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Sample records for two-loop matrix elements

  1. Two-loop operator matrix elements for massive fermionic local twist-2 operators in QED

    International Nuclear Information System (INIS)

    Bluemlein, J.; Freitas, A. de; Universidad Simon Bolivar, Caracas; Neerven, W.L. van

    2011-11-01

    We describe the calculation of the two--loop massive operator matrix elements with massive external fermions in QED. We investigate the factorization of the O(α 2 ) initial state corrections to e + e - annihilation into a virtual boson for large cms energies s >>m 2 e into massive operator matrix elements and the massless Wilson coefficients of the Drell-Yan process adapting the color coefficients to the case of QED, as proposed by F. A. Berends et. al. (Nucl. Phys. B 297 (1988)429). Our calculations show explicitly that the representation proposed there works at one-loop order and up to terms linear in ln (s/m 2 e ) at two-loop order. However, the two-loop constant part contains a few structural terms, which have not been obtained in previous direct calculations. (orig.)

  2. Two-loop massive operator matrix elements for polarized and unpolarized deep-inelastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Bierenbaum, I.; Bluemlein, J.; Klein, S.

    2007-06-15

    The O({alpha}{sup 2}{sub s}) massive operator matrix elements for unpolarized and polarized heavy flavor production at asymptotic values Q{sup 2} >> m{sup 2} are calculated in Mellin space without applying the integration-by-parts method. (orig.)

  3. Two-loop massive operator matrix elements for unpolarized heavy flavor production to O({epsilon})

    Energy Technology Data Exchange (ETDEWEB)

    Bierenbaum, I.; Bluemlein, J.; Klein, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

    2008-02-15

    We calculate the O({alpha}{sup 2}{sub s}) massive operator matrix elements for the twist-2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q{sup 2}>>m{sup 2}, up to the O({epsilon}) contributions. These terms contribute through the renormalization of the O({alpha}{sup 3}{sub s}) heavy flavor Wilson coefficients of the structure function F{sub 2}(x,Q{sup 2}). The calculation has been performed using light-cone expansion techniques without using the integration-by-parts method. We represent the individual Feynman diagrams by generalized hypergeometric structures, the {epsilon}-expansion of which leads to infinite sums depending on the Mellin variable N. These sums are finally expressed in terms of nested harmonic sums using the general summation techniques implemented in the Sigma package. (orig.)

  4. Two-loop massive fermionic operator matrix elements and intial state QED corrections to e{sup +}e{sup -}{yields}{gamma}{sup *}/Z{sup *}

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Universidad Simon Bolivar, Caracas (Venezuela). Dept. de Fisica; Neerven, W. van [Leiden Univ. (Netherlands). Lorentz Institute

    2008-12-15

    We describe the calculation of the two-loop massive operator matrix elements for massive external fermions. These matrix elements are needed for the calculation of the O({alpha}{sup 2}) initial state radiative corrections to e{sup +}e{sup -} annihilation into a neutral virtual gauge boson, based on the renormalization group technique. (orig.)

  5. A two-loop test of M(atrix) theory

    International Nuclear Information System (INIS)

    Becker, K.

    1997-01-01

    We consider the scattering of two Dirichlet zero-branes in M(atrix) theory. Using the formulation of M(atrix) theory in terms of ten-dimensional super Yang-Mills theory dimensionally reduced to (0+1) dimensions, we obtain the effective (velocity-dependent) potential describing these particles. At one loop we obtain the well-known result for the leading order of the effective potential V eff ∝v 4 /r 7 , where v and r are the relative velocity and distance between the two zero-branes, respectively. A calculation of the effective potential at two loops shows that no renormalizations of the v 4 term of the effective potential occur at this order. (orig.)

  6. Application of FIRE for the calculation of photon matrix elements

    Indian Academy of Sciences (India)

    to evaluate the two-loop Feynman diagrams for the photon matrix element of the ... sum of scalar Feynman integrals to a linear combination of a few master integrals. .... Then, FIRE is used to express these scalar integrals as a linear combi-.

  7. Two loop integrals and QCD scattering

    International Nuclear Information System (INIS)

    Anastasiou, C.

    2001-04-01

    We present the techniques for the calculation of one- and two-loop integrals contributing to the virtual corrections to 2→2 scattering of massless particles. First, tensor integrals are related to scalar integrals with extra powers of propagators and higher dimension using the Schwinger representation. Integration By Parts and Lorentz Invariance recurrence relations reduce the number of independent scalar integrals to a set of master integrals for which their expansion in ε = 2 - D/2 is calculated using a combination of Feynman parameters, the Negative Dimension Integration Method, the Differential Equations Method, and Mellin-Barnes integral representations. The two-loop matrix-elements for light-quark scattering are calculated in Conventional Dimensional Regularisation by direct evaluation of the Feynman diagrams. The ultraviolet divergences are removed by renormalising with the MS-bar scheme. Finally, the infrared singular behavior is shown to be in agreement with the one anticipated by the application of Catani's formalism for the infrared divergences of generic QCD two-loop amplitudes. (author)

  8. Electromagnetic matrix elements in baryons

    International Nuclear Information System (INIS)

    Lipkin, H.J.; Moinester, M.A.

    1992-01-01

    Some simple symmetry relations between matrix elements of electromagnetic operators are investigated. The implications are discussed for experiments to study hyperon radiative transitions and polarizabilities and form factors. (orig.)

  9. Higgs bosons and QCD jets at two loops

    International Nuclear Information System (INIS)

    Koukoutsakis, Athanasios

    2003-04-01

    In this thesis we present techniques for the calculation of two-loop integrals contributing to the virtual corrections to physical processes with three on-shell and one off-shell external particles. First, we describe a set of basic tools that simplify the manipulation of complicated two-loop integrals. A technique for deriving helicity amplitudes with use of a set of projectors is demonstrated. Then we present an algorithm, introduced by Laporta, that helps reduce all possible two-loop integrals to a basic set of 'master integrals'. Subsequently, these master integrals are analytically evaluated by deriving and solving differential equations on the external scales of the process. Two-loop matrix elements and helicity amplitudes are calculated for the physical processes γ* → qq-barg and H → ggg respectively. Conventional Dimensional Regularization is used in the evaluation of Feynman diagrams. For both processes the infrared singular behavior is shown to agree with the one predicted by Catani. (author)

  10. Two-loop renormalization of quantum gravity simplified

    Science.gov (United States)

    Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex

    2017-02-01

    The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

  11. Analytic matrix elements with shifted correlated Gaussians

    DEFF Research Database (Denmark)

    Fedorov, D. V.

    2017-01-01

    Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....

  12. Parton-parton scattering at two-loops

    International Nuclear Information System (INIS)

    Tejeda Yeomans, M.E.

    2001-01-01

    Abstract We present an algorithm for the calculation of scalar and tensor one- and two-loop integrals that contribute to the virtual corrections of 2 → 2 partonic scattering. First, the tensor integrals are related to scalar integrals that contain an irreducible propagator-like structure in the numerator. Then, we use Integration by Parts and Lorentz Invariance recurrence relations to build a general system of equations that enables the reduction of any scalar integral (with and without structure in the numerator) to a basis set of master integrals. Their expansions in ε = 2 - D/2 have already been calculated and we present a summary of the techniques that have been used to this end, as well as a compilation of the expansions we need in the different physical regions. We then apply this algorithm to the direct evaluation of the Feynman diagrams contributing to the O(α s 4 ) one- and two-loop matrix-elements for massless like and unlike quark-quark, quark-gluon and gluon-gluon scattering. The analytic expressions we provide are regularised in Convensional Dimensional Regularisation and renormalised in the MS-bar scheme. Finally, we show that the structure of the infrared divergences agrees with that predicted by the application of Catani's formalism to the analysis of each partonic scattering process. The results presented in this thesis provide the complete calculation of the one- and two-loop matrix-elements for 2 → 2 processes needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders. (author)

  13. Analytic continuation of massless two-loop four-point functions

    International Nuclear Information System (INIS)

    Gehrmann, T.; Remiddi, E.

    2002-01-01

    We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like 1→3 decay to Minkowskian regions relevant to all 1→3 and 2→2 reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix elements for hadronic vector-boson-plus-jet production and deep inelastic two-plus-one-jet production, from results previously obtained for three-jet production in electron-positron annihilation. (author)

  14. Rovibrational matrix elements of the multipole moments

    Indian Academy of Sciences (India)

    Rovibrational matrix elements of the multipole moments ℓ up to rank 10 and of the linear polarizability of the H2 molecule in the condensed phase have been computed taking into account the effect of the intermolecular potential. Comparison with gas phase matrix elements shows that the effect of solid state interactions is ...

  15. Two-Loop Splitting Amplitudes

    International Nuclear Information System (INIS)

    Bern, Z.

    2004-01-01

    Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

  16. Two-loop splitting amplitudes

    International Nuclear Information System (INIS)

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

    2004-01-01

    Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

  17. Analytic vibrational matrix elements for diatomic molecules

    International Nuclear Information System (INIS)

    Bouanich, J.P.; Ogilvie, J.F.; Tipping, R.H.

    1986-01-01

    The vibrational matrix elements and expectation values for a diatomic molecule, including the rotational dependence, are calculated for powers of the reduced displacement in terms of the parameters of the Dunham potential-energy function. (orig.)

  18. Lattice results for heavy light matrix elements

    International Nuclear Information System (INIS)

    Soni, A.

    1994-09-01

    Lattice results for heavy light matrix elements are reviewed and some of their implications are very briefly discussed. Despite the fact that in most cases the lattice results for weak matrix elements at the moment have only a modest accuracy of about 20--30% they already have important phenomenological repercussions; e.g. for V td /V ts , x s /x d and B → K*γ

  19. Matrix Elements in Fermion Dynamical Symmetry Model

    Institute of Scientific and Technical Information of China (English)

    LIU Guang-Zhou; LIU Wei

    2002-01-01

    In a neutron-proton system, the matrix elements of the generators for SO(8) × SO(8) symmetry areconstructed explicitly, and with these matrix elements the low-lying excitation spectra obtained by diagonalization arepresented. The excitation spectra for SO(7) nuclei Pd and Ru isotopes and SO(6) r-soft rotational nuclei Xe, Ba, andCe isotopes are calculated, and comparison with the experimental results is carried out.

  20. Matrix Elements in Fermion Dynamical Symmetry Model

    Institute of Scientific and Technical Information of China (English)

    LIUGuang-Zhou; LIUWei

    2002-01-01

    In a neutron-proton system,the matrix elements of the generators for SO(8)×SO(8) symmetry are constructed exp;icitly,and with these matrix elements the low-lying excitation spsectra obtained by diagonalization are presented.The excitation spectra for SO(7) nuclei Pd and Ru isotopes and SO(6) r-soft rotational nuclei Xe,Ba,and Ce isotopes are calculated,and comparison with the experimental results is carried out.

  1. The finite element response matrix method

    International Nuclear Information System (INIS)

    Nakata, H.; Martin, W.R.

    1983-02-01

    A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt

  2. Renormalon ambiguities in NRQCD operator matrix elements

    International Nuclear Information System (INIS)

    Bodwin, G.T.; Chen, Y.

    1999-01-01

    We analyze the renormalon ambiguities that appear in factorization formulas in QCD. Our analysis contains a simple argument that the ambiguities in the short-distance coefficients and operator matrix elements are artifacts of dimensional-regularization factorization schemes and are absent in cutoff schemes. We also present a method for computing the renormalon ambiguities in operator matrix elements and apply it to a computation of the ambiguities in the matrix elements that appear in the NRQCD factorization formulas for the annihilation decays of S-wave quarkonia. Our results, combined with those of Braaten and Chen for the short-distance coefficients, provide an explicit demonstration that the ambiguities cancel in the physical decay rates. In addition, we analyze the renormalon ambiguities in the Gremm-Kapustin relation and in various definitions of the heavy-quark mass. copyright 1999 The American Physical Society

  3. Proton decay matrix elements from lattice QCD

    International Nuclear Information System (INIS)

    Aoki, Yasumichi; Shintani, Eigo

    2012-01-01

    We report on the calculation of the matrix elements of nucleon to pseudoscalar decay through a three quark operator, a part of the low-energy, four-fermion, baryon-number-violating operator originating from grand unified theories. The direct calculation of the form factors using domain-wall fermions on the lattice, incorporating the u, d and s sea-quarks effects yields the results with all the relevant systematic uncertainties controlled for the first time.

  4. Higgs Decay to Photons at Two Loops

    International Nuclear Information System (INIS)

    Fugel, F.

