

  15. Continual integral in perturbation theory

    International Nuclear Information System (INIS)

    Slavnov, A.A.

    1975-01-01

    It is shown that all results obtained by means of continual integration within the framework of perturbation theory are completely equivalent to those obtained by the usual diagram technique and are therfore just as rigorous. A rigorous justification is given for the rules for operating with continual integrals in perturbation theory. (author)

  16. Resumming the string perturbation series

    Energy Technology Data Exchange (ETDEWEB)

    Grassi, Alba; Mariño, Marcos; Zakany, Szabolcs [Département de Physique Théorique et section de Mathématiques,Université de Genève, Genève, CH-1211 (Switzerland)

    2015-05-07

    We use the AdS/CFT correspondence to study the resummation of a perturbative genus expansion appearing in the type II superstring dual of ABJM theory. Although the series is Borel summable, its Borel resummation does not agree with the exact non-perturbative answer due to the presence of complex instantons. The same type of behavior appears in the WKB quantization of the quartic oscillator in Quantum Mechanics, which we analyze in detail as a toy model for the string perturbation series. We conclude that, in these examples, Borel summability is not enough for extracting non-perturbative information, due to non-perturbative effects associated to complex instantons. We also analyze the resummation of the genus expansion for topological string theory on local ℙ{sup 1}×ℙ{sup 1}, which is closely related to ABJM theory. In this case, the non-perturbative answer involves membrane instantons computed by the refined topological string, which are crucial to produce a well-defined result. We give evidence that the Borel resummation of the perturbative series requires such a non-perturbative sector.

  17. Perturbative QCD (1/3)

    CERN Multimedia

    CERN. Geneva

    2013-01-01

    Perturbative QCD is the general theoretical framework for describing hard scattering processes yielding multiparticle production at hadron colliders. In these lectures, we shall introduce fundamental features of perturbative QCD and describe its application to several high energy collider processes, including jet production in electron-positron annihilation, deep inelastic scattering, Higgs boson and gauge boson production at the LHC.

  18. Reconstruction of black hole metric perturbations from the Weyl curvature

    International Nuclear Information System (INIS)

    Lousto, Carlos O.; Whiting, Bernard F.

    2002-01-01

    Perturbation theory of rotating black holes is usually described in terms of Weyl scalars ψ 4 and ψ 0 , which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials Ψ in outgoing or ingoing radiation gauges. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e. ψ 4 and ψ 0 . We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole

  19. Perturbative vs non-perturbative impurity scattering in a narrow Si nanowire GAA transistor: A NEGF study

    Energy Technology Data Exchange (ETDEWEB)

    Martinez, Antonio; Brown, Andrew R; Seoane, Natalia; Asenov, Asen, E-mail: antonio@elec.gla.ac.u [Department Electronics and Electrical Engineering, University of Glasgow, G12 8LT (United Kingdom)

    2009-11-15

    In this paper we study the effect of impurity scattering on the performance of a Si gate-all-around nanowire transistors. The non-equilibrium Green function formalism is used in order to describe the carrier transport. Impurity scattering is introduced using two different formalisms, one that considers the impurity potential as a small perturbation by introducing self energies and the other in which the impurity potential is described exactly by included the impurity potential through the Poisson equation. The non-perturbative method does not use a fitting parameter but the perturbative one uses a phenomenological constant that can be calibrated to match the result of the non-perturbative method. We confirm Ohms-law-type behaviour by using the perturbative approach for larger channel lengths.

  20. Higher-order hadronic and heavy-lepton contributions to the anomalous magnetic moment

    International Nuclear Information System (INIS)

    Kurz, Alexander; Liu, Tao; Steinhauser, Matthias

    2014-07-01

    We report about recent results obtained for the muon anomalous magnetic moment. Three-loop kernel functions have been computed to obtain the next-to-next-to-leading-order hadronic vacuum polarization contributions. The numerical result, a μ had,NNLO = 1.24 ± 0.01 x 10 -10 , is of the same order of magnitude as the current uncertainty from the hadronic contributions. For heavy-lepton corrections, analytical results are obtained at four-loop order and compared with the known results.

  1. Disformal transformation of cosmological perturbations

    Directory of Open Access Journals (Sweden)

    Masato Minamitsuji

    2014-10-01

    Full Text Available We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (nonconservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.

  2. Perturbative Gaussianizing transforms for cosmological fields

    Science.gov (United States)

    Hall, Alex; Mead, Alexander

    2018-01-01

    Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

  3. Perturbation theory of effective Hamiltonians

    International Nuclear Information System (INIS)

    Brandow, B.H.

    1975-01-01

    This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)

  4. Inflationary Perturbations from Deformed CFT

    CERN Document Server

    Van der Schaar, J P

    2004-01-01

    We present a new method to calculate the spectrum of (slow-roll) inflationary perturbations, inspired by the conjectured dS/CFT correspondence. We show how the standard result for the spectrum of inflationary perturbations can be obtained from deformed CFT correlators, whose behavior is determined by the Callan-Symanzik equation. We discuss the possible advantages of this approach and end with some comments on the role of holography in dS/CFT and its relation to the universal nature of the spectrum of inflationary perturbations.

  5. The theory of singular perturbations

    CERN Document Server

    De Jager, E M

    1996-01-01

    The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat

  6. Equation-of-motion coupled cluster perturbation theory revisited

    DEFF Research Database (Denmark)

    Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe

    2014-01-01

    The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...

  7. Optimized Perturbation Theory for Wave Functions of Quantum Systems

    International Nuclear Information System (INIS)

    Hatsuda, T.; Tanaka, T.; Kunihiro, T.

    1997-01-01

    The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society

  8. Numerical stochastic perturbation theory in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2013-11-15

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  9. Numerical stochastic perturbation theory in the Schroedinger functional

    International Nuclear Information System (INIS)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron

    2013-11-01

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  10. Infrared problems in field perturbation theory

    International Nuclear Information System (INIS)

    David, Francois.

    1982-12-01

    The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr

  11. Design optimization using depletion perturbation theory

    International Nuclear Information System (INIS)

    Worley, B.A.

    1984-06-01

    Analysis of the fuel cycle performance of a reactor requires knowledge of the entire fuel burnup history. The optimal design depends upon the desired performance parameter or combination of parameters to be minimized (or maximized). The emphasis to date has been to use some combination of iterations involving a number of direct calculations, static perturbation theory, binary exchange methods, and empirical relationships. The object of this study is to demonstrate an approach to optimization based upon Depletion Perturbation Theory (DPT). The DPT equations directly couple the nuclide burnup equations and the neutron balance equations. The equations require the calculation of forward and adjoint solutions for the neutron flux and nuclide transmutations. The application is for analysis of a modular HTGR. The reactor has axially dependent fuel loadings in order to achieve an axial power shape that keeps fuel temperatures below a specified maximum

  12. Do we need Feynman diagrams for higher order perturbation theory?

    International Nuclear Information System (INIS)

    Jora, Renata

    2012-01-01

    We compute the two loop and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.

  13. Perturbation theory of quantum resonances

    Czech Academy of Sciences Publication Activity Database

    Durand, P.; Paidarová, Ivana

    2016-01-01

    Roč. 135, č. 7 (2016), s. 159 ISSN 1432-2234 Institutional support: RVO:61388955 Keywords : Partitioning technique * Analytic continuation * Perturbative expansion Subject RIV: CF - Physical ; Theoretical Chemistry

  14. Review of chiral perturbation theory

    Indian Academy of Sciences (India)

    Abstract. A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.

  15. Perturbation theory and importance functions in integral transport formulations

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first-order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory

  16. Leading order relativistic chiral nucleon-nucleon interaction

    Science.gov (United States)

    Ren, Xiu-Lei; Li, Kai-Wen; Geng, Li-Sheng; Long, Bingwei; Ring, Peter; Meng, Jie

    2018-01-01

    Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian. We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the {}1S0 and {}3P0 phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta J≥slant 1, the relativistic results are almost the same as their leading order non-relativistic counterparts. )

  17. Quantum inflaton, primordial perturbations, and CMB fluctuations

    International Nuclear Information System (INIS)

    Cao, F.J.; Vega, H.J. de; Sanchez, N.G.

    2004-01-01

    We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. Quantum field inflation (under conditions that are the quantum analog of slow-roll) leads, upon evolution, to the formation of a condensate starting a regime of effective classical inflation. We compute the primordial perturbations taking the dominant quantum effects into account. The results for the scalar, vector and tensor primordial perturbations are expressed in terms of the classical inflation results. For a N-component field in a O(N) symmetric model, adiabatic fluctuations dominate while isocurvature or entropy fluctuations are negligible. The results agree with the current Wilkinson Microwave Anisotropy Probe observations and predict corrections to the power spectrum in classical inflation. Such corrections are estimated to be of the order of (m 2 /NH 2 ), where m is the inflaton mass and H the Hubble constant at the moment of horizon crossing. An upper estimate turns to be about 4% for the cosmologically relevant scales. This quantum field treatment of inflation provides the foundations to the classical inflation and permits to compute quantum corrections to it

  18. Multifrequency perturbations in matter-wave interferometry

    Science.gov (United States)

    Günther, A.; Rembold, A.; Schütz, G.; Stibor, A.

    2015-11-01

    High-contrast matter-wave interferometry is essential in various fundamental quantum mechanical experiments as well as for technical applications. Thereby, contrast and sensitivity are typically reduced by decoherence and dephasing effects. While decoherence accounts for a general loss of quantum information in a system due to entanglement with the environment, dephasing is due to collective time-dependent external phase shifts, which can be related to temperature drifts, mechanical vibrations, and electromagnetic oscillations. In contrast to decoherence, dephasing can, in principle, be reversed. Here, we demonstrate in experiment and theory a method for the analysis and reduction of the influence of dephasing noise and perturbations consisting of several external frequencies in an electron interferometer. This technique uses the high spatial and temporal resolution of a delay-line detector to reveal and remove dephasing perturbations by second-order correlation analysis. It allows matter-wave experiments under perturbing laboratory conditions and can be applied, in principle, to electron, atom, ion, neutron, and molecule interferometers.

  19. Perturbation method for periodic solutions of nonlinear jerk equations

    International Nuclear Information System (INIS)

    Hu, H.

    2008-01-01

    A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method

  20. Heavy quark form factors at two loops in perturbative QCD

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Behring, A. [RWTH Aachen Univ. (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie; Bluemlein, J.; Freitas, A. de; Marquard, P.; Rana, N. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Falcioni, G. [Nikhef, Amsterdam (Netherlands). Theory Group

    2017-11-15

    We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.

  1. Perturbation theory for water with an associating reference fluid

    Science.gov (United States)

    Marshall, Bennett D.

    2017-11-01

    The theoretical description of the thermodynamics of water is challenged by the structural transition towards tetrahedral symmetry at ambient conditions. As perturbation theories typically assume a spherically symmetric reference fluid, they are incapable of accurately describing the liquid properties of water at ambient conditions. In this paper we address this problem by introducing the concept of an associated reference perturbation theory (APT). In APT we treat the reference fluid as an associating hard sphere fluid which transitions to tetrahedral symmetry in the fully hydrogen bonded limit. We calculate this transition in a theoretically self-consistent manner without appealing to molecular simulations. This associated reference provides the reference fluid for a second order Barker-Henderson perturbative treatment of the long-range attractions. We demonstrate that this approach gives a significantly improved description of water as compared to standard perturbation theories.

  2. On the systematic construction of convergent perturbation series

    International Nuclear Information System (INIS)

    Schmidt, C.

    1993-12-01

    Starting from the general decomposition of the many-body Hamiltonian parametrized by an operator Λwe derive the class of 'Λ-transformed' perturbation series. Aiming at practical applications we consider many-body perturbation theory of atoms and molecules in finite dimensional Hilbert spaces. Investigation of the analyticity properties of the eigenvalues and eigenstates of the Hamiltonian as functions of the coupling parameter defined by the particular decomposition of H allows for the construction of (minimal) Λoperators mapping an originally divergent series to a convergent one. There exists an operator Λ opt leading to the exact results in first order. Further improvements of the above mentioned minimal Λoperators can be achieved by approximations of Λ opt leading to fast convergent perturbation series. As the size of the remaining perturbation is given by the Λoperator chosen this method provides an a priori estimate of the convergence properties. (orig.)

  3. Modified potentials in many-body perturbation theory

    International Nuclear Information System (INIS)

    Silver, D.M.; Bartlett, R.J.

    1976-01-01

    Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential

  4. Analytic continuation in perturbative QCD

    International Nuclear Information System (INIS)

    Caprini, Irinel

    2002-01-01

    We discuss some attempts to improve standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the normalized coupling constant a. The new expansion functions have branch point and essential singularities at the origin of the complex a-plane and divergent Taylor expansions in powers of a. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions. (author)

  5. Historical developments in singular perturbations

    CERN Document Server

    O'Malley, Robert E

    2014-01-01

    This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a  number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley  has written a number of books on singular perturbations.  This book has developed from many of his works in the field of perturbation theory.