    2007-01-01

    The calculation of the two-loop corrections to the partial width of an intermediate-mass Higgs boson decaying into a pair of photons is reviewed. The main focus lies on the electroweak (EW) contributions. The sum of the EW corrections ranges from -4% to 0% for a Higgs mass between 100 GeV and 150 GeV, while the complete correction at two-loop order amounts to less than ± 1.5% in this regime. (author)

  5. The finite element response Matrix method

    International Nuclear Information System (INIS)

    Nakata, H.; Martin, W.R.

    1983-01-01

    A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed

  6. Single-particle Glauber matrix elements

    International Nuclear Information System (INIS)

    Oset, E.; Strottman, D.

    1983-01-01

    The single-particle matrix elements of the Glauber profile function are tabulated for harmonic oscillator single-particle wave functions. The tables are presented in such a manner as to be applicable if the hadron--nucleon elementary scattering amplitude is specified by either a partial wave expansion or a Gaussian in momentum transfer squared. The table is complete through the 1 g/sub 9/2/ orbital and contains entries for the 3s/sub 1/2/ orbital for use if realistic wave functions are expanded in terms of harmonic oscillator functions

  7. Two-loop feed water control system in BWR plants

    International Nuclear Information System (INIS)

    Omori, Takashi; Watanabe, Takao; Hirose, Masao.

    1982-01-01

    In the process of the start-up and shutdown of BWR plants, the operation of changing over feed pumps corresponding to plant output is performed. Therefore, it is necessary to develop the automatic changeover system for feed pumps, which minimizes the variation of water level in reactors and is easy to operate. The three-element control system with the water level in reactors, the flow rate of main steam and the flow rate of feed water as the input is mainly applied, but long time is required for the changeover of feed pumps. The two-loop feed control system can control simultaneously two pumps being changed over, therefore it is suitable to the automatic changeover control system for feed pumps. Also it is excellent for the control of the recirculating valves of feed pumps. The control characteristics of the two-loop feed water control system against the external disturbance which causes the variation of water level in reactors were examined. The results of analysis by simulation are reported. The features of the two-loop feed water control system, the method of simulation and the evaluation of the two-loop feed water control system are described. Its connection with a digital feed water recirculation control system is expected. (Kako, I.)

  8. An Explicit Consistent Geometric Stiffness Matrix for the DKT Element

    Directory of Open Access Journals (Sweden)

    Eliseu Lucena Neto

    Full Text Available Abstract A large number of references dealing with the geometric stiffness matrix of the DKT finite element exist in the literature, where nearly all of them adopt an inconsistent form. While such a matrix may be part of the element to treat nonlinear problems in general, it is of crucial importance for linearized buckling analysis. The present work seems to be the first to obtain an explicit expression for this matrix in a consistent way. Numerical results on linear buckling of plates assess the element performance either with the proposed explicit consistent matrix, or with the most commonly used inconsistent matrix.

  9. The quark beam function at two loops

    International Nuclear Information System (INIS)

    Gaunt, Jonathan R.; Stahlhofen, Maximilian; Tackmann, Frank J.

    2014-01-01

    In differential measurements at a hadron collider, collinear initial-state radiation is described by process-independent beam functions. They are the field-theoretic analog of initial-state parton showers. Depending on the measured observable they are differential in the virtuality and/or transverse momentum of the colliding partons in addition to their usual longitudinal momentum fractions. Perturbatively, the beam functions can be calculated by matching them onto standard quark and gluon parton distribution functions. We calculate the inclusive virtuality-dependent quark beam function at NNLO, which is relevant for any observables probing the virtuality of the incoming partons, including N-jettiness and beam thrust. For such observables, our results are an important ingredient in the resummation of large logarithms at N 3 LL order, and provide all contributions enhanced by collinear t-channel singularities at NNLO for quark-initiated processes in analytic form. We perform the calculation in both Feynman and axial gauge and use two different methods to evaluate the discontinuity in the two-loop Feynman diagrams, providing nontrivial checks of the calculation. As part of our results we reproduce the known two-loop QCD splitting functions and confirm at two loops that the virtuality-dependent beam and final-state jet functions have the same anomalous dimension.

  10. Two-loop string theory on null compactifications

    International Nuclear Information System (INIS)

    Cove, Henry C.D.; Szabo, Richard J.

    2006-01-01

    We compute the two-loop contributions to the free energy in the null compactification of perturbative string theory at finite temperature. The cases of bosonic, type II and heterotic strings are all treated. The calculation exploits an explicit reductive parametrization of the moduli space of infinite-momentum frame string worldsheets in terms of branched cover instantons. Various arithmetic and physical properties of the instanton sums are described. Applications to symmetric product orbifold conformal field theories and to the matrix string theory conjecture are also briefly discussed

  11. Hadronic matrix elements in lattice QCD

    International Nuclear Information System (INIS)

    Jaeger, Benjamin

    2014-01-01

    The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5-10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is

  12. Elements of matrix modeling and computing with Matlab

    CERN Document Server

    White, Robert E

    2006-01-01

    As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables. Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applicat

  13. Analytic vibration-rotational matrix elements for diatomic molecules

    International Nuclear Information System (INIS)

    Bouanich, J.P.

    1987-01-01

    The vibration-rotational matrix elements for infrared or Raman transitions vJ → v'J' of diatomic molecules are calculated for powers of the reduced displacement X from parameters of the Dunham potential-energy function. (orig.)

  14. Hierarchy of Poisson brackets for elements of a scattering matrix

    International Nuclear Information System (INIS)

    Konopelchenko, B.G.; Dubrovsky, V.G.

    1984-01-01

    The infinite family of Poisson brackets [Ssub(i1k1) (lambda 1 ), Ssub(i2k2) (lambda 2 )]sub(n) (n=0, 1, 2, ...) between the elements of a scattering matrix is calculated for the linear matrix spectral problem. (orig.)

  15. Direct calculation of off-diagonal matrix elements

    International Nuclear Information System (INIS)

    Killingbeck, J P; Jolicard, G

    2011-01-01

    Gauss elimination is used in a sequence of calculations which give the squares of the off-diagonal matrix elements of x between quartic oscillator eigenstates, in a modification of the original sum rule approach of Tipping et al to the problem. New and more flexible methods are then devised and tested and are shown to permit the isolation and calculation of individual squared matrix elements of x and x 2 .

  16. Finite size effects of a pion matrix element

    International Nuclear Information System (INIS)

    Guagnelli, M.; Jansen, K.; Palombi, F.; Petronzio, R.; Shindler, A.; Wetzorke, I.

    2004-01-01

    We investigate finite size effects of the pion matrix element of the non-singlet, twist-2 operator corresponding to the average momentum of non-singlet quark densities. Using the quenched approximation, they come out to be surprisingly large when compared to the finite size effects of the pion mass. As a consequence, simulations of corresponding nucleon matrix elements could be affected by finite size effects even stronger which could lead to serious systematic uncertainties in their evaluation

  17. Coulomb matrix elements in multi-orbital Hubbard models.

    Science.gov (United States)

    Bünemann, Jörg; Gebhard, Florian

    2017-04-26

    Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a d-shell and an f-shell and all point groups with up to 16 elements (O h , O, T d , T h , D 6h , and D 4h ). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.

  18. XLOOPS - a package calculating one- and two-loop diagrams

    International Nuclear Information System (INIS)

    Bruecher, L.

    1997-01-01

    A program package for calculating massive one- and two-loop diagrams is introduced. It consists of five parts: - a graphical user interface, - routines for generating diagrams from particle input, - procedures for calculating one-loop integrals both analytically and numerically, - routines for massive two-loop integrals, - programs for numerical integration of two-loop diagrams. Here the graphical user interface and the text interface to Maple are presented. (orig.)

  19. Empirical Coulomb matrix elements and the mass of 22Al

    International Nuclear Information System (INIS)

    Whitehead, R.R.; Watt, A.; Kelvin, D.; Rutherford, H.J.

    1976-01-01

    An attempt has been made to obtain a set of Coulomb matrix elements which fit the known Coulomb energy shifts in the nuclei of mass 18 to 22. The interaction obtained fits the data well with only a few exceptions, one of these being the Coulomb shift of the notorious third 0 + state in 18 Ne. These Coulomb matrix elements are used together with the Chung-Wildenthal interaction to obtain a new prediction for the mass excess of 22 Al. The results indicate that 22 Al should be bound against proton emission. (Auth.)

  20. The effects of flavour symmetry breaking on hadron matrix elements

    International Nuclear Information System (INIS)

    Cooke, A.N.; Horsley, R.; Pleiter, D.; Zanotti, J.M.

    2012-12-01

    By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between the strange and light quarks. We find the expansions to be highly constrained along a mass trajectory where the singlet quark mass is held constant, which proves beneficial for extrapolations of 2+1 flavour lattice data to the physical point. We investigate these effects numerically via a lattice calculation of the flavour-conserving and flavour-changing matrix elements of the vector and axial operators between octet baryon states.

  1. Rotational covariance and light-front current matrix elements

    International Nuclear Information System (INIS)

    Keister, B.D.

    1994-01-01

    Light-front current matrix elements for elastic scattering from hadrons with spin 1 or greater must satisfy a nontrivial constraint associated with the requirement of rotational covariance for the current operator. Using a model ρ meson as a prototype for hadronic quark models, this constraint and its implications are studied at both low and high momentum transfers. In the kinematic region appropriate for asymptotic QCD, helicity rules, together with the rotational covariance condition, yield an additional relation between the light-front current matrix elements

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

    OpenAIRE

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

    2012-01-01

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

  3. The effects of flavour symmetry breaking on hadron matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Cooke, A.N.; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Pleiter, D. [Juelich Research Centre (Germany); Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Division; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Zanotti, J.M. [Adelaide Univ. (Australia). School of Chemistry and Physics

    2012-12-15

    By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between the strange and light quarks. We find the expansions to be highly constrained along a mass trajectory where the singlet quark mass is held constant, which proves beneficial for extrapolations of 2+1 flavour lattice data to the physical point. We investigate these effects numerically via a lattice calculation of the flavour-conserving and flavour-changing matrix elements of the vector and axial operators between octet baryon states.

  4. Nucleon matrix elements using the variational method in lattice QCD

    International Nuclear Information System (INIS)

    Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ., SA

    2016-06-01

    The extraction of hadron matrix elements in lattice QCD using the standard two- and threepoint correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current g_A, the scalar current g_S and the quark momentum fraction left angle x right angle of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.

  5. Optimization of Coil Element Configurations for a Matrix Gradient Coil.

    Science.gov (United States)

    Kroboth, Stefan; Layton, Kelvin J; Jia, Feng; Littin, Sebastian; Yu, Huijun; Hennig, Jurgen; Zaitsev, Maxim

    2018-01-01

    Recently, matrix gradient coils (also termed multi-coils or multi-coil arrays) were introduced for imaging and B 0 shimming with 24, 48, and even 84 coil elements. However, in imaging applications, providing one amplifier per coil element is not always feasible due to high cost and technical complexity. In this simulation study, we show that an 84-channel matrix gradient coil (head insert for brain imaging) is able to create a wide variety of field shapes even if the number of amplifiers is reduced. An optimization algorithm was implemented that obtains groups of coil elements, such that a desired target field can be created by driving each group with an amplifier. This limits the number of amplifiers to the number of coil element groups. Simulated annealing is used due to the NP-hard combinatorial nature of the given problem. A spherical harmonic basis set up to the full third order within a sphere of 20-cm diameter in the center of the coil was investigated as target fields. We show that the median normalized least squares error for all target fields is below approximately 5% for 12 or more amplifiers. At the same time, the dissipated power stays within reasonable limits. With a relatively small set of amplifiers, switches can be used to sequentially generate spherical harmonics up to third order. The costs associated with a matrix gradient coil can be lowered, which increases the practical utility of matrix gradient coils.

  6. Effects of quenching and partial quenching on penguin matrix elements

    NARCIS (Netherlands)

    Golterman, Maarten; Pallante, Elisabetta

    2001-01-01

    In the calculation of non-leptonic weak decay rates, a "mismatch" arises when the QCD evolution of the relevant weak hamiltonian down to hadronic scales is performed in unquenched QCD, but the hadronic matrix elements are then computed in (partially) quenched lattice QCD. This mismatch arises

  7. S-matrix elements from T-duality

    International Nuclear Information System (INIS)

    Babaei Velni, Komeil; Garousi, Mohammad R.

    2013-01-01

    Recently it has been speculated that the S-matrix elements satisfy the Ward identity associated with the T-duality. This indicates that a group of S-matrix elements is invariant under the linear T-duality transformations on the external states. If one evaluates one component of such T-dual multiplet, then all other components may be found by the simple use of the linear T-duality. The assumption that fields must be independent of the Killing coordinate, however, may cause, in some cases, the T-dual multiplet not to be gauge invariant. In those cases, the S-matrix elements contain more than one T-dual multiplet which are intertwined by the gauge symmetry. In this paper, we apply the T-dual Ward identity on the S-matrix element of one RR (p−3)-form and two NSNS states on the world volume of a D p -brane to find its corresponding T-dual multiplet. In the case that the RR potential has two transverse indices, the T-dual multiplet is gauge invariant, however, in the case that it has one transverse index the multiplet is not gauge invariant. We find a new T-dual multiplet in this case by imposing the gauge symmetry. We show that the multiplets are reproduced by explicit calculation, and their low energy contact terms at order α ′2 are consistent with the existing couplings in the literature

  8. Structure of nuclear transition matrix elements for neutrinoless ...

    Indian Academy of Sciences (India)

    Abstract. The structure of nuclear transition matrix elements (NTMEs) required for the study of neutrinoless double- decay within light Majorana neutrino mass mechanism is disassembled in the PHFB model. The NTMEs are calculated using a set of HFB intrinsic wave functions, the reliability of which has been previously ...

  9. Rovibrational matrix elements of the multipole moments and of the ...

    Indian Academy of Sciences (India)

    The rovibrational matrix elements of the multipole moments and polarizability of molecules find applications in the study of infrared spectra, intermolecular potential and collision-induced absorption phenomena, especially in homonuclear molecules. Because of its simplicity and fundamental importance, the hydrogen ...

  10. Structure of nuclear transition matrix elements for neutrinoless ...

    Indian Academy of Sciences (India)

    Abstract. The structure of nuclear transition matrix elements (NTMEs) required for the study of neutrinoless double-β decay within light Majorana neutrino mass mechanism is disassembled in the PHFB model. The NTMEs are calculated using a set of HFB intrinsic wave functions, the reliability of which has been previously ...

  11. Weak matrix elements on the lattice - Circa 1995

    International Nuclear Information System (INIS)

    Soni, A.

    1995-01-01

    Status of weak matrix elements is reviewed. In particular, e'/e, B → K*γ, B B and B B , are discussed and the overall situation with respect to the lattice effort and some of its phenomenological implications are summarised. For e'/e the need for the relevant matrix elements is stressed in view of the forthcoming improved experiments. For some of the operators, (e.g. O 6 ), even bound on their matrix elements would be very helpful. On B → K degrees γ, a constant behavior of T 2 appears disfavored although dependence of T 2 could, of course, be milder than a simple pole. Improved data is badly needed to settle this important issue firmly, especially in view of its ramification for extractions of V td from B → ργ. On B κ , the preliminary result from JLQCD appears to contradict Sharpe et al. JLQCD data seems to fit very well to linear α dependence and leads to an appreciably lower value of B κ . Four studies of B κ in the open-quotes fullclose quotes (n f = 2) theory indicate very little quenching effects on B κ ; the full theory value seems to be just a little less than the quenched result. Based on expectations from HQET, analysis of B-parameter (B h ell) for the heavy-light mesons via B h ell) = constant + constants'/m h ell is suggested. A summary of an illustrative sample of hadron matrix elements is given and constraints on CKM parameters (e.g. V td /V ts , on the unitarity triangle and on x s /x d , emerging from the lattice calculations along with experimental results are briefly discussed. In quite a few cases, for the first time, some indication of quenching errors on weak matrix elements are now becoming available

  12. The massless two-loop two-point function

    International Nuclear Information System (INIS)

    Bierenbaum, I.; Weinzierl, S.

    2003-01-01

    We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter ε. As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals. (orig.)

  13. Glueball Spectrum and Matrix Elements on Anisotropic Lattices

    Energy Technology Data Exchange (ETDEWEB)

    Y. Chen; A. Alexandru; S.J. Dong; T. Draper; I. Horvath; F.X. Lee; K.F. Liu; N. Mathur; C. Morningstar; M. Peardon; S. Tamhankar; B.L. Young; J.B. Zhang

    2006-01-01

    The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in J/{psi} radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.

  14. A collocation finite element method with prior matrix condensation

    International Nuclear Information System (INIS)

    Sutcliffe, W.J.

    1977-01-01

    For thin shells with general loading, sixteen degrees of freedom have been used for a previous finite element solution procedure using a Collocation method instead of the usual variational based procedures. Although the number of elements required was relatively small, nevertheless the final matrix for the simultaneous solution of all unknowns could become large for a complex compound structure. The purpose of the present paper is to demonstrate a method of reducing the final matrix size, so allowing solution for large structures with comparatively small computer storage requirements while retaining the accuracy given by high order displacement functions. Collocation points, a number are equilibrium conditions which must be satisfied independently of the overall compatibility of forces and deflections for a complete structure. (Auth.)

  15. Inert matrix fuel in dispersion type fuel elements

    Energy Technology Data Exchange (ETDEWEB)

    Savchenko, A.M. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation)]. E-mail: sav@bochvar.ru; Vatulin, A.V. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation); Morozov, A.V. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation); Sirotin, V.L. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation); Dobrikova, I.V. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation); Kulakov, G.V. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation); Ershov, S.A. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation); Kostomarov, V.P. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation); Stelyuk, Y.I. [A.A. Bochvar All-Russia Research Institute of Inorganic Materials (VNIINM) 123060, P.O. Box 369, Rogova Street, 5A, Moscow (Russian Federation)

    2006-06-30

    The advantages of using inert matrix fuel (IMF) as a dispersion fuel in an aluminium alloy matrix are considered, in particular, low temperatures in the fuel centre, achievable high burn-ups, serviceability in transients and an environmentally friendly process of fuel rod fabrication. Two main versions of IMF are under development at A.A. Bochvar Institute, i.e. heterogeneous or isolated distribution of plutonium. The out-of-pile results on IMF loaded with uranium dioxide as plutonium simulator are presented. Fuel elements with uranium dioxide composition fabricated at A.A. Bochvar Institute are currently under MIR tests (RIAR, Dimitrovgrad). The fuel elements reached a burn-up of 88 MW d kg{sup -1} (equivalent to the burn up of the standard uranium dioxide pelletized fuel) without loss of leak-tightness of the cladding. The feasibility of fabricating IMF of these particular types with plutonium dioxide is considered with a view to in-pile irradiation.

  16. Inert matrix fuel in dispersion type fuel elements

    Science.gov (United States)

    Savchenko, A. M.; Vatulin, A. V.; Morozov, A. V.; Sirotin, V. L.; Dobrikova, I. V.; Kulakov, G. V.; Ershov, S. A.; Kostomarov, V. P.; Stelyuk, Y. I.

    2006-06-01

    The advantages of using inert matrix fuel (IMF) as a dispersion fuel in an aluminium alloy matrix are considered, in particular, low temperatures in the fuel centre, achievable high burn-ups, serviceability in transients and an environmentally friendly process of fuel rod fabrication. Two main versions of IMF are under development at A.A. Bochvar Institute, i.e. heterogeneous or isolated distribution of plutonium. The out-of-pile results on IMF loaded with uranium dioxide as plutonium simulator are presented. Fuel elements with uranium dioxide composition fabricated at A.A. Bochvar Institute are currently under MIR tests (RIAR, Dimitrovgrad). The fuel elements reached a burn-up of 88 MW d kg-1 (equivalent to the burn up of the standard uranium dioxide pelletized fuel) without loss of leak-tightness of the cladding. The feasibility of fabricating IMF of these particular types with plutonium dioxide is considered with a view to in-pile irradiation.

  17. Scattering-matrix elements of coated infinite-length cylinders

    International Nuclear Information System (INIS)

    Manickavasagam, S.; Menguec, M.P.

    1998-01-01

    The angular variations of scattering-matrix elements of coated cylindrical particles are presented. The sensitivity of different elements for a number of physical parameters are discussed, including size parameter, real and imaginary parts of the refractive index of the outer coat, and the inner core. The numerical predictions are presented for typical index-of-refraction values of cotton fibers. These results show that the physical structure of coated cylinders can be determined from carefully conducted light-scattering experiments. copyright 1998 Optical Society of America

  18. The scattering matrix element of the three body reactive collision

    International Nuclear Information System (INIS)

    Morsy, M.W.; Hilal, A.A.; El-Sabagh, M.A.

    1980-08-01

    The optical model approximation has been applied to a previously derived set of coupled equations representing the dynamics of the three-body reactive scattering. The Schroedinger equation obtained describing the scattering problem has then been solved by inserting the effective mass approximation. The asymptotic requirements for both the entrance and exit channels, respectively, have been supplied to give the scattering matrix element of the reactive collision. (author)

  19. Reweighting QCD matrix-element and parton-shower calculations

    Energy Technology Data Exchange (ETDEWEB)

    Bothmann, Enrico; Schumann, Steffen [Universitaet Goettingen, II. Physikalisches Institut, Goettingen (Germany); Schoenherr, Marek [Universitaet Zuerich, Physik-Institut, Zuerich (Switzerland)

    2016-11-15

    We present the implementation and validation of the techniques used to efficiently evaluate parametric and perturbative theoretical uncertainties in matrix-element plus parton-shower simulations within the Sherpa event-generator framework. By tracing the full α{sub s} and PDF dependences, including the parton-shower component, as well as the fixed-order scale uncertainties, we compute variational event weights on-the-fly, thereby greatly reducing the computational costs to obtain theoretical-uncertainty estimates. (orig.)

  20. Double β-decay nuclear matrix elements and lepton conservation

    International Nuclear Information System (INIS)

    Vergados, J.D.

    1976-01-01

    The nuclear matrix elements involved in the double β-decay of 48 Ca, 130 Te, and 128 Te were calculated using realistic nuclear interactions and shell model nuclear wave functions. The double doorway state is not appreciably mixed in the ground state of the final nuclei. So the ground state transitions contain a small fraction of the sum rule. A lepton nonconservation parameter eta -4 was deduced

  1. A stochastic method for computing hadronic matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computational-based Science and Technology Research Center; Dinter, Simon; Drach, Vincent [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Jansen, Karl [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Hadjiyiannakou, Kyriakos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Renner, Dru B. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Collaboration: European Twisted Mass Collaboration

    2013-02-15

    We present a stochastic method for the calculation of baryon three-point functions that is more versatile compared to the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume and find a favorable signal-to-noise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements.

  2. Weak matrix elements efforts on the lattice: Status and prospects

    International Nuclear Information System (INIS)

    Soni, A.

    1995-01-01

    Lattice approach to weak matrix elements is reviewed. Recent progress in treating heavy quarks on the lattice is briefly discussed. Illustrative sample of results obtained so far is given. Among them I elaborate on B K , line-integral B and B → K* γ . Experimental implications especially with regard to constraints on the Standard Model (i.e. Wolfenstein) parameters, V td measurements and expectations for B s -bar B s , oscillations are briefly discussed

  3. Rules for matrix element evaluations in JWKB approximation

    International Nuclear Information System (INIS)

    Giler, S.

    1990-01-01

    Using the properties of the so-called fundamental solutions to the one-dimensional Schroedinger equation having Froeman and Froeman form the rules are formulated which allow one to evaluate matrix elements in the JWKB approximation and its generalizations. The rules apply to operators M(x, d/dx), M being polynomial functions of their arguments. The applicability of the rules depends on the properties of the so-called canonical indices introduced in this paper. The canonical indices are global characteristics of underlying Stokes graphs. If sufficiently small in comparison with unity they allow one to apply safely the JWKB approximation within the so-called ε-reduced canonical domains of a given Stokes graph. The Oth canonical index for the nth energy level Stokes graph corresponding to the harmonic oscillator potential is found to be ε CAN = 0.678/(2n+1). If the application of the rules is allowed then approximated matrix elements are obtained in an unambiguous way and with an accuracy controlled by corresponding canonical indices. Several examples of matrix elements are considered to illustrate how the rules should be used. Limitations to the rules are also discussed with the aid of suitably chosen examples. (author)

  4. Hadronic matrix elements in the QCD on the lattice

    International Nuclear Information System (INIS)

    Altmeyer, R.