  6. Energy-energy correlation in electron-positron annihilation at NNLL + NNLO accuracy

    Energy Technology Data Exchange (ETDEWEB)

    Tulipant, Zoltan; Kardos, Adam; Somogyi, Gabor [University of Debrecen, MTA-DE Particle Physics Research Group, Debrecen (Hungary)

    2017-11-15

    We present the computation of energy-energy correlation in e{sup +}e{sup -} collisions in the back-to-back region at next-to-next-to-leading logarithmic accuracy matched with the next-to-next-to-leading order perturbative prediction. We study the effect of the fixed higher-order corrections in a comparison of our results to LEP and SLC data. The next-to-next-to-leading order correction has a sizable impact on the extracted value of α{sub S}(M{sub Z}), hence its inclusion is mandatory for a precise measurement of the strong coupling using energy-energy correlation. (orig.)

  7. Perturbative coherence in field theory

    International Nuclear Information System (INIS)

    Aldrovandi, R.; Kraenkel, R.A.

    1987-01-01

    A general condition for coherent quantization by perturbative methods is given, because the basic field equations of a fild theory are not always derivable from a Lagrangian. It's seen that non-lagrangian models way have well defined vertices, provided they satisfy what they call the 'coherence condition', which is less stringent than the condition for the existence of a Lagrangian. They note that Lagrangian theories are perturbatively coherent, in the sense that they have well defined vertices, and that they satisfy automatically that condition. (G.D.F.) [pt

  8. Symmetry and perturbation theory

    Science.gov (United States)

    Gaeta, Giuseppe

    A co-chain map for the G invariant De Rham complex -- New examples of trihamiltonian structures linking different Lenard chains -- Wave propagation in an elastic medium: GDS equations -- Parametric excitation in nonlinear dynamics -- Collisionless action-minimizing trajectories for the equivariant 3-body problem in R2 -- The Lagrangian and Hamiltonian formulations for a special class of non-conservative systems -- Shadowing chains of collision orbits for the elliptic 3-body problem -- Similarity reductions of an optical model -- Fold, transcritical and pitchfork singularities for time-reversible systems -- Homographic three-body motions with positive and negative masses -- Remarks on conformal Killing tensors and separation of variables -- A regularity theory for optimal partition problems -- Lambda and mu-symmetries -- Potential symmetries and linearization of some evolution equations -- Periodic solutions for zero mass nonlinear wave equations -- Fundamental covariants in the invariant theory of Killing tensors -- Global geometry of 3-body trajectories with vanishing angular momentum -- The relation between the topological structure of the set of controllable affine systems and topological structures of the set of controllable homogenuous systems in low dimension -- On preservation of action variables for satellite librations in elliptic orbits with account of solar light pressure -- An explicit solution of the (quantum) elliptic Calogero-Sutherland model -- An application of the Melnikov integral to a restricted three body problem -- Reductions of integrable equations and automorphic Lie algebras -- Geometric reduction of Poisson operators -- Closed manifolds admitting metrics with the same geodesics -- A transcritical-flip bifurcation in a model for a robot-arm -- Alignment and the classification of Lorentz-signature tensors -- Renormalization group symmetry and gas dynamics -- Refined computation of hypernormal forms -- New order reductions for Euler

  9. Chaotic inflation with metric and matter perturbations

    International Nuclear Information System (INIS)

    Feldman, H.A.; Brandenberger, R.H.

    1989-01-01

    A perturbative scheme to analyze the evolution of both metric and scalar field perturbations in an expanding universe is developed. The scheme is applied to study chaotic inflation with initial metric and scalar field perturbations present. It is shown that initial gravitational perturbations with wavelength smaller than the Hubble radius rapidly decay. The metric simultaneously picks up small perturbations determined by the matter inhomogeneities. Both are frozen in once the wavelength exceeds the Hubble radius. (orig.)

  10. Analytic treatment of leading-order parton evolution equations: Theory and tests

    International Nuclear Information System (INIS)

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

    2009-01-01

    We recently derived an explicit expression for the gluon distribution function G(x,Q 2 )=xg(x,Q 2 ) in terms of the proton structure function F 2 γp (x,Q 2 ) in leading-order (LO) QCD by solving the LO Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for the Q 2 evolution of F 2 γp (x,Q 2 ) analytically, using a differential-equation method. We showed that accurate experimental knowledge of F 2 γp (x,Q 2 ) in a region of Bjorken x and virtuality Q 2 is all that is needed to determine the gluon distribution in that region. We rederive and extend the results here using a Laplace-transform technique, and show that the singlet quark structure function F S (x,Q 2 ) can be determined directly in terms of G from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi gluon evolution equation. To illustrate the method and check the consistency of existing LO quark and gluon distributions, we used the published values of the LO quark distributions from the CTEQ5L and MRST2001 LO analyses to form F 2 γp (x,Q 2 ), and then solved analytically for G(x,Q 2 ). We find that the analytic and fitted gluon distributions from MRST2001LO agree well with each other for all x and Q 2 , while those from CTEQ5L differ significantly from each other for large x values, x > or approx. 0.03-0.05, at all Q 2 . We conclude that the published CTEQ5L distributions are incompatible in this region. Using a nonsinglet evolution equation, we obtain a sensitive test of quark distributions which holds in both LO and next-to-leading order perturbative QCD. We find in either case that the CTEQ5 quark distributions satisfy the tests numerically for small x, but fail the tests for x > or approx. 0.03-0.05--their use could potentially lead to significant shifts in predictions of quantities sensitive to large x. We encountered no problems with the MRST2001LO distributions or later CTEQ distributions. We suggest caution in the use of the CTEQ5 distributions.

  11. Basics of QCD perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Soper, D.E. [Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science

    1997-06-01

    This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.

  12. Basics of QCD perturbation theory

    International Nuclear Information System (INIS)

    Soper, D.E.

    1997-01-01

    This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs

  13. Current issues in perturbative QCD

    International Nuclear Information System (INIS)

    Hinchliffe, I.

    1994-12-01

    This review talk discusses some issues of active research in perturbative QCD. The following topics are discussed: (1) current value of αs; (2) heavy quark production in hadron collisions; (3) production of Ψ and Υ in p anti p collisions; (4) prompt photon production; (5) small-x and related phenomena; and (6) particle multiplicity in heavy quark jets

  14. Principles of chiral perturbation theory

    International Nuclear Information System (INIS)

    Leutwyler, H.

    1995-01-01

    An elementary discussion of the main concepts used in chiral perturbation theory is given in textbooks and a more detailed picture of the applications may be obtained from the reviews. Concerning the foundations of the method, the literature is comparatively scarce. So, I will concentrate on the basic concepts and explain why the method works. (author)

  15. Perturbation theory from stochastic quantization

    International Nuclear Information System (INIS)

    Hueffel, H.

    1984-01-01

    By using a diagrammatical method it is shown that in scalar theories the stochastic quantization method of Parisi and Wu gives the usual perturbation series in Feynman diagrams. It is further explained how to apply the diagrammatical method to gauge theories, discussing the origin of ghost effects. (Author)

  16. Odd-parity perturbations of the self-similar LTB spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Duffy, Emily M; Nolan, Brien C, E-mail: emilymargaret.duffy27@mail.dcu.ie, E-mail: brien.nolan@dcu.ie [School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9 (Ireland)

    2011-05-21

    We consider the behaviour of odd-parity perturbations of those self-similar LemaItre-Tolman-Bondi spacetimes which admit a naked singularity. We find that a perturbation which evolves from initially regular data remains finite on the Cauchy horizon. Finiteness is demonstrated by considering the behaviour of suitable energy norms of the perturbation (and pointwise values of these quantities) on natural spacelike hypersurfaces. This result holds for a general choice of initial data and initial data surface. Finally, we examine the perturbed Weyl scalars in order to provide a physical interpretation of our results. Taken on its own, this result does not support cosmic censorship; however, a full perturbation of this spacetime would include even-parity perturbations, so we cannot conclude that this spacetime is stable to all linear perturbations.

  17. Two-parameter nonlinear spacetime perturbations gauge transformations and gauge invariance

    CERN Document Server

    Bruni, M; Sopuerta, C F

    2003-01-01

    An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity OMEGA), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by lambda) are then built on top of the axisymmetric perturbations in OMEGA. Clearly, any interesting physics requires nonlinear perturbations, as at least terms lambda OMEGA need to be considered. In this paper, we analyse the gauge dependence of nonlinear perturbations depending on two parameters, derive explicit higher-order gauge transformation rules and define gauge ...

  18. Electromagnetic couplings of the chiral perturbation theory Lagrangian from the perturbative chiral quark model

    International Nuclear Information System (INIS)

    Lyubovitskij, V.E.; Gutsche, Th.; Faessler, Amand; Mau, R. Vinh

    2002-01-01

    We apply the perturbative chiral quark model to the study of the low-energy πN interaction. Using an effective chiral Lagrangian we reproduce the Weinberg-Tomozawa result for the S-wave πN scattering lengths. After inclusion of the photon field we give predictions for the electromagnetic O(p 2 ) low-energy couplings of the chiral perturbation theory effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e 2 ) radiative corrections to the πN scattering amplitude. Finally, we estimate the leading isospin-breaking correction to the strong energy shift of the π - p atom in the 1s state, which is relevant for the experiment 'pionic hydrogen' at PSI

  19. SMD-based numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Dalla Brida, Mattia [Universita di Milano-Bicocca, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano-Bicocca (Italy); Luescher, Martin [CERN, Theoretical Physics Department, Geneva (Switzerland); AEC, Institute for Theoretical Physics, University of Bern (Switzerland)

    2017-05-15

    The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)

  20. Optimization and the ultimate convergence of QCD perturbation theory

    International Nuclear Information System (INIS)

    Stevenson, P.M.

    1984-01-01

    I suggest that QCD perturbation theory can be convergent, and that 'optimization' of the renormalization scheme choice is essential in achieving this. Arguing that higher orders probe shorter distances, I suggest that the effective expansion parameter (the 'optimized' couplant) decreases at high orders, leading to an induced convergence. The mechanism is illustrated by a simple mathematical example. The point is that, even if the perturbation series is divergent in all fixed renormalization schemes, the sequence of 'optimized' approximations may still converge. It is emphasized that the limit approached by perturbation theory, if any, will not be the exact result of the full theory. Allegations that QCD series are not Borel-summable are critically re-examined in this light. (orig.)

  1. Small-x physics in perturbative QCD

    International Nuclear Information System (INIS)

    Lipatov, L.N.

    1996-07-01

    We review the parton model and the Regge approach to the QCD description of the deep-inelastic ep scattering at the small Bjorken variable x and demonstrate their relation with the DGLAP and BFKL evolution equations. It is shown, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The conformal invariance of the BFKL pomeron in the impact parameter space is used to investigate the scattering amplitudes at high energies and fixed momentum transfers. The remarkable properties of the Schroedinger equation for compound states of an arbitrary number of reggeized gluons in the multi-colour QCD are reviewed. The gauge-invariant effective action describing the gluon-Reggeon interactions is constructed. The known next-to-leading corrections to the QCD pomeron are discussed. (orig.)

  2. A degree theory for a class of perturbed Fredholm maps II

    Directory of Open Access Journals (Sweden)

    Calamai Alessandro

    2006-01-01

    Full Text Available In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces. Our purpose here is to extend that notion in order to include the degree introduced by Nussbaum for local -condensing perturbations of the identity, as well as the degree for locally compact perturbations of Fredholm maps of index zero recently defined by the first and third authors.

  3. A degree theory for a class of perturbed Fredholm maps II

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces. Our purpose here is to extend that notion in order to include the degree introduced by Nussbaum for local α -condensing perturbations of the identity, as well as the degree for locally compact perturbations of Fredholm maps of index zero recently defined by the first and third authors.

  4. The status of perturbative QCD

    International Nuclear Information System (INIS)

    Ellis, R.K.

    1988-10-01

    The advances in perturbative QCD are reviewed. The status of determinations of the coupling constant α/sub S/ and the parton distribution functions is presented. New theoretical results on the spin dependent structure functions of the proton are also reviewed. The theoretical description of the production of vector bosons, jets and heavy quarks is outlined with special emphasis on new results. Expected rates for top quark production at hadronic colliders are presented. 111 refs., 8 figs

  5. Perturbative QCD at finite temperature

    International Nuclear Information System (INIS)

    Altherr, T.