    1995-01-01

    The work describes a lattice simulation of full QCD with dynamical Kogut-Susskind fermions. We evaluated different hadronic matrix elements which are related to the static and low-energy behaviour of hadrons. The analysis was performed on a 16 3 x 24 lattice with a coupling constant of β = 5.35 and a quark mass of m = 0.010. The calculations are based on a set of 85 configurations created by using a Hybrid-Monte-Carlo algorithm. First we evaluated the mass and energy spectrum of the low-lying hadrons using local operators as well as non-local operators. As the complete spectrum of the different pion and ρ meson lattice representations has been calculated we were able to check the restoration of continuum flavor symmetry. Moreover, the determination of energies E of hadron states with non-vanishing momentum vector q made it possible to investigate the lattice dispersion function E( vector q). Another part of the presented work is the determination of mesonic decay constants which parameterise the weak decay of mesons. They are related to hadronic matrix elements of the respective quark currents and through the calculation of these matrix elements we were able to determine the decay constants f π and f ρ . Before doing so, we calculated non-perturbatively renormalization constants for the currents under consideration. The next part is the determination of hadronic coupling constants. These parameterise in an effective low-energy model the interactions of different hadrons. They are related to hadronic matrix elements whose lattice calculation can be dpme bu evaluating 3-point correlation functions. Thus we evaluted the hadronic coupling constants g ρππ and g NNπ . Finally, an investigation of the pion-nucleon σterm was done. The σterm is defined through a hadronic matrix element of a quark-antiquark operator and can thus be evaluated on the lattice via the calculation of a 3-point correlation function. As we determined the connected and the disconnected

  5. Intermediate coupling collision strengths from LS coupled R-matrix elements

    International Nuclear Information System (INIS)

    Clark, R.E.H.

    1978-01-01

    Fine structure collision strength for transitions between two groups of states in intermediate coupling and with inclusion of configuration mixing are obtained from LS coupled reactance matrix elements (R-matrix elements) and a set of mixing coefficients. The LS coupled R-matrix elements are transformed to pair coupling using Wigner 6-j coefficients. From these pair coupled R-matrix elements together with a set of mixing coefficients, R-matrix elements are obtained which include the intermediate coupling and configuration mixing effects. Finally, from the latter R-matrix elements, collision strengths for fine structure transitions are computed (with inclusion of both intermediate coupling and configuration mixing). (Auth.)

  6. Calculations of hadronic weak matrix elements: A status report

    International Nuclear Information System (INIS)

    Sharpe, S.R.

    1988-01-01

    I review the calculations of hadronic matrix elements of the weak Hamiltonian. My major emphasis is on lattice calculations. I discuss the application to weak decay constants (f/sub K/, f/sub D/, f/sub B/), K 0 /minus/ /bar K/sup 0// and B 0 /minus/ /bar B/sup 0// mixing, K → ππ decays, and the CP violation parameters ε and ε'. I close with speculations on future progress. 57 refs., 4 figs., 2 tabs

  7. Controlling inclusive cross sections in parton shower + matrix element merging

    International Nuclear Information System (INIS)

    Plaetzer, Simon

    2012-11-01

    We propose an extension of matrix element plus parton shower merging at tree level to preserve inclusive cross sections obtained from the merged and showered sample. Implementing this constraint generates approximate next-to-leading order (NLO) contributions similar to the LoopSim approach. We then show how full NLO, or in principle even higher order, corrections can be added consistently, including constraints on inclusive cross sections to account for yet missing parton shower accuracy at higher logarithmic order. We also show how NLO accuracy below the merging scale can be obtained.

  8. Calculation of hadronic matrix elements using lattice QCD

    International Nuclear Information System (INIS)

    Gupta, R.

    1993-01-01

    The author gives a brief introduction to the scope of lattice QCD calculations in his effort to extract the fundamental parameters of the standard model. This goal is illustrated by two examples. First the author discusses the extraction of CKM matrix elements from measurements of form factors for semileptonic decays of heavy-light pseudoscalar mesons such as D → Keν. Second, he presents the status of results for the kaon B parameter relevant to CP violation. He concludes the talk with a short outline of his experiences with optimizing QCD codes on the CM5

  9. Controlling inclusive cross sections in parton shower + matrix element merging

    Energy Technology Data Exchange (ETDEWEB)

    Plaetzer, Simon

    2012-11-15

    We propose an extension of matrix element plus parton shower merging at tree level to preserve inclusive cross sections obtained from the merged and showered sample. Implementing this constraint generates approximate next-to-leading order (NLO) contributions similar to the LoopSim approach. We then show how full NLO, or in principle even higher order, corrections can be added consistently, including constraints on inclusive cross sections to account for yet missing parton shower accuracy at higher logarithmic order. We also show how NLO accuracy below the merging scale can be obtained.

  10. Something different - caching applied to calculation of impedance matrix elements

    CSIR Research Space (South Africa)

    Lysko, AA

    2012-09-01

    Full Text Available of the multipliers, the approximating functions are used any required parameters, such as input impedance or gain pattern etc. The method is relatively straightforward but, especially for small to medium matrices, requires spending time on filling... of the computing the impedance matrix for the method of moments, or a similar method, such as boundary element method (BEM) [22], with the help of the flowchart shown in Figure 1. Input Parameters (a) Search the cached data for a match (b) A match found...

  11. Calculation of hadronic matrix elements using lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, R.

    1993-08-01

    The author gives a brief introduction to the scope of lattice QCD calculations in his effort to extract the fundamental parameters of the standard model. This goal is illustrated by two examples. First the author discusses the extraction of CKM matrix elements from measurements of form factors for semileptonic decays of heavy-light pseudoscalar mesons such as D {yields} Ke{nu}. Second, he presents the status of results for the kaon B parameter relevant to CP violation. He concludes the talk with a short outline of his experiences with optimizing QCD codes on the CM5.

  12. Improved determination of hadron matrix elements using the variational method

    International Nuclear Information System (INIS)

    Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ.

    2015-11-01

    The extraction of hadron form factors in lattice QCD using the standard two- and three-point correlator functions has its limitations. One of the most commonly studied sources of systematic error is excited state contamination, which occurs when correlators are contaminated with results from higher energy excitations. We apply the variational method to calculate the axial vector current g A and compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.

  13. Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2

    Science.gov (United States)

    Bentalha, Zine el abidine

    2018-06-01

    Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

  14. Two-loop hard-thermal-loop thermodynamics with quarks

    International Nuclear Information System (INIS)

    Andersen, Jens O.; Petitgirard, Emmanuel; Strickland, Michael

    2004-01-01

    We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N f =2 and with exact numerical results obtained in the large-N f limit

  15. Measurement of the CKM matrix element |V_ts|²

    CERN Document Server

    Unverdorben, Christopher Gerhard

    This is the first direct measurement of the CKM matrix element |V_ts|, using data collected by the ATLAS detector in 2012 at √s=8 TeV pp-collisions with a total integrated luminosity of 20.3 fb⁻¹. The analysis is based on 112171 reconstructed tt̅ candidate events in the lepton+jets channel, having a purity of 90.0 %. 183 tt̅→WWbs̅ decays are expected (charge conjugation implied), which are available for the extraction of the CKM matrix element |V_ts|². To identify these rare decays, several observables are examined, such as the properties of jets, tracks and of b-quark identification algorithms. Furthermore, the s-quark hadrons K0s are considered, reconstructed by a kinematic fit. The best observables are combined in a multivariate analysis, called "boosted decision trees". The responses from Monte Carlo simulations are used as templates for a fit to data events yielding a significance value of 0.7σ for t→s+W decays. An upper limit of |V_ts|² < 1.74 % at 95 % confidence level is set, includi...

  16. The current matrix elements from HAL QCD method

    Science.gov (United States)

    Watanabe, Kai; Ishii, Noriyoshi

    2018-03-01

    HAL QCD method is a method to construct a potential (HAL QCD potential) that reproduces the NN scattering phase shift faithful to the QCD. The HAL QCD potential is obtained from QCD by eliminating the degrees of freedom of quarks and gluons and leaving only two particular hadrons. Therefor, in the effective quantum mechanics of two nucleons defined by HAL QCD potential, the conserved current consists not only of the nucleon current but also an extra current originating from the potential (two-body current). Though the form of the two-body current is closely related to the potential, it is not straight forward to extract the former from the latter. In this work, we derive the the current matrix element formula in the quantum mechanics defined by the HAL QCD potential. As a first step, we focus on the non-relativistic case. To give an explicit example, we consider a second quantized non-relativistic two-channel coupling model which we refer to as the original model. From the original model, the HAL QCD potential for the open channel is constructed by eliminating the closed channel in the elastic two-particle scattering region. The current matrix element formula is derived by demanding the effective quantum mechanics defined by the HAL QCD potential to respond to the external field in the same way as the original two-channel coupling model.

  17. Two-loop electroweak top corrections are they under control?

    CERN Document Server

    Degrassi, G.; Feruglio, F.; Gambino, P.; Vicini, A.; Degrassi, G; Fanchiotti, S; Feruglio, F; Gambino, P; Vicini, A

    1995-01-01

    The assumption that two-loop top corrections are well approximated by the O(G_mu^2 mt^4) contribution is investigated. It is shown that in the case of the ratio neutral-to-charged current amplitudes at zero momentum transfer the O(G_mu^2 mt^2 M_Z^2) terms are numerically comparable to the m_t^4 contribution for realistic values of the top mass. An estimate of the theoretical error due to unknown two-loop top effect is presented for a few observables of LEP interest.

  18. Two-loop off-shell QCD amplitudes in FDR

    CERN Document Server

    Page, Ben

    2015-01-01

    We link the FDR treatment of ultraviolet (UV) divergences to dimensional regularization up to two loops in QCD. This allows us to derive the one-loop and two-loop coupling constant and quark mass shifts necessary to translate infrared finite quantities computed in FDR to the MSbar renormalization scheme. As a by-product of our analysis, we solve a problem analogous to the breakdown of unitarity in the Four Dimensional Helicity (FDH) method beyond one loop. A fix to FDH is then presented that preserves the renormalizability properties of QCD without introducing evanescent quantities.

  19. The two-loop renormalization of general quantum field theories

    International Nuclear Information System (INIS)

    Damme, R.M.J. van.

    1984-01-01

    This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)

  20. Comments on two-loop Kac-Moody algebras

    Energy Technology Data Exchange (ETDEWEB)

    Ferreira, L A; Gomes, J F; Zimerman, A H [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Schwimmer, A [Istituto Nazionale di Fisica Nucleare, Trieste (Italy)

    1991-10-01

    It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decouple {beta}-{gamma} system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity to versions of the corresponding ordinary models and decoupled Abelian fields. (author). 15 refs.

  1. Elastic ππ scattering to two loops

    International Nuclear Information System (INIS)

    Bijnens, J.; Colangelo, G.; Gasser, J.; Ecker, G.; Sainio, M.E.

    1995-11-01

    We evaluate analytically the elastic ππ scattering amplitude to two loops in chiral perturbation theory and give numerical values for the two S-wave scattering lengths and for the phase shift difference δ 0 0 -δ 1 1 . (author)

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

    International Nuclear Information System (INIS)

    Ablinger, J.; Schneider, C.; Behring, A.; Falcioni, G.

    2017-11-01

    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.

  3. The two loop superstring vacuum amplitude and canonical divisors

    International Nuclear Information System (INIS)

    Parkes, A.

    1989-01-01

    I use the prescription of placing the picture changing operators at the zeroes of some holomorphic one-form and calculate the two loop superstring vacuum amplitude in the language of theta functions. It vanishes pointwise on moduli space after the use of Fay's trisecant identity and generalised Riemann identities. I briefly discuss the higher genus case. (orig.)

  4. Two-loop matching coefficients for heavy quark currents

    International Nuclear Information System (INIS)

    Kniehl, B.A.; Onishchenko, A.; Petersburg Nuclear Physics Institute, Gatchina; Piclum, J.H.; Karlsruhe Univ.; Steinhauser, M.

    2006-04-01

    In this paper we consider the matching coefficients up to two loops between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) for the vector, axial-vector, scalar and pseudo-scalar currents. The structure of the effective theory is discussed and analytical results are presented. Particular emphasis is put on the singlet diagrams. (Orig.)

  5. Two-loop neutrino model with exotic leptons

    Science.gov (United States)

    Okada, Hiroshi; Orikasa, Yuta

    2016-01-01

    We propose a two-loop induced neutrino mass model, in which we show some bench mark points to satisfy the observed neutrino oscillation, the constraints of lepton flavor violations, and the relic density in the coannihilation system satisfying the current upper bound on the spin independent scattering cross section with nuclei. We also discuss new sources of muon anomalous magnetic moments.

  6. Two-loop polygon Wilson loops in N = 4 SYM

    International Nuclear Information System (INIS)

    Anastasiou, C.; Brandhuber, A.; Heslop, P.; Spence, B.; Travaglini, G.; Khoze, V.V.

    2009-01-01

    We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in N = 4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between the finite part of planar six-point MHV amplitudes and hexagon Wilson loops which has been observed at two loops. At n = 6 we confirm that the ABDK/BDS ansatz must be corrected by adding a remainder function, which depends only on conformally invariant ratios of kinematic variables. We numerically compute remainder functions for n = 7,8 and verify dual conformal invariance. Furthermore, we study simple and multiple collinear limits of the Wilson loop remainder functions and demonstrate that they have precisely the form required by the collinear factorisation of the corresponding two-loop n-point amplitudes. The number of distinct diagram topologies contributing to the n-gon Wilson loops does not increase with n, and there is a fixed number of 'master integrals', which we have computed. Thus we have essentially computed general polygon Wilson loops, and if the correspondence with amplitudes continues to hold, all planar n-point two-loop MHV amplitudes in the N = 4 theory.

  7. The heavy quark form factors at two loops

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Behring, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); 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. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Nikhef, Amsterdam (Netherlands). Theory Group

    2017-12-15

    We compute the two-loop QCD corrections to the heavy quark form factors in case of the vector, axial-vector, scalar and pseudo-scalar currents up to second order in the dimensional parameter ε=(4-D)/2. These terms are required in the renormalization of the higher order corrections to these form factors.

  8. Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts

    International Nuclear Information System (INIS)

    Dixon, Lance

    2002-01-01

    We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for ''observed'' particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg → gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS coupling, α s . The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD β function in the FDH and dimensional reduction schemes

  9. Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, Lance

    2002-03-08

    We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for ''observed'' particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg {yields} gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard {bar M}{bar S} coupling, {alpha}{sub s}. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD {beta} function in the FDH and dimensional reduction schemes.

  10. Finite volume at two-loops in chiral perturbation theory

    International Nuclear Information System (INIS)

    Bijnens, Johan; Rössler, Thomas

    2015-01-01

    We calculate the finite volume corrections to meson masses and decay constants in two and three flavour Chiral Perturbation Theory to two-loop order. The analytical results are compared with the existing result for the pion mass in two-flavour ChPT and the partial results for the other quantities. We present numerical results for all quantities.

  11. 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.

  12. Matching Matrix Elements and Parton Showers with HERWIG and PYTHIA

    CERN Document Server

    Mrenna, S; Mrenna, Stephen; Richardson, Peter

    2004-01-01

    We report on our exploration of matching matrix element calculations with the parton-shower models contained in the event generators HERWIG and Pythia. We describe results for e+e- collisions and for the hadroproduction of W bosons and Drell--Yan pairs. We compare methods based on (1) a strict implementation of ideas proposed by Catani, et al., (2) a generalization based on using the internal Sudakov form factors of HERWIG and Pythia, and (3) a simpler proposal of M. Mangano. Where appropriate, we show the dependence on various choices of scales and clustering that do not affect the soft and collinear limits of the predictions, but have phenomenological implications. Finally, we comment on how to use these results to state systematic errors on the theoretical predictions.

  13. Neutrinoless Double Beta Decay Matrix Elements in Light Nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Pastore, S.; Carlson, J.; Cirigliano, V.; Dekens, W.; Mereghetti, E.; Wiringa, R. B.

    2018-01-17

    We present the first ab initio calculations of neutrinoless double-β decay matrix elements in A=6-12 nuclei using variational Monte Carlo wave functions obtained from the Argonne v18 two-nucleon potential and Illinois-7 three-nucleon interaction. We study both light Majorana neutrino exchange and potentials arising from a large class of multi-TeV mechanisms of lepton-number violation. Our results provide benchmarks to be used in testing many-body methods that can be extended to the heavy nuclei of experimental interest. In light nuclei we also study the impact of two-body short-range correlations and the use of different forms for the transition operators, such as those corresponding to different orders in chiral effective theory.

  14. Measurements of the CKM matrix element V(cb)

    CERN Document Server

    Di Ciaccio, L

    1996-01-01

    A review of the measurements of the element V ch of the CabibboKobayashi-Maskawa matrix is presented. The experimental results discussed here are based on the selection of the decays B -t D' lv and on the study of the differential decay rate as a function of the momentum transfer from the B to D' particle. This method allows to measure IV chi with a reduced model dependence. This review describes mainly the most recent analyses which have been performed by the LEP Collaborations. The IVcbl determination based on the inclusive semileptonic decay width of the B hadrons is also shortly presented. The results obtained with these two methods are averaged and prospects for the future are discussed

  15. Generalized hypervirial and Blanchard's recurrence relations for radial matrix elements

    International Nuclear Information System (INIS)

    Dong Shihai; Chen Changyuan; Lozada-Cassou, M

    2005-01-01

    Based on the Hamiltonian identity, we propose a generalized expression of the second hypervirial for an arbitrary central potential wavefunction in arbitrary dimensions D. We demonstrate that the new proposed second hypervirial formula is very powerful in deriving the general Blanchard's and Kramers' recurrence relations among the radial matrix elements. As their useful and important applications, we derive all general Blanchard's and Kramers' recurrence relations and some identities for the Coulomb-like potential, harmonic oscillator and Kratzer oscillator. The recurrence relation and identity between the exponential functions and the powers of the radial function are established for the Morse potential. The corresponding general Blanchard's and Kramers' recurrence relations in 2D are also briefly studied

  16. Anatomy of double beta decay nuclear matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Vogel, Petr, E-mail: pxv@caltech.ed [Kellogg Radiation Laboratory 106-38 Caltech. Pasadena, CA 91125 (United States)

    2009-06-01

    The necessary ingredients for a realistic evaluation of the 0vbetabeta nuclear matrix elements are reviewed. It is argued that the short range nucleon correlations, nucleon finite size, and higher order nuclear currents need to be included in the calculation, even though a consensus on the best way to treat all of these effects has not been reached. Another positive development is the realization that the two alternative and complementary methods, the Quasiparticle Random Phase Approximation and the Nuclear Shell Model, agree on many aspects of the calculation, in particular on the competition, or cancelation, between the contribution of nuclear pairing on one hand, and the other pieces of interaction that result in admixtures of broken pairs or higher seniority states on the other hand. The relatively short range (r <= 2-3 fm) of the effective 0vbetabeta operator found in both methods is a consequence of that competition.

  17. Matrix elements of the relativistic electron-transition operators

    International Nuclear Information System (INIS)

    Rudzikas, Z.B.; Slepcov, A.A.; Kickin, I.S.

    1976-01-01

    The formulas, which enable us to calculate the electric and magnetic multipole transition probabilities in relativistic approximation under various gauge conditions of the electromagnetic potential, are presented. The numerical values of the coefficients of the one-electron reduced matrix elements of the relativistic operators of the electric and magnetic dipole transitions between the configurations K 0 n 2 l 2 j 2 α 0 J 0 j 2 J--K 0 n 1 l 1 j 1 α 0 'J 0 'j 1 J', where K 0 represents any electronic configuration, having the quantum number of the total angular momentum 0 less than or equal to J 0 less than or equal to 8 (the step is 1 / 2 ), and 1 / 2 less than or equal to j 2 , j 1 less than or equal to 7 / 2 , are given

  18. Fabrication of synthetic diffractive elements using advanced matrix laser lithography

    International Nuclear Information System (INIS)

    Škeren, M; Svoboda, J; Kveton, M; Fiala, P

    2013-01-01

    In this paper we present a matrix laser writing device based on a demagnified projection of a micro-structure from a computer driven spatial light modulator. The device is capable of writing completely aperiodic micro-structures with resolution higher than 200 000 DPI. An optical system is combined with ultra high precision piezoelectric stages with an elementary step ∼ 4 nm. The device operates in a normal environment, which significantly decreases the costs compared to competitive technologies. Simultaneously, large areas can be exposed up to 100 cm2. The capabilities of the constructed device will be demonstrated on particular elements fabricated for real applications. The optical document security is the first interesting field, where the synthetic image holograms are often combined with sophisticated aperiodic micro-structures. The proposed technology can easily write simple micro-gratings creating the color and kinetic visual effects, but also the diffractive cryptograms, waveguide couplers, and other structures recently used in the field of optical security. A general beam shaping elements and special photonic micro-structures are another important applications which will be discussed in this paper.

  19. Fabrication of synthetic diffractive elements using advanced matrix laser lithography

    Science.gov (United States)

    Škereň, M.; Svoboda, J.; Květoň, M.; Fiala, P.

    2013-02-01

    In this paper we present a matrix laser writing device based on a demagnified projection of a micro-structure from a computer driven spatial light modulator. The device is capable of writing completely aperiodic micro-structures with resolution higher than 200 000 DPI. An optical system is combined with ultra high precision piezoelectric stages with an elementary step ~ 4 nm. The device operates in a normal environment, which significantly decreases the costs compared to competitive technologies. Simultaneously, large areas can be exposed up to 100 cm2. The capabilities of the constructed device will be demonstrated on particular elements fabricated for real applications. The optical document security is the first interesting field, where the synthetic image holograms are often combined with sophisticated aperiodic micro-structures. The proposed technology can easily write simple micro-gratings creating the color and kinetic visual effects, but also the diffractive cryptograms, waveguide couplers, and other structures recently used in the field of optical security. A general beam shaping elements and special photonic micro-structures are another important applications which will be discussed in this paper.

  20. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    International Nuclear Information System (INIS)

    Actis, S.; Passarino, G.

    2006-12-01

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  1. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

    2006-12-15

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  2. Two-loop SL(2) form factors and maximal transcendentality

    International Nuclear Information System (INIS)

    Loebbert, Florian; Sieg, Christoph; Wilhelm, Matthias; Yang, Gang

    2016-01-01

    Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited number of loop momenta in the integrand’s numerator. At one loop, we derive the full minimal form factor to all orders in the dimensional regularisation parameter. At two loops, we construct the complete integrand for composite operators with an arbitrary number of covariant derivatives, and we obtain the remainder functions as well as the dilatation operator for composite operators with up to three covariant derivatives. The remainder functions reveal curious patterns suggesting a hidden maximal uniform transcendentality for the full form factor. Finally, we speculate about an extension of these patterns to QCD.

  3. Two-loop SL(2) form factors and maximal transcendentality

    Energy Technology Data Exchange (ETDEWEB)

    Loebbert, Florian [Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); Sieg, Christoph [Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); Institut für Mathematik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); Wilhelm, Matthias [Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); Institut für Mathematik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, 2100 Copenhagen Ø (Denmark); Yang, Gang [CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,Beijing 100190 (China); Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany)

    2016-12-19

    Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited number of loop momenta in the integrand’s numerator. At one loop, we derive the full minimal form factor to all orders in the dimensional regularisation parameter. At two loops, we construct the complete integrand for composite operators with an arbitrary number of covariant derivatives, and we obtain the remainder functions as well as the dilatation operator for composite operators with up to three covariant derivatives. The remainder functions reveal curious patterns suggesting a hidden maximal uniform transcendentality for the full form factor. Finally, we speculate about an extension of these patterns to QCD.

  4. Two-loop Dirac neutrino mass and WIMP dark matter

    OpenAIRE

    Bonilla, Cesar; Ma, Ernest; Peinado, Eduardo; Valle, Jose W.F.

    2018-01-01

    We propose a "scotogenic" mechanism relating small neutrino mass and cosmological dark matter. Neutrinos are Dirac fermions with masses arising only in two--loop order through the sector responsible for dark matter. Two triality symmetries ensure both dark matter stability and strict lepton number conservation at higher orders. A global spontaneously broken U(1) symmetry leads to a physical $Diracon$ that induces invisible Higgs decays which add up to the Higgs to dark matter mode. This enhan...

  5. Theory of the particle matrix elements for Helium atom scattering in surfaces

    International Nuclear Information System (INIS)

    Khater, A.; Toennies, J.P.

    2000-01-01

    Full text.A brief review is presented for the recent development of the theory of the particle transition matrix elements, basic to the cross section for Helium and inert particle scattering at thermal energies in solid surfaces. the Jackson and Mott matrix elements are presented and discussed for surface scattering processes, habitually classified as elastic and inelastic. Modified transition matrix elements, introduced originally to account for the cut-off effects, are presented in a direct and simple manner. the Debye-Waller factor is introduced and discussed. A recent calculation for the particle transition matrix elements is presented for the specular and inelastic transition matrix elements and the corresponding inelastic scattering cross section is compared in detail to experimental data. the specular and inelastic transition matrix elements are found to be intrinsically similar owing to the intermediate role of a proposed virtual particle squeezed state near the surface

  6. Controlling excited-state contamination in nucleon matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joó, Bálint; Lin, Huey-Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank

    2016-06-01

    We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \\times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_\\pi=312$~MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation $t_{\\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\\rm sep} \\to \\infty $ estimates is presented.

  7. Two-loop ladder diagram contributions to Bhabha scattering. III

    International Nuclear Information System (INIS)

    Bjoerkevoll, K.S.; Osland, P.; Faeldt, G.