    1989-03-01

    We discuss an application of finite temperature QCD to lepton-pair production in a quark-gluon plasma. The perturbative calculation is performed within the realtime formalism. After cancellation of infrared and mass singularities, the corrections at O (α s ) are found to be very small in the region where the mass of the Drell-Yan pair is much larger than the temperature of the plasma. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks

  6. Asymptotic absolute continuity for perturbed time-dependent ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Under various conditions on the second term, the perturbation, including (as a mini- mum) boundedness of second order derivatives (being locally uniform in t), we study the large-time behaviour of the dynamics U(t) generated by the family of H(t)'s. We are interested in a generalization of the notion of asymptotic velocity ...

  7. Perturbative effects on ultra-short soliton self-switching

    Indian Academy of Sciences (India)

    A numerical study of ultra-short self-soliton switching along with the corresponding analysis of coupler parameters is carried out for a Kerr coupler with intermodal dispersion. The influence of perturbations like third-order dispersion, self-steepening and intrapulse Raman scattering, on switching characteristics is also studied ...

  8. Perturbed segmented domain collocation Tau-method for the ...

    African Journals Online (AJOL)

    This paper concerns the numerical solution of second order boundary value problems using a Perturbed segmented domain collocation-Tau method. The entire interval for which the problem is defined is partitioned into two segments and the solution technique is demonstrated on each of the segments. The Chebyshev ...

  9. History-Dependent Patterns in Randomly Perturbed Nematic Liquid Crystals

    Directory of Open Access Journals (Sweden)

    A. Ranjkesh

    2013-01-01

    Full Text Available We study the characteristics of nematic structures in a randomly perturbed nematic liquid crystal (LC phase. We focus on the impact of the samples history on the universal behavior. The obtained results are of interest for every randomly perturbed system exhibiting a continuous symmetry-breaking phase transition. A semimicroscopic lattice simulation is used where the LC molecules are treated as cylindrically symmetric, rod-like objects interacting via a Lebwohl-Lasher (LL interaction. Pure LC systems exhibit a first order phase transition into the orientationally ordered nematic phase at T=Tc on lowering the temperature T. The orientational ordering of LC molecules is perturbed by the quenched, randomly distributed rod-like impurities of concentration p. Their orientation is randomly distributed, and they are coupled with the LC molecules via an LL-type interaction. Only concentrations below the percolation threshold are considered. The key macroscopic characteristics of perturbed LC structures in the symmetry-broken nematic phase are analyzed for two qualitatively different histories at T≪Tc. We demonstrate that, for a weak enough interaction among the LC molecules and impurities, qualitatively different history-dependent states could be obtained. These states could exhibit either short-range, quasi-long-range, or even long-range order.

  10. Fitted-Stable Finite Difference Method for Singularly Perturbed Two ...

    African Journals Online (AJOL)

    A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of ...

  11. Finite difference order doubling in two dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Killingbeck, John P [Mathematics Centre, University of Hull, Hull HU6 7RX (United Kingdom); Jolicard, Georges [Universite de Franche-Comte, Institut Utinam (UMR CNRS 6213), Observatoire de Besancon, 41 bis Avenue de l' Observatoire, BP1615, 25010 Besancon cedex (France)

    2008-03-28

    An order doubling process previously used to obtain eighth-order eigenvalues from the fourth-order Numerov method is applied to the perturbed oscillator in two dimensions. A simple method of obtaining high order finite difference operators is reported and an odd parity boundary condition is found to be effective in facilitating the smooth operation of the order doubling process.

  12. Asymptotic Behaviour of the QED Perturbation Series

    Directory of Open Access Journals (Sweden)

    Idrish Huet

    2017-01-01

    Full Text Available I will summarize the present state of a long-term effort to obtain information on the large-order asymptotic behaviour of the QED perturbation series through the effective action. Starting with the constant-field case, I will discuss the Euler-Heisenberg Lagrangian in various dimensions and up to the three-loop level. This Lagrangian holds the information on the N-photon amplitudes in the low-energy limit, and combining it with Spinor helicity methods explicit all-N results can be obtained at the one-loop and, for the “all +” amplitudes, also at the two-loop level. For the imaginary part of the Euler-Heisenberg Lagrangian, an all-loop formula has been conjectured independently by Affleck, Alvarez, and Manton for Scalar QED and by Lebedev and Ritus for Spinor QED. This formula can be related through a Borel dispersion relation to the leading large-N behaviour of the N-photon amplitudes. It is analytic in the fine structure constant, which is puzzling and suggests a diagrammatic investigation of the large-N limit in perturbation theory. Preliminary results of such a study for the 1+1 dimensional case throw doubt on the validity of the conjecture.

  13. Quantum cosmological perturbations of multiple fluids

    Science.gov (United States)

    Peter, Patrick; Pinto-Neto, N.; Vitenti, Sandro D. P.

    2016-01-01

    The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).

  14. Perturbation of an exact strong gravity solution

    International Nuclear Information System (INIS)

    Baran, S.A.

    1982-10-01

    Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)

  15. The impact of quark masses on pQCD thermodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Graf, Thorben; Schaffner-Bielich, Juergen [Goethe University, Institute for Theoretical Physics, Frankfurt am Main (Germany); Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, Rio de Janeiro (Brazil)

    2016-07-15

    We present results for several thermodynamic quantities within the next-to-leading order calculation of the thermodynamic potential in perturbative QCD at finite temperature and chemical potential including non-vanishing quark masses. These results are compared to lattice data and to higher-order optimized perturbative calculations to investigate the trend brought about by mass corrections. (orig.)

  16. Nucleon and delta masses in twisted mass chiral perturbation theory

    International Nuclear Information System (INIS)

    Walker-Loud, Andre; Wu, Jackson M.S.

    2005-01-01

    We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing, a, and the quark masses, m q , to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We show that the mass splitting between the degenerate pairs of the deltas first appears at quadratic order in the lattice spacing. We discuss the subtleties in the effective chiral theory that arise from the inclusion of isospin breaking

  17. The Hill-determinant perturbation theory with triangular propagators

    International Nuclear Information System (INIS)

    Znojil, M.

    1996-01-01

    A new version of the Rayleigh-Schroedinger perturbation prescription is proposed. Its main formal feature lies in an unusual choice of the model space and unperturbed H 0 and in a resulting lower-triangular matrix structure of its propagators. Within the framework of the so-called Hill-determinant method, an admissibility of any incompletely solvable zero-order Hamiltonian is achieved in this way. As a consequence, the range of practical applicability of our new perturbative formalism may be expected to incorporate many new phenomenological interactions with a strongly anharmonic character. 18 refs

  18. Perturbative approach to non-Markovian stochastic Schroedinger equations

    International Nuclear Information System (INIS)

    Gambetta, Jay; Wiseman, H.M.

    2002-01-01

    In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)

  19. Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations

    DEFF Research Database (Denmark)

    Sørensen, Dan Erik Krarup

    1996-01-01

    We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.Polynomials...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...

  20. Geometric Hamiltonian structures and perturbation theory

    International Nuclear Information System (INIS)

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging

  1. Matrix perturbations: bounding and computing eigenvalues

    NARCIS (Netherlands)

    Reis da Silva, R.J.

    2011-01-01

    Despite the somewhat negative connotation of the word, not every perturbation is a bad perturbation. In fact, while disturbing the matrix entries, many perturbations still preserve useful properties such as the orthonormality of the basis of eigenvectors or the Hermicity of the original matrix. In

  2. FRW Cosmological Perturbations in Massive Bigravity

    CERN Document Server

    Comelli, D; Pilo, L

    2014-01-01

    Cosmological perturbations of FRW solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that sub horizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations.

  3. Multiplicative perturbations of local C-semigroups

    Indian Academy of Sciences (India)

    2016-08-26

    Aug 26, 2016 ... In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S(⋅) may not be densely defined and the perturbation operator is a bounded linear operator from ¯D(A) into () such that = ...

  4. Multiplicative perturbations of local C-semigroups

    Indian Academy of Sciences (India)

    In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S ( ⋅ ) may not be densely defined and the perturbation operator is a bounded linear operator from D ( A ) ¯ into () such that = on D ( A ) ¯ ...

  5. Jacobian approach to optimal determination of perturbation ...

    African Journals Online (AJOL)

    In this work, the optimal determination of the perturbation factor (λ) or perturbation parameter for gradient method is considered. The spectrum analysis of the associated Jacobian of the associated matrix has laid the basis for the judicious selection of the perturbation factor. Numerical work is carried out to prove our ...

  6. Challenges in the extraction of TMDs from SIDIS data: perturbative vs non-perturbative aspects

    Energy Technology Data Exchange (ETDEWEB)

    Boglione, Mariaelena [aDipartimento di Fisica Teorica, Università di Torino, Via P. Giuria 1, I-10125 Torino, Italy; Gonzalez Hernandez, Jose O. [INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Università di Torino, Via P. Giuria 1, I-10125 Torino, Italy; Melis, Stefano [Univ. Torino, Torino, Italy; Prokudin, Alexey [Jefferson Laboratory, 12000 Jeerson Avenue, Newport News, VA 23606, USA

    2015-09-01

    We present our recent results on the study of the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, qT. Using the Collins-Soper-Sterman (CSS) formalism, we study the matching between the region where fixed-order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. We comment on the impact that the nonperturbative component has even at relatively high energies.

  7. Chiral perturbation theory for nucleon generalized parton distributions

    Energy Technology Data Exchange (ETDEWEB)

    Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Manashov, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik]|[Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik

    2006-08-15

    We analyze the moments of the isosinglet generalized parton distributions H, E, H, E of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. (orig.)

  8. Chiral perturbation theory for nucleon generalized parton distributions

    Energy Technology Data Exchange (ETDEWEB)

    Diehl, M. [Deutsches Elektronen-Synchroton DESY, Theory Group, Hamburg (Germany); Manashov, A. [Universitaet Regensburg, Institut fuer Theoretische Physik, Regensburg (Germany); Schaefer, A. [Sankt-Petersburg State University, Department of Theoretical Physics, St.-Petersburg (Russian Federation)

    2006-09-15

    We analyze the moments of the isosinglet generalized parton distributions H, E, H, E of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. (orig.)

  9. Screening of Coulomb interaction and many-body perturbation theory in atoms

    International Nuclear Information System (INIS)

    Dzyuba, V.A.; Flambaum, V.V.; Sil'vestrov, P.G.; Sushkov, O.P.

    1988-01-01

    Taking into account the electron Coulomb interaction screening considerably improves the convergence of perturbation theory in residual interaction. The developed technique allows to take into account screening diagrams in all orders of perturbation theory. Calculation of the correlation corrections to the thallium energy levels is carried out as an example

  10. Lagrangian perturbation theory for modified gravity

    Science.gov (United States)

    Aviles, Alejandro; Cervantes-Cota, Jorge L.

    2017-12-01

    We present a formalism to compute Lagrangian displacement fields for a wide range of cosmologies in the context of perturbation theory up to third order. We emphasize the case of theories with scale-dependent gravitational strengths, such as chameleons, but our formalism can be accommodated to other modified gravity theories. In the nonlinear regime, two qualitative features arise. One, as is well known, is that nonlinearities lead to a screening of the force mediated by the scalar field. The second is a consequence of the transformation of the Klein-Gordon equation from Eulerian to Lagrangian coordinates, producing frame lagging terms that are important especially at large scales, and if not considered, the theory does not reduce to the Λ CDM model in that limit. We apply our formalism to compute the one-loop power spectrum and the correlation function in f (R ) gravity by using different resummation schemes. We further discuss the IR divergences of these formalisms.

  11. Designing perturbative metamaterials from discrete models.

    Science.gov (United States)

    Matlack, Kathryn H; Serra-Garcia, Marc; Palermo, Antonio; Huber, Sebastian D; Daraio, Chiara

    2018-04-01

    Identifying material geometries that lead to metamaterials with desired functionalities presents a challenge for the field. Discrete, or reduced-order, models provide a concise description of complex phenomena, such as negative refraction, or topological surface states; therefore, the combination of geometric building blocks to replicate discrete models presenting the desired features represents a promising approach. However, there is no reliable way to solve such an inverse problem. Here, we introduce 'perturbative metamaterials', a class of metamaterials consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model with individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing two-dimensional elastic metamaterials that realize Veselago lenses, zero-dispersion bands and topological surface phonons. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal and photonic metamaterials composed of weakly interacting unit cells.

  12. A perturbative framework for jet quenching

    CERN Document Server

    Zapp, Korinna C; Wiedemann, Urs A

    2013-01-01

    We present a conceptually new framework for describing jet evolution in the dense medium produced in ultra-relativistic nucleus-nucleus collisions using perturbative QCD and its implementation into the Monte Carlo event generator JEWEL. The rescattering of hard partons in the medium is modelled by infrared continued pQCD matrix elements supplemented with parton showers. The latter approximate higher order real-emission matrix elements and thus generate medium-induced gluon emissions. The interplay between different emissions is governed by their formation times. The destructive interference between subsequent scattering processes, the non-Abelian version of the Landau-Pomeranchuk-Migdal effect, is also taken into account. In this way the complete radiation pattern is consistently treated in a uniform way. Results obtained within this minimal and theoretically well constrained framework are compared with a variety of experimental data susceptible to jet-quenching effects at both RHIC and the LHC. Overall, a go...

  13. Toroidal Energy Principle (TEP) and perturbed equilibrium code STB

    Science.gov (United States)

    Zakharov, Leonid; Hu, Di

    2016-10-01

    The MHD energy principle TEP is presented in terms of perturbations of the vector potential, rather than plasma displacement. This form makes TEP capable to discribe both the ideal plasmas stability and the perturbed equilibria. The functional is expressed in two terms. The first one represents the energy of magnetic field and is calculated using working equilibrium coordinate system. The second term, containing plasma displacement is expressed in the compact form using Hamada coordinates. This representation uses the same combinations of metric coefficients as in the equilibrium calculations. The STB code implements the TEP for both ideal MHD and perturbed equilibria. In the first case, it uses the matching conditions of the ideal MHD. In the second case, the 2-D equilibrium islands are introduced in order to resolve the singularity and match the solutions across the resonant surfaces Partially by (a) US DoE Contract No. DE-AC02-09-CH11466, (b) General Fusion Inc.

  14. Perturbative algebraic quantum field theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Lindner, Falk

    2013-08-15

    We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.

  15. Geometric singular perturbation analysis of systems with friction

    DEFF Research Database (Denmark)

    Bossolini, Elena

    This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter...... use a Poincaré compactification to study the system near infinity. At infinity, the critical manifold loses hyperbolicity with an exponential rate. We use an adaptation of the blow-up method to recover the hyperbolicity. This enables the identification of a new attracting manifold, that organises...... singular, in contrast to the regular stiction solutions that are forward unique. In order to further the understanding of the non-unique dynamics, we introduce a regularization of the model. This gives a singularly perturbed problem that captures the main features of the original discontinuous problem. We...

  16. A convergent reformulation of perturbative QCD

    International Nuclear Information System (INIS)

    Alves, R.J.G.

    2000-10-01

    We present and explore a new formulation of perturbative QCD based not on the renormalised coupling but on the dimensional transmutation parameter of the theory and the property of asymptotic scaling. The approach yields a continued function, the iterated function being that involved in the solution of the two-loop β-function equation. In the so-called large-b limit the continued function reduces to a continued fraction and the successive approximants are diagonal Pade approximants. We investigate numerically the convergence of successive approximants using the leading-b approximation, motivated by renormalons, to model the all-orders result. We consider the Adler D-function of vacuum polarisation, the Polarised Bjorken and Gross-LIewellyn Smith sum rules, the (unpolarised) Bjorken sum rule, and the Minkowskian quantities R τ and the R-ratio of e + e - annihilation. In contrast to diagonal Pade approximants the truncated continued function method gives remarkably stable large-order approximants in cases where infrared renormalon effects are important. We also use the new approach to determine the QCD fundamental parameters from the R τ and the R-ratio measurements, where we find Λ-tilde (3)/MS = 516 ± 48 MeV (which yields α s (μ = m τ ) = 0.360 -0.020 +0.021 ), and Λ-tilde (5)/MS = 299 -7 +6 MeV (which yields α s (μ = m z 0 ) = 0.1218 ± 0.0004), respectively. The evolution of the former value to the m z 0 energy results in α s (μ = m z 0 ) = 0.123 ± 0.002. These values are in line with other determinations available in the literature. We implement the Complete Renormalisation Group Improvement (CORGI) scheme throughout all the calculations. We report on how the mathematical concept of Stieltjes series can be used to assess the convergence of Pade approximants of perturbative series. We find that the combinations of UV renormalons which occur in perturbative QCD may or may not be Stieltjes series depending on the renormalisation scheme used. (author)

  17. Uniqueness of the gauge invariant action for cosmological perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)

    2012-12-01

    In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation.

  18. Higher-order predictions for supersymmetric particle decays

    Energy Technology Data Exchange (ETDEWEB)

    Landwehr, Ananda Demian Patrick

    2012-06-12

    We analyze particle decays including radiative corrections at the next-to-leading order (NLO) within the Minimal Supersymmetric Standard Model (MSSM). If the MSSM is realized at the TeV scale, squark and gluino production and decays yield relevant rates at the LHC. Hence, in the first part of this thesis, we compute decay widths including QCD and electroweak NLO corrections to squark and gluino decays. Furthermore, the Higgs sector of the MSSM is enhanced compared to the one of the Standard Model. Thus, the additional Higgs bosons decay also into supersymmetric particles. These decays and the according NLO corrections are analyzed in the second part of this thesis. The calculations are performed within a common renormalization framework and numerically evaluated in specific benchmark scenarios.

  19. Complete Normal Ordering 1: Foundations

    CERN Document Server

    Ellis, John; Skliros, Dimitri P.

    2016-01-01

    We introduce a new prescription for quantising scalar field theories perturbatively around a true minimum of the full quantum effective action, which is to `complete normal order' the bare action of interest. When the true vacuum of the theory is located at zero field value, the key property of this prescription is the automatic cancellation, to any finite order in perturbation theory, of all tadpole and, more generally, all `cephalopod' Feynman diagrams. The latter are connected diagrams that can be disconnected into two pieces by cutting one internal vertex, with either one or both pieces free from external lines. In addition, this procedure of `complete normal ordering' (which is an extension of the standard field theory definition of normal ordering) reduces by a substantial factor the number of Feynman diagrams to be calculated at any given loop order. We illustrate explicitly the complete normal ordering procedure and the cancellation of cephalopod diagrams in scalar field theories with non-derivative i...

  20. Smeared quasidistributions in perturbation theory

    Science.gov (United States)

    Monahan, Christopher

    2018-03-01

    Quasi- and pseudodistributions provide a new approach to determining parton distribution functions from first principles' calculations of QCD. Here, I calculate the flavor nonsinglet unpolarized quasidistribution at one loop in perturbation theory, using the gradient flow to remove ultraviolet divergences. I demonstrate that, as expected, the gradient flow does not change the infrared structure of the quasidistribution at one loop and use the results to match the smeared matrix elements to those in the MS ¯ scheme. This matching calculation is required to relate numerical results obtained from nonperturbative lattice QCD computations to light-front parton distribution functions extracted from global analyses of experimental data.

  1. "Phonon" scattering beyond perturbation theory

    Science.gov (United States)

    Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing

    2016-02-01

    Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.

  2. EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

    Science.gov (United States)

    Sasaki, Misao; Wands, David

    2010-06-01

    In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

  3. The Schroedinger equation and canonical perturbation theory

    International Nuclear Information System (INIS)

    Graffi, S.; Paul, T.

    1987-01-01

    Let T 0 (ℎ,ω)+εV be the Schroedinger operator corresponding to the classical Hamiltonian H 0 (ω)+εV, where H 0 (ω) is the d-dimensional harmonic oscillator with non-resonant frequencies ω=(ω 1 ..., ω d ) and the potential V(q 1 , ..., q d ) is an entire function of order (d+l) -1 . We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schroedinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schroedinger series near any eigenvalue of T 0 (ℎ,ω) admits a convergent expansion in powers of ℎ of initial point the corresponding term of the classical Birkhoff expansion. Moreover if V is an even polynomial, the above result and the KAM theorem show that all eigenvalues λ n (ℎ,ε) of T 0 +εV such that nℎ coincides with a KAM torus are given, up to order ε ∞ , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in ℎ. (orig.)

  4. Perturbations i have Known and Loved

    Science.gov (United States)

    Field, Robert W.

    2011-06-01

    A spectroscopic perturbation is a disruption of a ^1Σ-^1Σ-like regular pattern that can embody level-shifts, extra lines, and intensity anomalies. Once upon a time, when a band was labeled ``perturbed,'' it was considered worthless because it could at best yield molecular constants unsuited for archival tables. Nevertheless, a few brave spectroscopists, notably Albin Lagerqvist and Richard Barrow, collected perturbations because they knew that the pattern of multiple perturbations formed an intricate puzzle that would eventually reveal the presence and electronic symmetry of otherwise unobservable electronic states. There are many kinds of patterns of broken patterns. In my PhD thesis I showed how to determine absolute vibrational assignments for the perturber from patterns among the observed values of perturbation matrix elements. When a ^3Π state is perturbed, its six (Ω, parity) components capture a pattern of level shifts and intensity anomalies that reveals more about the nature of the perturber than a simple perturbation of the single component of a ^1Σ state. In perturbation-facilitated OODR, a perturbed singlet level acts as a spectroscopic doorway through which the entire triplet manifold may be systematically explored. For polyatomic molecule vibrations, a vibrational polyad (a group of mutually perturbing vibrational levels, among which the perturbation matrix elements are expected to follow harmonic oscillator scaling rules) can contain more components than a ^3Π state and intrapolyad patterns can be exquisitely sensitive not merely to the nature of an interloper within the polyad but also to the eigenvector character of the vibronic state from which the polyad is viewed. Variation of scaled polyad interaction parameters from one polyad to the next, a pattern of patterns, can signal proximity to an isomerization barrier. Everything in Rydberg-land seems to scale as N⋆-3, yet a trespassing valence state causes all scaling and propensity rules go

  5. A pedagogical remark on the main theorem of perturbative renormalization theory

    Energy Technology Data Exchange (ETDEWEB)

    Popineau, G.; Stora, R.

    2016-11-15

    In this note, it is proven that, given two perturbative constructions of time-ordered products via the Bogoliubov-Epstein-Glaser recursion, both sets of coupling functions are related by a local formal power series, recursively determined by causality.

  6. NEXCADE: perturbation analysis for complex networks.

    Directory of Open Access Journals (Sweden)

    Gitanjali Yadav

    Full Text Available Recent advances in network theory have led to considerable progress in our understanding of complex real world systems and their behavior in response to external threats or fluctuations. Much of this research has been invigorated by demonstration of the 'robust, yet fragile' nature of cellular and large-scale systems transcending biology, sociology, and ecology, through application of the network theory to diverse interactions observed in nature such as plant-pollinator, seed-dispersal agent and host-parasite relationships. In this work, we report the development of NEXCADE, an automated and interactive program for inducing disturbances into complex systems defined by networks, focusing on the changes in global network topology and connectivity as a function of the perturbation. NEXCADE uses a graph theoretical approach to simulate perturbations in a user-defined manner, singly, in clusters, or sequentially. To demonstrate the promise it holds for broader adoption by the research community, we provide pre-simulated examples from diverse real-world networks including eukaryotic protein-protein interaction networks, fungal biochemical networks, a variety of ecological food webs in nature as well as social networks. NEXCADE not only enables network visualization at every step of the targeted attacks, but also allows risk assessment, i.e. identification of nodes critical for the robustness of the system of interest, in order to devise and implement context-based strategies for restructuring a network, or to achieve resilience against link or node failures. Source code and license for the software, designed to work on a Linux-based operating system (OS can be downloaded at http://www.nipgr.res.in/nexcade_download.html. In addition, we have developed NEXCADE as an OS-independent online web server freely available to the scientific community without any login requirement at http://www.nipgr.res.in/nexcade.html.

  7. NEXCADE: perturbation analysis for complex networks.

    Science.gov (United States)

    Yadav, Gitanjali; Babu, Suresh

    2012-01-01

    Recent advances in network theory have led to considerable progress in our understanding of complex real world systems and their behavior in response to external threats or fluctuations. Much of this research has been invigorated by demonstration of the 'robust, yet fragile' nature of cellular and large-scale systems transcending biology, sociology, and ecology, through application of the network theory to diverse interactions observed in nature such as plant-pollinator, seed-dispersal agent and host-parasite relationships. In this work, we report the development of NEXCADE, an automated and interactive program for inducing disturbances into complex systems defined by networks, focusing on the changes in global network topology and connectivity as a function of the perturbation. NEXCADE uses a graph theoretical approach to simulate perturbations in a user-defined manner, singly, in clusters, or sequentially. To demonstrate the promise it holds for broader adoption by the research community, we provide pre-simulated examples from diverse real-world networks including eukaryotic protein-protein interaction networks, fungal biochemical networks, a variety of ecological food webs in nature as well as social networks. NEXCADE not only enables network visualization at every step of the targeted attacks, but also allows risk assessment, i.e. identification of nodes critical for the robustness of the system of interest, in order to devise and implement context-based strategies for restructuring a network, or to achieve resilience against link or node failures. Source code and license for the software, designed to work on a Linux-based operating system (OS) can be downloaded at http://www.nipgr.res.in/nexcade_download.html. In addition, we have developed NEXCADE as an OS-independent online web server freely available to the scientific community without any login requirement at http://www.nipgr.res.in/nexcade.html.