    1992-01-01

    The authors evaluate, in the high-energy limit, the sum of the Feynman amplitudes corresponding the six two-loop ladder-like diagrams in Bhabha scattering. This is the limit where s→∞, while t, the electron mass m and the photon mass λ are all being held fixed. In this limit the sum of the six Feynman amplitudes does not depend on the electron mass. When specialized to the region s>>t>>m 2 >>λ 2 , this result complements the one previously obtained. The connection with Φ 3 theory is also investigated. 6 refs

  8. Gamow-Teller matrix elements from 00 ( p,n) cross section

    International Nuclear Information System (INIS)

    Goodman, C.D.; Goulding, C.A.; Greenfield, M.B.; Rapaport, J.; Bainum, D.E.; Foster, C.C.; Love, W.G.; Petrovich, F.

    1980-01-01

    After simple corrections for distortion effects, 120-MeV, 0 0 (p,n) cross sections are found to be proportional to the squares of the corresponding Fermi and Gamow-Teller matrix elements extracted from β-decay measurements. It is suggested that this proportionality can be used to extract Gamow-Teller matrix elements for transitions inaccessible to β decay

  9. Bag-model matrix elements of the parity-violating weak hamiltonian for charmed baryons

    International Nuclear Information System (INIS)

    Ebert, D.; Kallies, W.

    1983-01-01

    Baryon matrix elements of the parity-violating part of the charmchanging weak Hamiltonian might be significant and comparable with those of the parity-conserving one due to large symmetry breaking. Expression for these new matrix elements by using the MIT-bag model are derived and their implications on earlier calculations of nonleptonic charmed-baryon decays are estimated

  10. The temporal Fresnel number in terms of ray matrix elements

    International Nuclear Information System (INIS)

    Zhang Zhuhong; Fan Dianyuan

    1993-01-01

    By using the analogy between temporal ray matrix and the well known ray matrix, the temporal Fresnel number, which gives the qualitative and quasiquantitative characteristics (shape, width and chirp) of optical pulses, is derived. A concept of effective propagation time is introduced. Several typical examples are discussed. 6 refs

  11. Improved two-loop beam energy stabilizer for an FN tandem accelerator

    International Nuclear Information System (INIS)

    Trainor, T.A.

    1981-01-01

    A detailed analysis of the properties of various elements in a two-loop voltage regulator for a tandem accelerator enabled design of an optimum system which reduces effective accelerating voltage noise below 100 V. Essential features of the new system are high-quality slit preamplifiers, careful attention to removal of extraneous noise sources, and proper shaping of frequency responses to maximize stable gains and ensure compatibility of the two control loops. The resultant beam energy stabilizer system is easy to operate, has well defined indicators for proper adjustment of operating parameters, and recovers reliably from beam interruptions

  12. Two-Loop Scattering Amplitudes from the Riemann Sphere

    CERN Document Server

    Geyer, Yvonne; Monteiro, Ricardo; Tourkine, Piotr

    2016-01-01

    The scattering equations give striking formulae for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the worldsheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the colour dependence, which includes non-planar contributions.

  13. Comparison between phase shift derived and exactly calculated nucleon--nucleon interaction matrix elements

    International Nuclear Information System (INIS)

    Gregersen, A.W.

    1977-01-01

    A comparison is made between matrix elements calculated using the uncoupled channel Sussex approach to second order in DWBA and matrix elements calculated using a square well potential. The square well potential illustrated the problem of the determining parameter independence balanced with the concept of phase shift difference. The super-soft core potential was used to discuss the systematics of the Sussex approach as a function of angular momentum as well as the relation between Sussex generated and effective interaction matrix elements. In the uncoupled channels the original Sussex method of extracting effective interaction matrix elements was found to be satisfactory. In the coupled channels emphasis was placed upon the 3 S 1 -- 3 D 1 coupled channel matrix elements. Comparison is made between exactly calculated matrix elements, and matrix elements derived using an extended formulation of the coupled channel Sussex method. For simplicity the potential used is a nonseparable cut-off oscillator. The eigenphases of this potential can be made to approximate the realistic nucleon--nucleon phase shifts at low energies. By using the cut-off oscillator test potential, the original coupled channel Sussex method of determining parameter independence was shown to be incapable of accurately reproducing the exact cut-off oscillator matrix elements. The extended Sussex method was found to be accurate to within 10 percent. The extended method is based upon more general coupled channel DWBA and a noninfinite oscillator wave function solution to the cut-off oscillator auxiliary potential. A comparison is made in the coupled channels between matrix elements generated using the original Sussex method and the extended method. Tables of matrix elements generated using the original uncoupled channel Sussex method and the extended coupled channel Sussex method are presented for all necessary angular momentum channels

  14. Two loop virtual corrections to b → (d, s)l{sup +}l{sup -} and c → ul{sup +}l{sup -} for arbitrary momentum transfer

    Energy Technology Data Exchange (ETDEWEB)

    Boer, Stefan de [TU Dortmund, Fakultaet fuer Physik, Dortmund (Germany)

    2017-11-15

    Non-factorizable two loop corrections to heavy to light flavor changing neutral current transitions due to matrix elements of current-current operators are calculated analytically for arbitrary momentum transfer. This extends previous work on b → (d, s)l{sup +}l{sup -} transitions. New results for c → ul{sup +}l{sup -} transitions are presented. Recent work on polylogarithms is used for the master integrals. For b → sl{sup +}l{sup -} transitions, the corrections are most significant for the imaginary parts of the effective Wilson coefficients in the large hadronic recoil range. Analytical results and ready-to-use fitted results for a specific set of parameters are provided. (orig.)

  15. Two-loop fermionic corrections to massive Bhabha scattering

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S.; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Czakon, M. [Wuerzburg Univ. (Germany). Inst. fuer Theoretische Physik und Astrophysik]|[Institute of Nuclear Physics, NSCR DEMOKRITOS, Athens (Greece); Gluza, J. [Silesia Univ., Katowice (Poland). Inst. of Physics

    2007-05-15

    We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses m{sub e}, m{sub f} and the Mandelstam invariants s, t, u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales m{sup 2}{sub e}<

  16. Massive two-loop Bhabha scattering - the factorizable subset

    International Nuclear Information System (INIS)

    Fleischer, J.; Tarasov, O.V.; Werthenbach, A.

    2002-11-01

    The experimental precision that will be reached at the next generation of colliders makes it indispensable to improve theoretical predictions significantly. Bhabha scattering (e + e - → e + e - ) is one of the prime processes calling for a better theoretical precision, in particular for non-zero electron masses. We present a first subset of the full two-loop calculation, namely the factorizable subset. Our calculation is based on DIANA. We reduce tensor integrals to scalar integrals in shifted (increased) dimensions and additional powers of various propagators, so-called dots-on-lines. Recurrence relations remove those dots-on-lines as well as genuine dots-on-lines (originating from mass renormalization) and reduce the dimension of the integrals to the generic d=4-2ε dimensions. The resulting master integrals have to be expanded to O(ε) to ensure proper treatment of all finite terms. (orig.)

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

    International Nuclear Information System (INIS)

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

    2003-01-01

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

  18. Hadron matrix elements of quark operators in the relativistic quark model, 2. Model calculation

    Energy Technology Data Exchange (ETDEWEB)

    Arisue, H; Bando, M; Toya, M [Kyoto Univ. (Japan). Dept. of Physics; Sugimoto, H

    1979-11-01

    Phenomenological studies of the matrix elements of two- and four-quark operators are made on the basis of relativistic independent quark model for typical three cases of the potentials: rigid wall, linearly rising and Coulomb-like potentials. The values of the matrix elements of two-quark operators are relatively well reproduced in each case, but those of four-quark operators prove to be too small in the independent particle treatment. It is suggested that the short-range two-quark correlations must be taken into account in order to improve the values of the matrix elements of the four-quark operators.

  19. Hadron matrix elements of quark operators in the relativistic quark model

    Energy Technology Data Exchange (ETDEWEB)

    Bando, Masako; Toya, Mihoko [Kyoto Univ. (Japan). Dept. of Physics; Sugimoto, Hiroshi

    1979-07-01

    General formulae for evaluating matrix elements of two- and four-quark operators sandwiched by one-hadron states are presented on the basis of the relativistic quark model. Observed hadronic quantities are expressed in terms of those matrix elements of two- and four-quark operators. One observes various type of relativistic expression for the matrix elements which in the non-relativistic case reduce to simple expression of the so-called ''the wave function at the origin /sup +/psi(0)/sup +/''.

  20. Radial Matrix Elements of Hydrogen Atom and the Correspondence ...

    Indian Academy of Sciences (India)

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

    Hydrogen excited states—radial matrix element—corres- ... atoms, its availability, production, its spectras, and importance in astrophysics (Dupree ... far away revolving lazily around in a slow orbit like a distant planet in the solar system. As the electron orbit diameter grows rapidly, its energy also decreases rapidly. Currently ...

  1. Matrix elements of a hyperbolic vector operator under SO(2,1)

    International Nuclear Information System (INIS)

    Zettili, N.; Boukahil, A.

    2003-01-01

    We deal here with the use of Wigner–Eckart type arguments to calculate the matrix elements of a hyperbolic vector operator V-vector by expressing them in terms of reduced matrix elements. In particular, we focus on calculating the matrix elements of this vector operator within the basis of the hyperbolic angular momentum T-vector whose components T-vector 1 , T-vector 2 , T-vector 3 satisfy an SO(2,1) Lie algebra. We show that the commutation rules between the components of V-vector and T-vector can be inferred from the algebra of ordinary angular momentum. We then show that, by analogy to the Wigner–Eckart theorem, we can calculate the matrix elements of V-vector within a representation where T-vector 2 and T-vector 3 are jointly diagonal. (author)

  2. Program package for calculating matrix elements of two-cluster structures in nuclei

    International Nuclear Information System (INIS)

    Krivec, R.; Mihailovic, M.V.; Kernforschungszentrum Karlsruhe G.m.b.H.

    1982-01-01

    Matrix elements of operators between Slater determinants of two-cluster structures must be expanded into partial waves for the purpose of angular momentum projection. The expansion coefficients contain integrals over the spherical angles theta and phi. (orig.)

  3. Radiation and penetration matrix elements for magnetic quadrupole transitions between Nilsson states in odd nuclei

    International Nuclear Information System (INIS)

    Feresin, A.P.; Guseva, I.S.

    1984-01-01

    Single-particle matrix elements for magnetic quadrupole gamma radiation in odd deformed nuclei, calculated with the aid of Nilsson-potential wave functions, are presented. Also given are the internal conversion penetration matrix elements, calculated in the same manner. The penetration matrix elements are needed to estimate the nuclear penetration parameter, which determines the deviation of experimental internal conversion coefficients from their standard values given in tables. Matrix elements are given for transitions between all pairs of Nilsson single-particle states with ΔN = 1 and ΔK = 0, 1, and 2 for the nuclear shells with 4< or =N< or =7 and for the two deformation values epsilon = 0.2 and 0.3

  4. 3-Loop massive O(T2F) contributions to the DIS operator matrix element Agg

    International Nuclear Information System (INIS)

    Ablinger, J.; Schneider, C.; Bluemlein, J.; Freitas, A. de; Hasselhuhn, A.; Round, M.; Manteuffel, A. von

    2014-09-01

    Contributions to heavy flavour transition matrix elements in the variable flavour number scheme are considered at 3-loop order. In particular a calculation of the diagrams with two equal masses that contribute to the massive operator matrix element A (3) gg,Q is performed. In the Mellin space result one finds finite nested binomial sums. In x-space these sums correspond to iterated integrals over an alphabet containing also square-root valued letters.

  5. Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

    Institute of Scientific and Technical Information of China (English)

    XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian

    2007-01-01

    Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.

  6. Matrix elements of u and p for the modified Poeschl-Teller potential

    International Nuclear Information System (INIS)

    Gomez-Camacho, J; Lemus, R; Arias, J M

    2004-01-01

    Closed analytical expressions in terms of a single sum are obtained for the matrix elements of the momentum and the natural variable u tanh(αx) in the basis of the modified Poeschl-Teller (MPT) bound eigenstates. These matrix elements are first expressed in terms of Franck-Condon factors, which thereafter are substituted for analytic expressions. Expansions of the variables p and u in terms of creation and annihilation operators associated with the MPT bound eigenfunctions are also presented

  7. A pedagogical derivation of the matrix element method in particle physics data analysis

    Science.gov (United States)

    Sumowidagdo, Suharyo

    2018-03-01

    The matrix element method provides a direct connection between the underlying theory of particle physics processes and detector-level physical observables. I am presenting a pedagogically-oriented derivation of the matrix element method, drawing from elementary concepts in probability theory, statistics, and the process of experimental measurements. The level of treatment should be suitable for beginning research student in phenomenology and experimental high energy physics.

  8. The two-loop sunrise integral and elliptic polylogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Adams, Luise; Weinzierl, Stefan [Institut fuer Physik, Johannes Gutenberg-Universitaet Mainz (Germany); Bogner, Christian [Institut fuer Physik, Humboldt-Universitaet zu Berlin (Germany)

    2016-07-01

    In this talk, we present a solution for the two-loop sunrise integral with arbitrary masses around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. Furthermore we investigate the elliptic polylogarithms appearing in higher orders in the dimensional regularisation ε of the two-dimensional equal mass solution. Around two space-time dimensions the solution consists of a sum of three elliptic dilogarithms where the arguments have a nice geometric interpretation as intersection points of the integration region and an elliptic curve associated to the sunrise integral. Around four space-time dimensions the sunrise integral can be expressed with the ε{sup 0}- and ε{sup 1}-solution around two dimensions, mass derivatives thereof and simpler terms. Considering higher orders of the two-dimensional equal mass solution we find certain generalisations of the elliptic polylogarithms appearing in the ε{sup 0}- and ε{sup 1}-solutions around two and four space-time dimensions. We show that these higher order-solutions can be found by iterative integration within this class of functions.

  9. Composition Feature of the Element Tangent Stiffness Matrix of Geometrically Nonlinear 2D Frame Structures

    Directory of Open Access Journals (Sweden)

    Romanas Karkauskas

    2011-04-01

    Full Text Available The expressions of the finite element method tangent stiffness matrix of geometrically nonlinear constructions are not fully presented in publications. The matrixes of small displacements stiffness are usually presented only. To solve various problems of construction analysis or design and to specify the mode of the real deflection of construction, it is necessary to have a fully described tangent matrix analytical expression. This paper presents a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only. The obtained vector-function derivative of internal forces considering nodal displacements is the tangent stiffness matrix. The analytical expressions having nodal displacements of matrixes forming the content of the 2D frame construction element tangent stiffness matrix are presented in the article. The suggested methodology has been checked making symbolical calculations in the medium of MatLAB calculation complex. The analytical expression of the stiffness matrix has been obtained.Article in Lithuanian

  10. On the generalized eigenvalue method for energies and matrix elements in lattice field theory

    Energy Technology Data Exchange (ETDEWEB)

    Blossier, Benoit [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Paris-XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Morte, Michele della [CERN, Geneva (Switzerland). Physics Dept.]|[Mainz Univ. (Germany). Inst. fuer Kernphysik; Hippel, Georg von; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Mendes, Tereza [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Sao Paulo Univ. (Brazil). IFSC

    2009-02-15

    We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E{sub N+1}-E{sub n}) t). The gap E{sub N+1}-E{sub n} can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m{sub b} in HQET. (orig.)

  11. On the generalized eigenvalue method for energies and matrix elements in lattice field theory

    International Nuclear Information System (INIS)

    Blossier, Benoit; Mendes, Tereza; Sao Paulo Univ.

    2009-02-01

    We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E N+1 -E n ) t). The gap E N+1 -E n can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m b in HQET. (orig.)

  12. Experimental Study of Flexible Plate Vibration Control by Using Two-Loop Sliding Mode Control Strategy

    Science.gov (United States)

    Yang, Jingyu; Lin, Jiahui; Liu, Yuejun; Yang, Kang; Zhou, Lanwei; Chen, Guoping

    2017-08-01

    It is well known that intelligent control theory has been used in many research fields, novel modeling method (DROMM) is used for flexible rectangular active vibration control, and then the validity of new model is confirmed by comparing finite element model with new model. In this paper, taking advantage of the dynamics of flexible rectangular plate, a two-loop sliding mode (TSM) MIMO approach is introduced for designing multiple-input multiple-output continuous vibration control system, which can overcome uncertainties, disturbances or unstable dynamics. An illustrative example is given in order to show the feasibility of the method. Numerical simulations and experiment confirm the effectiveness of the proposed TSM MIMO controller.

  13. Evolution of the pion wave function in the scalar /phi/63 model: two-loop calculation

    International Nuclear Information System (INIS)

    Mikhailov, S.V.; Radyushkin, A.V.

    1986-01-01

    The authors study the structure of the contributions that violate the multiplicative renormalizability of the conformal operators in the model based on the /phi/ 6 3 theory in space-time of six dimensions. This theory has a number of features in common with QCD in four dimensions. The basic propositions are presented and the key elements of the calculation are demonstrated. The connection between the kernels for exclusive and inclusive processes are discused and the structure of the two-loop evolution kernel V(x,y) and the solution of the evolution equation are discussed. Main conclusions are formulated and the results of the calculations for concrete diagrams are deferred to in Appendix A. Formulas for the transition from the exclusive to the inclusive kernels are presented in Appendix B

  14. Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory

    Science.gov (United States)

    Lee, Jong-Wan

    2015-05-01

    We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.

  15. Correlation between eigenvalues and sorted diagonal matrix elements of a large dimensional matrix

    International Nuclear Information System (INIS)

    Arima, A.

    2008-01-01

    Functional dependences of eigenvalues as functions of sorted diagonal elements are given for realistic nuclear shell model (NSM) hamiltonian, the uniform distribution hamiltonian and the GOE hamiltonian. In the NSM case, the dependence is found to be linear. We discuss extrapolation methods for more accurate predictions for low-lying states. (author)

  16. Renormalization of vacuum expectation values in spontaneously broken gauge theories: two-loop results

    International Nuclear Information System (INIS)

    Sperling, Marcus; Stöckinger, Dominik; Voigt, Alexander

    2014-01-01

    We complete the two-loop calculation of β-functions for vacuum expectation values (VEVs) in gauge theories by the missing O(g 4 )-terms. The full two-loop results are presented for generic and supersymmetric theories up to two-loop level in arbitrary R ξ -gauge. The results are obtained by means of a scalar background field, identical to our previous analysis. As a by-product, the two-loop scalar anomalous dimension for generic supersymmetric theories is presented. As an application we compute the β-functions for VEVs and tan β in the MSSM, NMSSM, and E 6 SSM

  17. Quasi-exact evaluation of time domain MFIE MOT matrix elements

    KAUST Repository

    Shi, Yifei

    2013-07-01

    A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.

  18. Quasi-exact evaluation of time domain MFIE MOT matrix elements

    KAUST Repository

    Shi, Yifei; Bagci, Hakan; Shanker, Balasubramaniam; Lu, Mingyu; Michielssen, Eric

    2013-01-01

    A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.

  19. Method of computer algebraic calculation of the matrix elements in the second quantization language

    International Nuclear Information System (INIS)

    Gotoh, Masashi; Mori, Kazuhide; Itoh, Reikichi

    1995-01-01

    An automated method by the algebraic programming language REDUCE3 for specifying the matrix elements expressed in second quantization language is presented and then applied to the case of the matrix elements in the TDHF theory. This program works in a very straightforward way by commuting the electron creation and annihilation operator (a † and a) until these operators have completely vanished from the expression of the matrix element under the appropriate elimination conditions. An improved method using singlet generators of unitary transformations in the place of the electron creation and annihilation operators is also presented. This improvement reduces the time and memory required for the calculation. These methods will make programming in the field of quantum chemistry much easier. 11 refs., 1 tab

  20. Calculation of the Cholesky factor directly from the stiffness matrix of the structural element

    International Nuclear Information System (INIS)

    Prates, C.L.M.; Soriano, H.L.

    1978-01-01

    The analysis of the structures of nuclear power plants requires the evaluation of the internal forces. This is attained by the solution of a system of equations. This solution takes most of the computing time and memory. One of the ways it can be achieved is based on the Cholesky factor. The structural matrix of the coeficients is transformed into an upper triangular matrix by the Cholesky decomposition. Cholesky factor can be obtained directly from the stiffness matrix of the structural element. The result can thus be obtained in a more precise and quick way. (Author)

  1. Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

    Science.gov (United States)

    Alexander, Steven; Coldwell, R. L.

    2015-03-01

    The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

  2. Axial-Current Matrix Elements in Light Nuclei from Lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Savage, Martin [Univ. of Washington, Seattle, WA (United States); Shanahan, Phiala E. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Tiburzi, Brian C. [Univ. of Maryland, College Park, MD (United States); Wagman, Michael L. [Univ. of Washington, Seattle, WA (United States); Winter, Frank T. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Beane, Silas [Univ. of New Hampshire, Durham, NH (United States); Chang, Emmanuel [Univ. of Washington, Seattle, WA (United States); Davoudi, Zohreh; Detmold, William [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Orginos, Konstantinos [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)

    2016-12-01

    I present results from the first lattice QCD calculations of axial-current matrix elements in light nuclei, performed by the NPLQCD collaboration. Precision calculations of these matrix elements, and the subsequent extraction of multi-nucleon axial-current operators, are essential in refining theoretical predictions of the proton-proton fusion cross section, neutrino-nucleus cross sections and $\\beta\\beta$-decay rates of nuclei. In addition, they are expected to shed light on the phenomenological quenching of $g_A$ that is required in nuclear many-body calculations.

  3. The two-mass contribution to the three-loop pure singlet operator matrix element

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de; Schoenwald, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2017-11-15

    We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function F{sub 2}(x,Q{sup 2}) at O(α{sup 3}{sub s}) as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.

  4. Matrix elements of Yale potential and level properties of light nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, N; Prakash, O [Delhi Univ. (India). Dept. of Physics and Astrophysics

    1976-07-01

    Shell model calculations using bare and renormalized matrix elements of the Yale potential are reported for the normal-parity states of A = 6-9 nuclei. Renormalization of the two-body matrix elements using second-order perturbation theory is not found to improve the agreements with the experimental data. Inclusion of the energy shifts of ground state rotational bands in /sup 8/Be and /sup 9/Be are, however, found to improve the agreements with the excitation energies of nuclear levels. The need for carrying out more calculations of these nuclei with realistic forces is pointed out.

  5. SU(3) techniques for angular momentum projected matrix elements in multi-cluster problems

    International Nuclear Information System (INIS)

    Hecht, K.T.; Zahn, W.

    1978-01-01

    In the theory of integral transforms for the evaluation of the resonating group kernels needed for cluster model calculations, the evaluation of matrix elements in an angular momentum coupled basis has proved to be difficult for cluster problems involving more than two fragments. For multi-cluster wave functions SU(3) coupling and recoupling techniques can furnish a tool for the practical evaluation matrix elements in an angular momentum coupled basis if the several relative motion harmonic oscillator functions in Bargmann space have simple SU(3) coupling properties. The method is illustrated by a three-cluster problem, such as 12 C = α + α + α, involving three 1 S clusters. 2 references

  6. Matrix elements of vibration kinetic energy operator of tetrahedral molecules in non-orthogonal-dependent coordinates

    Science.gov (United States)

    Protasevich, Alexander E.; Nikitin, Andrei V.

    2018-01-01

    In this work, we propose an algorithm for calculating the matrix elements of the kinetic energy operator for tetrahedral molecules. This algorithm uses the dependent six-angle coordinates (6A) and takes into account the full symmetry of molecules. Unlike A.V. Nikitin, M. Rey, and Vl. G. Tyuterev who operate with the kinetic energy operator only in Radau orthogonal coordinates, we consider a general case. The matrix elements are shown to be a sum of products of one-dimensional integrals.

  7. Role of shell structure in the 2νββ nuclear matrix elements

    International Nuclear Information System (INIS)

    Nakada, H.

    1998-01-01

    Significance of the nuclear shell structure in the ββ nuclear matrix elements is pointed out. The 2νββ processes are mainly mediated by the low-lying 1 + states. The shell structure also gives rise to concentration or fragmentation of the 2νββ components over intermediate states, depending on nuclide. These roles of the shell structure are numerically confirmed by realistic shell model calculations. Some shell structure effects are suggested for 0νββ matrix elements; dominance of low-lying intermediate states and nucleus-dependence of their spin-parities. (orig.)