  8. Perturbativity in the seesaw mechanism

    International Nuclear Information System (INIS)

    Asaka, Takehiko; Tsuyuki, Takanao

    2016-01-01

    We consider the Standard Model extended by right-handed neutrinos to explain massive neutrinos through the seesaw mechanism. The new fermion can be observed when it has a sufficiently small mass and large mixings to left-handed neutrinos. If such a particle is the lightest right-handed neutrino, its contribution to the mass matrix of active neutrinos needs to be canceled by that of a heavier one. Yukawa couplings of the heavier one are then larger than those of the lightest one. We show that the perturbativity condition gives a severe upper bound on the mixing of the lightest right-handed neutrino, depending on the masses of heavier ones. Models of high energy phenomena, such as leptogenesis, can be constrained by low energy experiments.

  9. Perturbativity in the seesaw mechanism

    Directory of Open Access Journals (Sweden)

    Takehiko Asaka

    2016-02-01

    Full Text Available We consider the Standard Model extended by right-handed neutrinos to explain massive neutrinos through the seesaw mechanism. The new fermion can be observed when it has a sufficiently small mass and large mixings to left-handed neutrinos. If such a particle is the lightest right-handed neutrino, its contribution to the mass matrix of active neutrinos needs to be canceled by that of a heavier one. Yukawa couplings of the heavier one are then larger than those of the lightest one. We show that the perturbativity condition gives a severe upper bound on the mixing of the lightest right-handed neutrino, depending on the masses of heavier ones. Models of high energy phenomena, such as leptogenesis, can be constrained by low energy experiments.

  10. Initial conditions for cosmological perturbations

    Science.gov (United States)

    Ashtekar, Abhay; Gupt, Brajesh

    2017-02-01

    Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations.

  11. Initial conditions for cosmological perturbations

    International Nuclear Information System (INIS)

    Ashtekar, Abhay; Gupt, Brajesh

    2017-01-01

    Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations . (paper)

  12. Analytic perturbation theory in analyzing some QCD observables

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    2001-01-01

    The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD - ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f = 3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution (of an order of α s 3 ) is as a rule numerically inessential. This raises hope for practical solving the well-known problem of asymptotic nature of common QFT perturbation series. The second conclusion is that a common perturbative analysis of time-like events with the big π 2 term in the π 2 coefficient is not adequate at s ≤ 2 GeV 2 . In particular, this relates to τ decay. Then, for the 'high' (f = 5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at 10 GeV ≤ √s ≤ 170 GeV) for analysis of shape/events data contains a systematic negative error of a 1 - 2 per cent level for the extracted α bar s (2) values. Our physical conclusion is that the α bar s (M Z 2 ) value averaged over the f = 5 data s (M Z 2 )> APT; f= 5 ≅ 0.124 appreciably differs from the currently accepted 'world average' (= 0.118)

  13. A general formula for Rayleigh-Schroedinger perturbation energy utilizing a power series expansion of the quantum mechanical Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Herbert, J.M.

    1997-02-01

    Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonian in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.

  14. Closed form bound-state perturbation theory

    Directory of Open Access Journals (Sweden)

    Ollie J. Rose

    1980-01-01

    Full Text Available The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.

  15. Polemic Notes On IR Perturbative Quantum Gravity

    OpenAIRE

    Shapiro, Ilya L.

    2008-01-01

    Quantum gravity is an important and to great extent unsolved problem. There are many different approaches to the quantization of the metric field, both perturbative and non-perturbative. The current situation in the perturbative quantum gravity is characterized by a number of different models, some of them well elaborated but no one perfect nor mathematically neither phenomenologically, mainly because there are no theoretically derived observables which can be experimentally measured. A very ...

  16. Introduction to non-perturbative heavy quark effective theory

    Energy Technology Data Exchange (ETDEWEB)

    Sommer, R. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2010-08-15

    My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti {lambda} and {lambda}{sub 1} lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m){sup n+1} if the theory was treated including (1/m){sup n} terms. Clearly, the weakest point of HQET is that it

  17. Introduction to non-perturbative heavy quark effective theory

    International Nuclear Information System (INIS)

    Sommer, R.

    2010-08-01

    My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti Λ and λ 1 lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m) n+1 if the theory was treated including (1/m) n terms. Clearly, the weakest point of HQET is that it intrinsically is an expansion. In practise, carrying it

  18. Nucleon parton distributions in chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Moiseeva, Alena

    2013-11-19

    Properties of the chiral expansion of nucleon light-cone operators have been studied. In the framework of the chiral perturbation theory we have demonstrated that convergency of the chiral expansion of nucleon parton distributions strongly depends on the value of the variable x. Three regions in x with essentially different analytical properties of the resulting chiral expansion for parton distributions were found. For each of the regions we have elaborated special power counting rules corresponding to the partial resummation of the chiral series. The nonlocal effective operators for the vector and the axial nucleon parton distributions have been constructed at the zeroth and the first chiral order. Using the derived nonlocal operators and the derived power counting rules we have obtained the second order expressions for the nucleon GPDs H(x,ξ,Δ{sup 2}), H(x,ξ,Δ{sup 2}),E(x,ξ,Δ{sup 2}) valid in the region x>or similar a{sup 2}{sub χ}.

  19. Perturbative spacetimes from Yang-Mills theory

    Energy Technology Data Exchange (ETDEWEB)

    Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris 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)

    2017-04-12

    The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.

  20. On adiabatic perturbations in the ekpyrotic scenario

    International Nuclear Information System (INIS)

    Linde, A.; Mukhanov, V.; Vikman, A.

    2010-01-01

    In a recent paper, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in Khoury are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario

  1. Effective potential in the strong-coupling lattice QCD with next-to-next-to-learning order effects

    International Nuclear Information System (INIS)

    Nakano, Takashi Z.; Miura, Kohtaroh; Ohnishi, Akira

    2010-01-01

    We derive an analytic expression of the effective potential at finite temperature (T) and chemical potential (μ) in the strong-coupling lattice QCD for color SU(3) including next-to-next-to-leading order (NNLO) effects in the strong coupling expansion. NNLO effective action terms are systematically evaluated in the leading order of the large dimensional (1/d) expansion, and are found to come from some types of connected two-plaquette configurations. We apply the extended Hubbard-Stratonovich transformation and a gluonic-dressed fermion technique to the effective action, and obtain the effective potential as a function of T, μ, and two order parameters: chiral condensate and vector potential field. The next-to-leading order (NLO) and NNLO effects result in modifications of the wave function renormalization factor, quark mass, and chemical potential. We find that T c,μ =0 and μ c,T =0 are similar to the NLO results, whereas the position of the critical point is sensitive to NNLO corrections. (author)

  2. Perturbative dynamics of fuzzy spheres at large N

    International Nuclear Information System (INIS)

    Azuma, Takehiro; Nagao, Keiichi; Nishimura, Jun

    2005-01-01

    We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the 'one-loop dominance' does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the effective action and obtain various observables to all orders from one-loop calculation by simply shifting the center of expansion to the 'quantum solution', which extremizes the effective action. We confirm the validity of this method by comparison with the direct two-loop calculation and with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From the all order result we find that the perturbative expansion has a finite radius of convergence

  3. Mathematical inference and control of molecular networks from perturbation experiments

    Science.gov (United States)

    Mohammed-Rasheed, Mohammed

    One of the main challenges facing biologists and mathematicians in the post genomic era is to understand the behavior of molecular networks and harness this understanding into an educated intervention of the cell. The cell maintains its function via an elaborate network of interconnecting positive and negative feedback loops of genes, RNA and proteins that send different signals to a large number of pathways and molecules. These structures are referred to as genetic regulatory networks (GRNs) or molecular networks. GRNs can be viewed as dynamical systems with inherent properties and mechanisms, such as steady-state equilibriums and stability, that determine the behavior of the cell. The biological relevance of the mathematical concepts are important as they may predict the differentiation of a stem cell, the maintenance of a normal cell, the development of cancer and its aberrant behavior, and the design of drugs and response to therapy. Uncovering the underlying GRN structure from gene/protein expression data, e.g., microarrays or perturbation experiments, is called inference or reverse engineering of the molecular network. Because of the high cost and time consuming nature of biological experiments, the number of available measurements or experiments is very small compared to the number of molecules (genes, RNA and proteins). In addition, the observations are noisy, where the noise is due to the measurements imperfections as well as the inherent stochasticity of genetic expression levels. Intra-cellular activities and extra-cellular environmental attributes are also another source of variability. Thus, the inference of GRNs is, in general, an under-determined problem with a highly noisy set of observations. The ultimate goal of GRN inference and analysis is to be able to intervene within the network, in order to force it away from undesirable cellular states and into desirable ones. However, it remains a major challenge to design optimal intervention strategies

  4. CO2 perturbation in aquifers : reaction kinetics and metals behavior

    OpenAIRE

    Rillard, Jean

    2013-01-01

    The aim of this thesis was to investigate hydrogeochemical perturbation induced by CO2 in natural aquifers. In a first step, we used chemical data from natural CO2-rich hydrothermal water. We studied variation of fluid chemical composition as a function of CO2 content in order to evaluate reactivity of minerals composing the initial reservoir. Fluid chemical analyses showed decrease in pH, and systematic enrichment in alkalinity and major cations correlated to increase in CO2 content. Chemica...

  5. The sine Gordon model perturbation theory and cluster Monte Carlo

    CERN Document Server

    Hasenbusch, M; Pinn, K

    1994-01-01

    We study the expansion of the surface thickness in the 2-dimensional lattice Sine Gordon model in powers of the fugacity z. Using the expansion to order z**2, we derive lines of constant physics in the rough phase. We describe and test a VMR cluster algorithm for the Monte Carlo simulation of the model. The algorithm shows nearly no critical slowing down. We apply the algorithm in a comparison of our perturbative results with Monte Carlo data.

  6. BCFT and OSFT moduli. An exact perturbative comparison

    Energy Technology Data Exchange (ETDEWEB)

    Larocca, Pier Vittorio; Maccaferri, Carlo [Universita di Torino, Dipartimento di Fisica, Torino (Italy); INFN, Sezione di Torino (Italy)

    2017-11-15

    Starting from the pseudo-B{sub 0} gauge solution for marginal deformations in OSFT, we analytically compute the relation between the perturbative deformation parameter λ in the solution and the BCFT marginal parameter λ, up to fifth order, by evaluating the Ellwood invariants. We observe that the microscopic reason why λ and λ are different is that the OSFT propagator renormalizes contact-term divergences differently from the contour deformation used in BCFT. (orig.)

  7. Non-perturbative aspects of string theory from elliptic curves

    International Nuclear Information System (INIS)

    Reuter, Jonas

    2015-08-01

    We consider two examples for non-perturbative aspects of string theory involving elliptic curves. First, we discuss F-theory on genus-one fibered Calabi-Yau manifolds with the fiber being a hypersurface in a toric fano variety. We discuss in detail the fiber geometry in order to find the gauge groups, matter content and Yukawa couplings of the corresponding supergravity theories for the four examples leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z 2 , U(1) and Z 3 . The theories are connected by Higgsings on the field theory side and conifold transitions on the geometry side. We extend the discussion to the network of Higgsings relating all theories stemming from the 16 hypersurface fibrations. For the models leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z 2 and U(1) we discuss the construction of vertical G 4 fluxes. Via the D3-brane tadpole cancelation condition we can restrict the minimal number of families in the first two of these models to be at least three. As a second example for non-perturbative aspects of string theory we discuss a proposal for a non-perturbative completion of topological string theory on local B-model geometries. We discuss in detail the computation of quantum periods for the examples of local F 1 , local F 2 and the resolution of C 3 /Z 5 . The quantum corrections are calculated order by order using second order differential operators acting on the classical periods. Using quantum geometry we calculate the refined free energies in the Nekrasov-Shatashvili limit. Finally we check the non-perturbative completion of topological string theory for the geometry of local F 2 against numerical calculations.

  8. Generalized parton distributions for the nucleon in chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Manashov, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik]|[Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics; Schaefer, A. [Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics

    2006-11-15

    We complete the analysis of twist-two generalized parton distributions of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. Extending our previous study of the chiral-even isosinglet sector, we give results for chiral-even isotriplet distributions and for the chiral-odd sector. We also calculate the one-loop corrections for the chiral-odd generalized parton distributions of the pion. (orig.)

  9. Generalized parton distributions for the nucleon in chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Diehl, M. [Deutsches Elektronen-Synchroton DESY, Theory Group, Hamburg (Germany); Manashov, A. [Universitaet Regensburg, Institut fuer Theoretische Physik, Regensburg (Germany); Sankt-Petersburg State University, Department of Theoretical Physics, St.-Petersburg (Russian Federation); Schaefer, A. [Universitaet Regensburg, Institut fuer Theoretische Physik, Regensburg (Germany)

    2007-03-15

    We complete the analysis of twist-two generalized parton distributions of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. Extending our previous study of the chiral-even isosinglet sector, we give results for chiral-even isotriplet distributions and for the chiral-odd sector. We also calculate the one-loop corrections for the chiral-odd generalized parton distributions of the pion. (orig.)

  10. Non-perturbative aspects of string theory from elliptic curves

    Energy Technology Data Exchange (ETDEWEB)

    Reuter, Jonas

    2015-08-15

    We consider two examples for non-perturbative aspects of string theory involving elliptic curves. First, we discuss F-theory on genus-one fibered Calabi-Yau manifolds with the fiber being a hypersurface in a toric fano variety. We discuss in detail the fiber geometry in order to find the gauge groups, matter content and Yukawa couplings of the corresponding supergravity theories for the four examples leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z{sub 2}, U(1) and Z{sub 3}. The theories are connected by Higgsings on the field theory side and conifold transitions on the geometry side. We extend the discussion to the network of Higgsings relating all theories stemming from the 16 hypersurface fibrations. For the models leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z{sub 2} and U(1) we discuss the construction of vertical G{sub 4} fluxes. Via the D3-brane tadpole cancelation condition we can restrict the minimal number of families in the first two of these models to be at least three. As a second example for non-perturbative aspects of string theory we discuss a proposal for a non-perturbative completion of topological string theory on local B-model geometries. We discuss in detail the computation of quantum periods for the examples of local F{sub 1}, local F{sub 2} and the resolution of C{sub 3}/Z{sub 5}. The quantum corrections are calculated order by order using second order differential operators acting on the classical periods. Using quantum geometry we calculate the refined free energies in the Nekrasov-Shatashvili limit. Finally we check the non-perturbative completion of topological string theory for the geometry of local F{sub 2} against numerical calculations.

  11. Canard solutions of two-dimensional singularly perturbed systems

    Energy Technology Data Exchange (ETDEWEB)

    Chen Xianfeng [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)]. E-mail: chenxf@sjtu.edu.cn; Yu Pei [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Applied Mathematics, University of Western Ontario London, Ont., N6A 5B7 (Canada); Han Maoan [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Zhang Weijiang [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)

    2005-02-01

    In this paper, some new lemmas on asymptotic analysis are established. We apply an asymptotic method to study generalized two-dimensional singularly perturbed systems with one parameter, whose critical manifold has an m-22 th-order degenerate extreme point. Certain sufficient conditions are obtained for the existence of canard solutions, which are the extension and correction of some existing results. Finally, one numerical example is given.

  12. Control of a perturbed under-actuated mechanical system

    KAUST Repository

    Zayane, Chadia

    2015-11-05

    In this work, the trajectory tracking problem for an under-actuated mechanical system in presence of unknown input disturbances is addressed. The studied inertia wheel inverted pendulum falls in the class of non minimum phase systems. The proposed high order sliding mode control architecture including a controller and differentiator allows to track accurately the predefined trajectory and to stabilize the internal dynamics. The robustness of the proposed approach is illustrated through different perturbation and output noise configurations.

  13. High energy deep inelastic scattering in perturbative quantum chromodynamics

    International Nuclear Information System (INIS)

    Wallon, S.

    1996-01-01

    In this PhD thesis, we deal with high energy Deep Inelastic Scattering in Perturbative Quantum Chromodynamics (QCD). In this work, two main topics are emphasized: The first one deals with dynamics based on perturbative renormalization group, and on perturbative Regge approaches. We discuss the applicability of these predictions, the possibility of distinguishing them in the HERA experiments, and their unification. We prove that the perturbative Regge dynamic can be successfully applied to describe the HERA data. Different observables are proposed for distinguishing these two approaches. We show that these two predictions can be unified in a system of equations. In the second one, unitarization and saturation problems in high energy QCD are discussed. In the multi-Regge approach, equivalent to the integrable one-dimensional XXX Heisenberg spin chain, we develop methods in order to solve this system, based on the Functional Bethe Ansatz. In the dipole model context, we propose a new formulation of unitarity and saturation effects, using Wilson loops. (author)

  14. ORBITAL CONNECTIONS FOR PERTURBATION-DEPENDENT BASIS-SETS

    DEFF Research Database (Denmark)

    Olsen, Jeppe; Bak, Keld L.; Ruud, K.

    1995-01-01

    The use of perturbation-dependent basis sets is analysed with emphasis on the connection between the basis sets at different values of the perturbation strength. A particular connection, the natural connection, that minimizes the change of the basis set orbitals is devised and the second quantiza......The use of perturbation-dependent basis sets is analysed with emphasis on the connection between the basis sets at different values of the perturbation strength. A particular connection, the natural connection, that minimizes the change of the basis set orbitals is devised and the second...... quantization realization of this connection is introduced. It is shown that the natural connection is important for the efficient evaluation of molecular properties and for the physical interpretation of the terms entering the calculated properties. For example, in molecular Hessian calculations the natural...... connection reduces the size of the relaxation term, leading to faster convergence of the response equations. The physical separation of the terms also means that first-order non-adiabatic coupling matrix elements can be obtained in a very simple way from a molecular Hessian calculation....

  15. Sensitivity calculations of integral parameters by a generalyzed perturbation theory

    International Nuclear Information System (INIS)

    Santo, A.C.F. de.

    1981-12-01

    In this work, we first revise some concepts, concerning the neutron transport in nuclear systems. We derive the balance and importance equation. Then we discuss the neutron importance in subcritical, critical and supercritical systems. The adjoint flux is estabilished as the neutron importance for the fission process. The conventional perturbation theory is later presented. We developed a sistematic perturbative formulation in the first order variation in the distribution functions calculate the reactivity due to a system perturbation. We present in detail the flux difference and generalized functions methos. The above formulation is then extended for altered systems. We consider integral parameters of the type ratio of bilinear functionals (for which the reactivity is a particular case). We define sensitivity coeficients, for any integral parameter, corresponding to a especific system alterations. Possible aplication of the method are also discussed. In the last part of this work, we apply the perturbative formulation to the doppler reacitivity sensibility calculation, utilizing the generalized functions method. We describe in detail the compiler program written for this and some other possible aplications. (Author) [pt

  16. An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals

    Science.gov (United States)

    Lee, Timothy J.; Jayatilaka, Dylan

    1993-01-01

    A new open-shell perturbation theory is formulated in terms of symmetric spin orbitals. Only one set of spatial orbitals is required, thereby reducing the number of independent coefficients in the perturbed wavefunctions. For second order, the computational cost is shown to be similar to a closed-shell calculation. This formalism is therefore more efficient than the recently developed RMP, ROMP or RMP-MBPT theories. The perturbation theory described herein was designed to have a close correspondence with our recently proposed coupled-cluster theory based on symmetric spin orbitals. The first-order wavefunction contains contributions from only doubly excited determinants. Equilibrium structures and vibrational frequencies determined from second-order perturbation theory are presented for OH, NH, CH, 02, NH2 and CH2.

  17. Evolution of optical pulses in the presence of third-order dispersion

    Indian Academy of Sciences (India)

    of third-order dispersion experience corruption [2]. This appears to be the main reason to have in the literature a detailed theoretical study [3] for solving (2). The third-order dispersion in (2) perturbs the soliton of (1). The parameter β is a mea- sure of this perturbation. The main theoretical method for studying the perturbed.

  18. Quantum geometry of resurgent perturbative/nonperturbative relations

    Science.gov (United States)

    Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat

    2017-05-01

    For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain \\mathcal{N} = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.

  19. Chiral perturbation theory with nucleons

    Energy Technology Data Exchange (ETDEWEB)

    Meissner, U.G.

    1991-09-01

    I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, {pi}N scattering and the {sigma}-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon.

  20. Chiral perturbation theory with nucleons

    International Nuclear Information System (INIS)

    Meissner, U.G.

    1991-09-01

    I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, πN scattering and the σ-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon

  1. Perturbed angular correlations and distributions

    International Nuclear Information System (INIS)

    Makaryunas, K.

    1976-01-01

    The present index comprises original works and review papers on the perturbed angular correlations (PAC) and distributions (PAD). The articles published in the Soviet and foreign journals as well as the materials of conferences, monographs and collections published in the USSR and abroad, the preprints produced by various institutes and abstracts of disertations are included from 1948 up to 1973. The whole material compiled in this index is divided into three parts. Part one is a bibliographic index. All papers in this part are divided into three sections. Section one comprises the papers devoted to the theoretical works on PAC, review papers, monographs, materials of conferences. Section two deals with the works of methodical character where correlation spectrometers as well as the treatment of experimental data are described. In section three experimental works with concrete nuclei are compiled. Part two gives the characteristic of works performed with concrete nuclei. This part is presented in the form of the table in which the works are systematized according to the chemical elements and isotopes. The table shows the characteristics of the nuclear levels used in the investigations by PAC as well as brief characteristics of experiments and results obtained. Part three - appendix contains alphabetic index of the authors, the list of the used editions with the abbreviations of the titles of these editions. The lists indicating the dynamic of the quantity of works on PAC and the distribution according to the literature sources are also given

  2. Scalar Quantum Electrodynamics: Perturbation Theory and Beyond

    International Nuclear Information System (INIS)

    Bashir, A.; Gutierrez-Guerrero, L. X.; Concha-Sanchez, Y.

    2006-01-01

    In this article, we calculate scalar propagator in arbitrary dimensions and gauge and the three-point scalar-photon vertex in arbitrary dimensions and Feynman gauge, both at the one loop level. We also discuss constraints on their non perturbative structure imposed by requirements of gauge invariance and perturbation theory

  3. On the non-perturbative effects

    International Nuclear Information System (INIS)

    Manjavidze, J.; Voronyuk, V.

    2004-01-01

    The quantum correspondence principle based on the time reversibility is adopted to take into account the non-Abelian symmetry constrains. The main properties of the new strong-coupling perturbation theory which take into account non-perturbative effects are described. (author)

  4. Tests of Monte Carlo perturbation theory for the free energy of liquid copper.

    Science.gov (United States)

    Greeff, C W

    2008-05-14

    Monte Carlo perturbation theory, in which terms in the thermodynamic perturbation series are evaluated by Monte Carlo averaging, has potentially large advantages in efficiency for calculating free energies of liquids from ab initio potential surfaces. In order to test the accuracy of perturbation theory for liquid metals, a series of calculations has been done on liquid copper, modeled by an embedded atom potential. A simple 1/r(12) pair potential is used as the reference system. The free energy is calculated to third order in perturbation theory, and the results are compared to an exact formula. It is found that for optimal reference potential parameters, second order perturbation theory is essentially exact. Second and third order theories give accurate results for significantly nonoptimal reference parameters. The relation between perturbation theory and reweighting is discussed, and an approximate formula is derived that shows an exponential dependence of the efficiency of reweighting on the second order free energy correction. Finally, techniques for application to ab initio potentials are discussed. It is shown that with samples of 100 configurations, it is possible to obtain accuracy and precision at the level of approximately 1 meV/atom.

  5. On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

    International Nuclear Information System (INIS)

    Liu Hongzhun; Pan Zuliang; Li Peng

    2006-01-01

    In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.

  6. Flow in a circular expansion pipe flow: effect of a vortex perturbation on localised turbulence

    Science.gov (United States)

    Selvam, Kamal; Peixinho, Jorge; Willis, Ashley P.

    2016-12-01

    We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a sudden expansion. At the inlet, a parabolic velocity profile is applied together with a finite amplitude perturbation in the form of a vortex with its axis parallel to the axis of the pipe. At sufficiently high Reynolds numbers the recirculation region breaks into a turbulent patch that changes position axially, depending on the strength of the perturbation. This vortex perturbation is believed to produce a less abrupt transition than in previous studies, which applied a tilt perturbation, as the localised turbulence is observed via the formation of a wavy structure at a low order azimuthal mode, which resembles an optimally amplified perturbation. For large vortex amplitude, the localised turbulence remains at a constant axial position. It is further investigated using proper orthogonal decomposition, which indicates that the centre region close to the expansion is highly energetic.

  7. δ M formalism: a new approach to cosmological perturbation theory in anisotropic inflation

    Science.gov (United States)

    Talebian-Ashkezari, A.; Ahmadi, N.; Abolhasani, A. A.

    2018-03-01

    We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the δ M formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in almost the same way that the so-called δ N formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, δ N, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as δ N it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.

  8. Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

    KAUST Repository

    Higueras, Inmaculada

    2018-02-14

    Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.

  9. High energy deep inelastic scattering in perturbative quantum chromodynamics; Diffusion profondement inelastique a grande energie en chromodynamique quantique perturbative

    Energy Technology Data Exchange (ETDEWEB)

    Wallon, S.

    1996-09-17

    In this PhD thesis, we deal with high energy Deep Inelastic Scattering in Perturbative Quantum Chromodynamics (QCD). In this work, two main topics are emphasized: The first one deals with dynamics based on perturbative renormalization group, and on perturbative Regge approaches. We discuss the applicability of these predictions, the possibility of distinguishing them in the HERA experiments, and their unification. We prove that the perturbative Regge dynamic can be successfully applied to describe the HERA data. Different observables are proposed for distinguishing these two approaches. We show that these two predictions can be unified in a system of equations. In the second one, unitarization and saturation problems in high energy QCD are discussed. In the multi-Regge approach, equivalent to the integrable one-dimensional XXX Heisenberg spin chain, we develop methods in order to solve this system, based on the Functional Bethe Ansatz. In the dipole model context, we propose a new formulation of unitarity and saturation effects, using Wilson loops. (author). 120 refs.

  10. Deformation from symmetry for Schrodinger equations of higher order on unbounded domains

    Directory of Open Access Journals (Sweden)

    Addolorata Salvatore

    2003-06-01

    Full Text Available By means of a perturbation method recently introduced by Bolle, we discuss the existence of infinitely many solutions for a class of perturbed symmetric higher order Schrodinger equations with non-homogeneous boundary data on unbounded domains.

  11. Problems at the interface between perturbative and nonperturbative quantum chromodynamics

    International Nuclear Information System (INIS)

    Brodsky, S.J.; Bodwin, G.T.; Lepage, G.P.

    1983-06-01

    Predictions based on perturbative QCD rest on three premises: (1) that hadronic interactions become weak in strength at small invariant separation; (2) that the perturbative expansion in α/sub s/(Q) is well-defined; and (3) factorization: all effects of collinear singularities, confinement, nonperturbative interactions, and bound state dynamics can be isolated at large momentum transfer in terms of structure functions, fragmentation functions, or in the case of exclusive processes, distribution amplitudes. The assumption that the perturbative expansion for hard scattering amplitudes converges has certainly not been demonstrated; in addition, there are serious ambiguities concerning the choice of renormalization scheme and scale choice Q 2 for the expansion in α/sub s/(Q 2 ). We will discuss a new procedure to at least partly rectify the latter problem. In the case of exclusive processes, the factorization of hadronic amplitudes at large momentum transfer in the form of distribution amplitudes convoluted with hard scattering quark-gluon subprocess amplitudes can be demonstrated systematically to all orders in α/sub s/(Q 2 ). In the case of inclusive reactions, factorization remains an ansatz; general all-orders proofs do not exist because of the complications of soft initial state interactions for hadron-induced processes; thus far factorization has only been verified to two loops beyond lowest order in a regime where the applicability of perturbation theory is in doubt. However, we shall show that a necessary condition for the validity of factorization in inclusive reactions is that the momentum transfer must be large compared to the (rest frame) length of the target. We review the present status of the factorization ansatz. 52 references

  12. Constituent quark masses from modified perturbative QCD

    Energy Technology Data Exchange (ETDEWEB)

    Cabo Montes de Oca, A. [Instituto de Cibernetica, Matematica y Fisica, La Habana (Cuba); International Institute for Theoretical and Applied Physics (IITAP), UNESCO and Iowa State University, Ames, IA (United States); Rigol Madrazo, M. [Centro de Estudios Aplicados al Desarrollo Nuclear, La Habana (Cuba)

    2002-03-01

    A recently proposed modified perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in first approximation. The results predict mass values of 1/3 of the nucleon mass for the light quarks u, d, and s and a monotonously growing variation with the current mass. The only phenomenological input is that left angle G{sup 2} right angle is evaluated up to order g{sup 2} as a function of the unique parameter C defining the modified propagator, and then C is fixed to give a current estimate of left angle g{sup 2}G{sup 2} right angle. The light quarks u and d as a result are found to be confined and the s, c, b and t ones show damped propagation modes, suggesting a model for the large differences in stability between the nucleons and the higher resonances. The above properties of quark modes diverge from the fully confinement result following from the similar gluon propagator previously considered by Munczek and Nemirovski. On the other hand, the condensate effects on the gluon self-energy furnish a tachyonic mass shell as predicted by the Fukuda analysis of gluon condensation in QCD. (orig.)

  13. Threshold resummation in SCET vs. perturbative QCD. An analytic comparison

    Energy Technology Data Exchange (ETDEWEB)

    Bonvini, Marco [Genoa Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Genoa (Italy); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Forte, Stefano [Milano Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Milan (Italy); Ghezzi, Margherita [Milano Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Milan (Italy); Rome Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Rome (Italy); Ridolfi, Giovanni [Genoa Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Genoa (Italy)

    2012-01-15

    We compare threshold resummation in QCD, as performed using soft-collinear effective theory (SCET), to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross-sections. We consider various forms of the SCET result, which correspond to different choices of the soft scale {mu}{sub s} that characterizes this approach. We derive a master formula that relates the SCET resummation to the QCD result for any choice of {mu}{sub s}. We then use it first, to show that if SCET resummation is performed in N-Mellin moment space by suitable choice of {mu}{sub s} it is equivalent to the standard perturbative approach. Next, we show that if SCET resummation is performed by choosing for {mu}{sub s} a partonic momentum variable, the perturbative result for partonic resummed cross-sections is again reproduced, but like its standard perturbative counterpart it is beset by divergent behaviour at the endpoint. Finally, using the master formula we show that when {mu}{sub s} is chosen as a hadronic momentum variable the SCET and standard approach are related through a multiplicative (convolutive) factor, which contains the dependence on the Landau pole and associated divergence. This factor depends on the luminosity in a non-universal way; it lowers by one power of log the accuracy of the resummed result, but it is otherwise subleading if one assumes the luminosity not to contain logarithmically enhanced terms. Therefore, the SCET approach can be turned into a prescription to remove the Landau pole from the perturbative result, but the price to pay for this is the reduction by one logarithmic power of the accuracy at each order and the need to make assumptions on the parton luminosity. (orig.)

  14. Threshold resummation in SCET vs. perturbative QCD. An analytic comparison

    International Nuclear Information System (INIS)

    Bonvini, Marco; Forte, Stefano; Ghezzi, Margherita; Ridolfi, Giovanni

    2012-01-01

    We compare threshold resummation in QCD, as performed using soft-collinear effective theory (SCET), to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross-sections. We consider various forms of the SCET result, which correspond to different choices of the soft scale μ s that characterizes this approach. We derive a master formula that relates the SCET resummation to the QCD result for any choice of μ s . We then use it first, to show that if SCET resummation is performed in N-Mellin moment space by suitable choice of μ s it is equivalent to the standard perturbative approach. Next, we show that if SCET resummation is performed by choosing for μ s a partonic momentum variable, the perturbative result for partonic resummed cross-sections is again reproduced, but like its standard perturbative counterpart it is beset by divergent behaviour at the endpoint. Finally, using the master formula we show that when μ s is chosen as a hadronic momentum variable the SCET and standard approach are related through a multiplicative (convolutive) factor, which contains the dependence on the Landau pole and associated divergence. This factor depends on the luminosity in a non-universal way; it lowers by one power of log the accuracy of the resummed result, but it is otherwise subleading if one assumes the luminosity not to contain logarithmically enhanced terms. Therefore, the SCET approach can be turned into a prescription to remove the Landau pole from the perturbative result, but the price to pay for this is the reduction by one logarithmic power of the accuracy at each order and the need to make assumptions on the parton luminosity. (orig.)

  15. Black hole perturbation under a 2 +2 decomposition in the action

    Science.gov (United States)

    Ripley, Justin L.; Yagi, Kent

    2018-01-01

    Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations instead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a 2 +2 splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally reduce the action to two dimensions by integrating over the two sphere. We find that the axial perturbation degree of freedom is described by a two-dimensional massive vector action, and that the polar perturbation degree of freedom is described by a two-dimensional dilaton massive gravity action. Varying the dimensionally reduced actions, we rederive covariant and gauge-invariant master equations for the axial and polar degrees of freedom. Thus, the two-dimensional massive vector and massive gravity actions we derive by dimensionally reducing the perturbed Einstein-Hilbert action describe the dynamics of a well-studied physical system: the metric perturbations of a static black hole. The 2 +2 formalism we present can be generalized to m +n -dimensional spacetime splittings, which may be useful in more generic situations, such as expanding metric perturbations in higher dimensional gravity. We provide a self-contained presentation of m +n formalism for vacuum spacetime splittings.

  16. Sensitivity of regional ensemble data assimilation spread to perturbations of lateral boundary conditions

    Directory of Open Access Journals (Sweden)

    Rachida El Ouaraini

    2015-12-01

    Full Text Available The implementation of a regional ensemble data assimilation and forecasting system requires the specification of appropriate perturbations of lateral boundary conditions (LBCs, in order to simulate associated errors. The sensitivity of analysis and 6-h forecast ensemble spread to these perturbations is studied here formally and experimentally by comparing three different LBC configurations for the ensemble data assimilation system of the ALADIN-France limited-area model (LAM. While perturbed initial LBCs are provided by the perturbed LAM analyses in each ensemble, the three ensemble configurations differ with respect to LBCs used at 3- and 6-h forecast ranges, which respectively correspond to: (1 perturbed LBCs provided by the operational global ensemble data assimilation system (GLBC, which is considered as a reference configuration; (2 unperturbed LBCs (ULBC obtained from the global deterministic model; (3 perturbed LBCs obtained by adding random draws of an error covariance model (PLBC to the global deterministic system. A formal analysis of error and perturbation equations is first carried out, in order to provide an insight of the relative effects of observation perturbations and of LBC perturbations at different ranges, in the various ensemble configurations. Horizontal variations of time-averaged ensemble spread are then examined for 6-h forecasts. Despite the use of perturbed initial LBCs, the regional ensemble ULBC is underdispersive not only near the lateral boundaries, but also in approximately one-third of the inner area, due to advection during the data assimilation cycle. This artefact is avoided in PLBC through the additional use of non-zero LBC perturbations at 3- and 6-h ranges, and the sensitivity to the amplitude scaling of the covariance model is illustrated for this configuration. Some aspects of the temporal variation of ensemble spread and associated sensitivities to LBC perturbations are also studied. These results

  17. Perturbation approach to a molecular orbital theory of interaction energies

    International Nuclear Information System (INIS)

    Chipman, D.M.

    1982-01-01

    In order to provide a framework for better understanding of phenomena such as reaction mechanisms and photoelectron spectra that can be semiquantitatively described by molecular orbital theory, a formalism is developed to express the orbitals of a molecule in terms of orbitals of various fragments that make up the molecule. The total energy and individual orbital energies of the interacting fragments are obtained through second order in perturbation theory. Electrostatic interactions, orbital overlap effects, and self-consistency refinements are all considered explicitly and simultaneously to obtain the final results

  18. Unmatched Projector/Backprojector Pairs: Perturbation and Convergence Analysis

    DEFF Research Database (Denmark)

    Elfving, Tommy; Hansen, Per Christian

    2018-01-01

    are not each other's transpose. Surprisingly, the influence of such errors in algebraic iterative reconstruction methods has received little attention in the literature. The goal of this paper is to perform a rigorous first-order perturbation analysis of the minimization problems underlying the algebraic...... methods in order to understand the role played by the nonmatch of the matrices. We also study the convergence properties of linear stationary iterations based on unmatched matrix pairs, leading to insight into the behavior of some important row-and column-oriented algebraic iterative methods. We conclude...

  19. Baryon decuplet mass relations in chiral perturbation theory

    International Nuclear Information System (INIS)

    Lebed, Richard F.

    1994-01-01

    Baryon decuplet masses within an SU(3) L xSU(3) R chiral Lagrangian formalism are found to satisfy four relations at second order in flavor breaking. As a result, the one-loop corrections from Lagrangian terms up to first order in flavor breaking are observed to give finite and calculable corrections to these relations. The importance of group theory in establishing the relations and eliminating many loop corrections is emphasized. The formal expressions for these corrections are presented, followed by numerical evaluations. We find consistency between the experimental values of breaking of the relations and the loop corrections of these relations as predicted by chiral perturbation theory. ((orig.))

  20. Atomic and magnetic configurational energetics by the generalized perturbation method

    DEFF Research Database (Denmark)

    Ruban, Andrei V.; Shallcross, Sam; Simak, S.I.

    2004-01-01

    It is shown that, using the generalized perturbation method (GPM) with screened Coulomb interactions that ensures its consistency with the force theorem, one is able to obtain effective interactions that yield an accurate and physically transparent description of configurational energetics...... in the framework of the Korringa-Kohn-Rostoker method within the atomic sphere and coherent potential approximations. This is demonstrated with calculations of ordering energies, short-range order parameters, and transition temperatures in the CuZn, CuAu, CuPd, and PtCo systems. Furthermore, we show that the GPM...

  1. Perturbative Quantum Gravity and its Relation to Gauge Theory

    Directory of Open Access Journals (Sweden)

    Bern Zvi

    2002-01-01

    Full Text Available In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

  2. Non-perturbative effects in supersymmetry

    International Nuclear Information System (INIS)

    Veneziano, G.

    1987-01-01

    Some non perturbative aspects of globally supersymmetric (SUSY) gauge theories are discussed. These share with their non-supersymmetric analogues interesting non perturbative features, such as the spontaneous breaking of chiral symmetries via condensates. What is peculiar about supersymmetric theories, however, is that one is able to say a lot about non-perturbative effects even without resorting to elaborate numerical calculations: general arguments, supersymmetric and chiral Ward identities and analytic, dynamical calculations will turn out to effectively determine most of the supersymmetric vacuum properties. 28 references, 5 figures

  3. Critical behaviors of gravity under quantum perturbations

    Directory of Open Access Journals (Sweden)

    ZHANG Hongsheng

    2014-02-01

    Full Text Available Phase transition and critical phenomenon is a very interesting topic in thermodynamics and statistical mechanics. Gravity is believed to have deep and inherent relation to thermodynamics. Near the critical point,the perturbation becomes significant. Thus for ordinary matter (governed by interactions besides gravity the critical behavior will become very different if we ignore the perturbations around the critical point,such as mean field theory. We find that the critical exponents for RN-AdS spacetime keep the same values even when we consider the full quantum perturbations. This indicates a key difference between gravity and ordinary thermodynamic system.

  4. Intrinsic entropy perturbations from the dark sector

    Science.gov (United States)

    Celoria, Marco; Comelli, Denis; Pilo, Luigi

    2018-03-01

    Perfect fluids are modeled by using an effective field theory approach which naturally gives a self-consistent and unambiguous description of the intrinsic non-adiabatic contribution to pressure variations. We study the impact of intrinsic entropy perturbation on the superhorizon dynamics of the curvature perturbation Script R in the dark sector. The dark sector, made of dark matter and dark energy is described as a single perfect fluid. The non-perturbative vorticity's dynamics and the Weinberg theorem violation for perfect fluids are also studied.

  5. Perturbed generalized multicritical one-matrix models

    Science.gov (United States)

    Ambjørn, J.; Chekhov, L.; Makeenko, Y.

    2018-03-01

    We study perturbations around the generalized Kazakov multicritical one-matrix model. The multicritical matrix model has a potential where the coefficients of zn only fall off as a power 1 /n s + 1. This implies that the potential and its derivatives have a cut along the real axis, leading to technical problems when one performs perturbations away from the generalized Kazakov model. Nevertheless it is possible to relate the perturbed partition function to the tau-function of a KdV hierarchy and solve the model by a genus expansion in the double scaling limit.

  6. Solitonic Integrable Perturbations of Parafermionic Theories

    CERN Document Server

    Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L

    1997-01-01

    The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.

  7. Roles of dark energy perturbations in dynamical dark energy models: can we ignore them?

    Science.gov (United States)

    Park, Chan-Gyung; Hwang, Jai-chan; Lee, Jae-heon; Noh, Hyerim

    2009-10-09

    We show the importance of properly including the perturbations of the dark energy component in the dynamical dark energy models based on a scalar field and modified gravity theories in order to meet with present and future observational precisions. Based on a simple scaling scalar field dark energy model, we show that observationally distinguishable substantial differences appear by ignoring the dark energy perturbation. By ignoring it the perturbed system of equations becomes inconsistent and deviations in (gauge-invariant) power spectra depend on the gauge choice.

  8. Fermi interaction. Conservation of vector current and modified perturbation theory

    International Nuclear Information System (INIS)

    Rochev, V.E.

    1983-01-01

    The Fermi interaction (anti psi ysub(n) psi)sup(2) is investigated with the method of auxilary field. The analogues of the Ward-Takahashi electrodynamical identities and the gauge transformations of Green functions, that are the consequence of the conservation of vector current, have been obtained. The gauge function for the spinor propagator is the exponential superpropagator. The arguments are given in favour of the existence of a modified perturbation theory, which is finite in every order and non-analytical over its coupling constant, for the four-fermion interaction. The non-analytical part is defined unambiguously, and the analytical part contains a set of finite dimensionless constants to define which non-perturbative information is needed. The simplest model (the chain approximation) for the non-stable vector bound state is considered

  9. Local polynomial Whittle estimation of perturbed fractional processes

    DEFF Research Database (Denmark)

    Frederiksen, Per; Nielsen, Frank; Nielsen, Morten Ørregaard

    We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the spectrum of the perturbation as well as that of the short-memory component...... of the signal by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptotic variance of the long memory estimate by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal....... Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle estimator....

  10. Equivalence of two contour prescriptions in superstring perturbation theory

    Science.gov (United States)

    Sen, Ashoke

    2017-04-01

    Conventional superstring perturbation theory based on the world-sheet approach gives divergent results for the S-matrix whenever the total center of mass energy of the incoming particles exceeds the threshold of production of any final state consistent with conservation laws. Two systematic approaches have been suggested for dealing with this difficulty. The first one involves deforming the integration cycles over the moduli space of punctured Riemann surfaces into complexified moduli space. The second one treats the amplitude as a sum of superstring field theory Feynman diagrams and deforms the integration contours over loop energies of the Feynman diagram into the complex plane. In this paper we establish the equivalence of the two prescriptions to all orders in perturbation theory. Since the second approach is known to lead to unitary amplitudes, this establishes the consistency of the first prescription with unitarity.

  11. Limit cycles bifurcating from a perturbed quartic center

    Energy Technology Data Exchange (ETDEWEB)

    Coll, Bartomeu, E-mail: dmitcv0@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain); Llibre, Jaume, E-mail: jllibre@mat.uab.ca [Dept. de Matematiques, Universitat Autonoma de Barcelona, Edifici Cc 08193 Bellaterra, Barcelona, Catalonia (Spain); Prohens, Rafel, E-mail: dmirps3@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain)

    2011-04-15

    Highlights: We study polynomial perturbations of a quartic center. We get simultaneous upper and lower bounds for the bifurcating limit cycles. A higher lower bound for the maximum number of limit cycles is obtained. We obtain more limit cycles than the number obtained in the cubic case. - Abstract: We consider the quartic center x{sup .}=-yf(x,y),y{sup .}=xf(x,y), with f(x, y) = (x + a) (y + b) (x + c) and abc {ne} 0. Here we study the maximum number {sigma} of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n - 1)/2] + 4 {<=} {sigma} {<=} 5[(n - 1)/2] + 14, where [{eta}] denotes the integer part function of {eta}.

  12. Non-perturbative approach for laser radiation interactions with solids

    International Nuclear Information System (INIS)

    Jalbert, G.

    1985-01-01

    Multiphoton transitions in direct-gap crystals are studied considering non-perturbative approaches. Two methods currently used for atoms and molecules are revised, generalized and applied to solids. In the first one, we construct an S-matrix which incorporates the eletromagnetic field to all orders in an approximated way leading to analytical solution for the multiphoton transition rates. In the second one, the transition probability is calculated within the Bloch-Floquet formalism applieed to the specific case of solids. This formalism is interpreted as a classical approximation to the quantum treatment of the field. In the weak field limit, we compare our results with the usual perturbation calculations. We also incorporate, in the first approach, the non homogeneity and the multimodes effects of a real laser. (author) [pt

  13. Equivalence of two contour prescriptions in superstring perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Sen, Ashoke [Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019 (India); Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085 (India); School of Physics, Korea Institute for Advanced Study,Seoul 130-722 (Korea, Republic of)

    2017-04-05

    Conventional superstring perturbation theory based on the world-sheet approach gives divergent results for the S-matrix whenever the total center of mass energy of the incoming particles exceeds the threshold of production of any final state consistent with conservation laws. Two systematic approaches have been suggested for dealing with this difficulty. The first one involves deforming the integration cycles over the moduli space of punctured Riemann surfaces into complexified moduli space. The second one treats the amplitude as a sum of superstring field theory Feynman diagrams and deforms the integration contours over loop energies of the Feynman diagram into the complex plane. In this paper we establish the equivalence of the two prescriptions to all orders in perturbation theory. Since the second approach is known to lead to unitary amplitudes, this establishes the consistency of the first prescription with unitarity.

  14. Non-Perturbative Formulation of Time-Dependent String Solutions

    CERN Document Server

    Alexandre, J; Mavromatos, Nikolaos E; Alexandre, Jean; Ellis, John; Mavromatos, Nikolaos E.

    2006-01-01

    We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times.

  15. Perturbative improvement of staggered fermions using fat links

    International Nuclear Information System (INIS)

    Lee, Weonjong

    2002-01-01

    We study the possibility of improving staggered fermions using various fat links in order to reduce perturbative corrections to the gauge-invariant staggered fermion operators. We prove five theorems on SU(3) projection, triviality in renormalization, multiple SU(3) projections, uniqueness, and equivalence. As a result of these theorems, we show that, at the one-loop level, the renormalization of staggered fermion operators is identical between SU(3) projected Fat7 links and hypercubic links, as long as the action and operators are constructed by imposing the same perturbative improvement condition. In addition, we propose a new view of SU(3) projection as a tool of tadpole improvement for the staggered fermion doublers. As a conclusion, we present alternative choices of constructing fat links to improve the staggered fermion action and operators, which deserve further investigation

  16. A Schwarz alternating procedure for singular perturbation problems

    Energy Technology Data Exchange (ETDEWEB)

    Garbey, M. [Universit Claude Bernard Lyon, Villeurbanne (France); Kaper, H.G. [Argonne National Lab., IL (United States)

    1994-12-31

    The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.

  17. On the universal identity in second order hydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Grozdanov, S. [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Instituut-Lorentz for Theoretical Physics, Leiden University,Niels Bohrweg 2, Leiden 2333 CA (Netherlands); Starinets, A.O. [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom)

    2015-03-02

    We compute the ’t Hooft coupling correction to the infinite coupling expression for the second order transport coefficient λ{sub 2} in N=4SU(N{sub c}) supersymmetric Yang-Mills theory at finite temperature in the limit of infinite N{sub c}, which originates from the R{sup 4} terms in the low energy effective action of the dual type IIB string theory. Using this result, we show that the identity involving the three second order transport coefficients, 2ητ{sub Π}−4λ{sub 1}−λ{sub 2}=0, previously shown by Haack and Yarom to hold universally in relativistic conformal field theories with string dual descriptions to leading order in supergravity approximation, holds also at next to leading order in this theory. We also compute corrections to transport coefficients in a (hypothetical) strongly interacting conformal fluid arising from the generic curvature squared terms in the corresponding dual gravity action (in particular, Gauss-Bonnet action), and show that the identity holds to linear order in the higher-derivative couplings. We discuss potential implications of these results for the near-equilibrium entropy production rate at strong coupling.

  18. On the universal identity in second order hydrodynamics

    Science.gov (United States)

    Grozdanov, S.; Starinets, A. O.

    2015-03-01

    We compute the 't Hooft coupling correction to the infinite coupling expression for the second order transport coefficient λ 2 in SU( N c ) supersymmetric Yang-Mills theory at finite temperature in the limit of infinite N c , which originates from the R 4 terms in the low energy effective action of the dual type IIB string theory. Using this result, we show that the identity involving the three second order transport coefficients, 2 ητ Π - 4 λ 1 - λ 2 = 0, previously shown by Haack and Yarom to hold universally in relativistic conformal field theories with string dual descriptions to leading order in supergravity approximation, holds also at next to leading order in this theory. We also compute corrections to transport coefficients in a (hypothetical) strongly interacting conformal fluid arising from the generic curvature squared terms in the corresponding dual gravity action (in particular, Gauss-Bonnet action), and show that the identity holds to linear order in the higher-derivative couplings. We discuss potential implications of these results for the near-equilibrium entropy production rate at strong coupling.

  19. Word Order

    DEFF Research Database (Denmark)

    Rijkhoff, Jan

    2015-01-01

    The way constituents are ordered in a linguistic expression is determined by general principles and language specific rules. This article is mostly concerned with general ordering principles and the three main linguistic categories that are relevant for constituent order research: formal, functio...

  20. Order-by-order Analytic Solution to the BFKL Equation

    CERN Document Server

    Ross, D.A.

    2014-01-01

    We propose a regularization of the BFKL equation which allows for its solution in each order of perturbation theory by means of a sum over multiple poles. This sum can be presented in a rather simple formula for the Fourier transform in the azimuthal angle of the gluon Green function. In order to test our method, we have compared a few orders in the expansion to previous results by Del Duca, Dixon, Duhr and Pennington, finding agreement. Our formalism is general and can be applied to other, more complicated, kernels.