  8. LIBS detection of heavy metal elements in liquid solutions by using wood pellet as sample matrix

    International Nuclear Information System (INIS)

    Wen Guanhong; Sun Duixiong; Su Maogen; Dong Chenzhong

    2013-01-01

    Laser-induced breakdown spectroscopy (LIBS) has been applied to the analysis of heavy metals in liquid sample. A new approach was presented to improve the detection limit and minimize the sample matrix effects, in which dried wood pellets absorbed the given amounts of Cr standard solutions and then were baked because they have stronger and rapid absorption properties for liquid samples as well as simple elemental compositions. In this work, we have taken a typical heavy metal Cr element as an example, and investigated the spectral feasibility of Cr solutions and dried wood pellets before and after absorbing Cr solutions at the same experimental conditions, respectively. The results were demonstrated to successfully produce a superior analytical response for heavy metal elements by using wood pellet as sample matrix according to obtained LOD of 0.07 ppm for Cr element in solutions. (author)

  9. LIBS Detection of Heavy Metal Elements in Liquid Solutions by Using Wood Pellet as Sample Matrix

    International Nuclear Information System (INIS)

    Wen Guanhong; Sun Duixiong; Su Maogen; Dong Chenzhong

    2014-01-01

    Laser-induced breakdown spectroscopy (LIBS) has been applied to the analysis of heavy metals in liquid samples. A new approach was presented to lower the limit of detection (LOD) and minimize the sample matrix effects, in which dried wood pellets absorbed the given amounts of Cr standard solutions and then were baked because they have stronger and rapid absorption properties for liquid samples as well as simple elemental compositions. In this work, we have taken a typical heavy metal Cr element as an example, and investigated the spectral feasibility of Cr solutions and dried wood pellets before and after absorbing Cr solutions at the same experimental conditions. The results were demonstrated to successfully produce a superior analytical response for heavy metal elements by using wood pellet as sample matrix according to the obtained LOD of 0.07 ppm for Cr element in solutions

  10. Comparison of Material Behavior of Matrix Graphite for HTGR Fuel Elements upon Irradiation: A literature Survey

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Young-Woo; Yeo, Seunghwan; Cho, Moon Sung [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2015-05-15

    The fuel elements for the HTGRs (i.e., spherical fuel element in pebble-bed type core design and fuel compact in prismatic core design) consists of coated fuel particles dispersed and bonded in a closely packed array within a carbonaceous matrix. This matrix is generally made by mixing fully graphitized natural and needle- or pitchcoke originated powders admixed with a binder material (pitch or phenolic resin), The resulting resinated graphite powder mixture, when compacted, may influence a number of material properties as well as its behavior under neutron irradiation during reactor operation. In the fabrication routes of these two different fuel element forms, different consolidation methods are employed; a quasi-isostatic pressing method is generally adopted to make pebbles while fuel compacts are fabricated by uni-axial pressing mode. The result showed that the hardness values obtained from the two directions showed an anisotropic behavior: The values obtained from the perpendicular section showed much higher micro hardness (176.6±10.5MPa in average) than from the parallel section ((125.6±MPa in average). This anisotropic behavior was concluded to be related to the microstructure of the matrix graphite. This may imply that the uni-axial pressing method to make compacts influence the microstructure of the matrix and hence the material properties of the matrix graphite.

  11. Bessel equation as an operator identity's matrix element in quantum mechanics

    International Nuclear Information System (INIS)

    Fan Hongyi; Li Chao

    2004-01-01

    We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented

  12. Analytical matrix elements of semifinite 2D two centre nuclear potential

    International Nuclear Information System (INIS)

    Niculescu, V. L. R.; Catana, S.; Catana, D.; Babin, V.

    1998-01-01

    In the present work we introduce a new 2D potential which is a symmetric double-well in one variable and with one centre in the other. The factorable potential matrix elements are expressed by analytical formulas. This implies a shorter computational time. (author)

  13. Nuclear Matrix Elements for the $\\beta\\beta$ Decay of the $^{76}$Ge

    CERN Document Server

    Brown, B A; Horoi, M

    2015-01-01

    The nuclear matrix elements for two-neutrino double-beta (2 n$\\beta\\beta$ ) and zero-neutrino double-beta (0 n$\\beta\\beta$) decay of 76 Ge are evaluated in terms of the configuration interaction (CI), quasiparticle random phase approximation (QRPA) and interacting boson model (IBM) methods. We show that the decomposition of the matrix elements in terms of interemediate states in 74 Ge is dominated by ground state of this nucleus. We consider corrections to the CI results that arise from configurations admixtures involving orbitals out-side of the CI configuration space by using results from QRPA, many-body-perturbation theory, and the connections to related observables. The CI two-neutrino matrix element is reduced due to the inclusion of spin-orbit partners, and to many-body correlations connected with Gamow-Teller beta decay. The CI zero-neutrino matrix element for the heavy neutrino is enhanced due to particle-particle correlations that are connected with the odd-even oscillations in the nuclear masse...

  14. Effects of quenching and partial quenching on QCD penguin matrix elements

    NARCIS (Netherlands)

    Golterman, Maarten; Pallante, Elisabetta

    2002-01-01

    We point out that chiral transformation properties of penguin operators change in the transition from unquenched to (partially) quenched QCD. The way in which this affects the lattice determination of weak matrix elements can be understood in the framework of (partially) quenched chiral perturbation

  15. Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator

    Institute of Scientific and Technical Information of China (English)

    LI Ning; JU Guo-Xing; REN Zhong-Zhou

    2004-01-01

    The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The twodimensional Dirac oscillator has similar behavior to that for three-dimensional one.

  16. Rigorous constraints on the matrix elements of the energy–momentum tensor

    Directory of Open Access Journals (Sweden)

    Peter Lowdon

    2017-11-01

    Full Text Available The structure of the matrix elements of the energy–momentum tensor play an important role in determining the properties of the form factors A(q2, B(q2 and C(q2 which appear in the Lorentz covariant decomposition of the matrix elements. In this paper we apply a rigorous frame-independent distributional-matching approach to the matrix elements of the Poincaré generators in order to derive constraints on these form factors as q→0. In contrast to the literature, we explicitly demonstrate that the vanishing of the anomalous gravitomagnetic moment B(0 and the condition A(0=1 are independent of one another, and that these constraints are not related to the specific properties or conservation of the individual Poincaré generators themselves, but are in fact a consequence of the physical on-shell requirement of the states in the matrix elements and the manner in which these states transform under Poincaré transformations.

  17. Matrix elements of the potential energy operator for the six nucleon system between the generating invariants

    International Nuclear Information System (INIS)

    Filippov, G.F.; Lopez Trujillo, A.; Rybkin, I.Yu.

    1993-01-01

    The matrix elements of the potential energy operator (which includes central, spin-orbit and tensor components) are calculated between the generating invariants of the cluster basis describing α + d and t+h configurations of the six-nucleon system. (author). 12 refs

  18. Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Somogyi, Gabor [University of Debrecen and Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, PO Box 51 (Hungary); Trocsanyi, Zoltan [University of Debrecen and Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, PO Box 51 (Hungary); Duca, Vittorio Del [Istituto Nazionale di Fisica Nucleare, Sez. di Torino, via P. Giuria, 1 - 10125 Torino (Italy)

    2005-06-01

    We describe how to disentangle the singly- and doubly-unresolved (soft and/or collinear) limits of tree-level QCD squared matrix elements. Using the factorization formulae presented in this paper, we outline a viable general subtraction scheme for computing next-to-next-to-leading order corrections for electron-positron annihilation into jets.

  19. Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements

    International Nuclear Information System (INIS)

    Eberspaecher, M.; Amos, K.; Apagyi, B.

    1999-12-01

    The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed

  20. A Literature Study of Matrix Element Influenced to the Result of Analysis Using Absorption Atomic Spectroscopy Method (AAS)

    International Nuclear Information System (INIS)

    Tyas-Djuhariningrum

    2004-01-01

    The gold sample analysis can be deviated more than >10% to those thrue value caused by the matrix element. So that the matrix element character need to be study in order to reduce the deviation. In rock samples, the matrix elements can cause self quenching, self absorption and ionization process, so there is a result analysis error. In the rock geochemical process, the elements of the same group at the periodic system have the tendency to be together because of their same characteristic. In absorption Atomic Spectroscopy analysis, the elements associate can absorb primer energy with similar wave length so that it can cause deviation in the result interpretation. The aim of study is to predict matrix element influences from rock sample with application standard method for reducing deviation. In quantitative way, assessment of primer light intensity that will be absorbed is proportional to the concentration atom in the sample that relationship between photon intensity with concentration in part per million is linier (ppm). These methods for eliminating matrix elements influence consist of three methods : external standard method, internal standard method, and addition standard method. External standard method for all matrix element, internal standard method for elimination matrix element that have similar characteristics, addition standard methods for elimination matrix elements in Au, Pt samples. The third of standard posess here accuracy are about 95-97%. (author)

  1. Modelling of polypropylene fibre-matrix composites using finite element analysis

    Directory of Open Access Journals (Sweden)

    2009-01-01

    Full Text Available Polypropylene (PP fibre-matrix composites previously prepared and studied experimentally were modelled using finite element analysis (FEA in this work. FEA confirmed that fibre content and composition controlled stress distribution in all-PP composites. The stress concentration at the fibre-matrix interface became greater with less fibre content. Variations in fibre composition were more significant in higher stress regions of the composites. When fibre modulus increased, the stress concentration at the fibres decreased and the shear stress at the fibre-matrix interface became more intense. The ratio between matrix modulus and fibre modulus was important, as was the interfacial stress in reducing premature interfacial failure and increasing mechanical properties. The model demonstrated that with low fibre concentration, there were insufficient fibres to distribute the applied stress. Under these conditions the matrix yielded when the applied stress reached the matrix yield stress, resulting in increased fibre axial stress. When the fibre content was high, there was matrix depletion and stress transfer was inefficient. The predictions of the FEA model were consistent with experimental and published data.

  2. Efficient improvement of virtual crack extension method by a derivative of the finite element stiffness matrix

    International Nuclear Information System (INIS)

    Ishikawa, H.; Nakano, S.; Yuuki, R.; Chung, N.Y.

    1991-01-01

    In the virtual crack extension method, the stress intensity factor, K, is obtained from the converged value of the energy release rate by the difference of the finite element stiffness matrix when some crack extension are taken. Instead of the numerical difference of the finite element stiffness, a new method to use a direct dirivative of the finite element stiffness matrix with respect to crack length is proposed. By the present method, the results of some example problems, such as uniform tension problems of a square plate with a center crack and a rectangular plate with an internal slant crack, are obtained with high accuracy and good efficiency. Comparing with analytical results, the present values of the stress intensity factors of the problems are obtained with the error that is less than 0.6%. This shows the numerical assurance of the usefulness of the present method. A personal computer program for the analysis is developed

  3. Determinant representations of spin-operator matrix elements in the XX spin chain and their applications

    Science.gov (United States)

    Wu, Ning

    2018-01-01

    For the one-dimensional spin-1/2 XX model with either periodic or open boundary conditions, it is shown by using a fermionic approach that the matrix element of the spin operator Sj- (Sj-Sj'+ ) between two eigenstates with numbers of excitations n and n +1 (n and n ) can be expressed as the determinant of an appropriate (n +1 )×(n +1 ) matrix whose entries involve the coefficients of the canonical transformations diagonalizing the model. In the special case of a homogeneous periodic XX chain, the matrix element of Sj- reduces to a variant of the Cauchy determinant that can be evaluated analytically to yield a factorized expression. The obtained compact representations of these matrix elements are then applied to two physical scenarios: (i) Nonlinear optical response of molecular aggregates, for which the determinant representation of the transition dipole matrix elements between eigenstates provides a convenient way to calculate the third-order nonlinear responses for aggregates from small to large sizes compared with the optical wavelength; and (ii) real-time dynamics of an interacting Dicke model consisting of a single bosonic mode coupled to a one-dimensional XX spin bath. In this setup, full quantum calculation up to N ≤16 spins for vanishing intrabath coupling shows that the decay of the reduced bosonic occupation number approaches a finite plateau value (in the long-time limit) that depends on the ratio between the number of excitations and the total number of spins. Our results can find useful applications in various "system-bath" systems, with the system part inhomogeneously coupled to an interacting XX chain.

  4. MS vs. pole masses of gauge bosons II: Two-loop electroweak fermion correct

    International Nuclear Information System (INIS)

    Jegerlehner, F.; Kalmykov, M.Yu.; Veretin, O.

    2002-12-01

    We have calculated the fermion contributions to the shift of the position of the poles of the massive gauge boson propagators at two-loop order in the Standard Model. Together with the bosonic contributions calculated previously the full two-loop corrections are available. This allows us to investigate the full correction in the relationship between anti M anti S and pole masses of the vector bosons Z and W. Two-loop renormalization and the corresponding renormalization group equations are discussed. Analytical results for the master-integrals appearing in the massless fermion contributions are given. A new approach of summing multiple binomial sums has been developed. (orig.)

  5. Iterative structure within the five-particle two-loop amplitude

    International Nuclear Information System (INIS)

    Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia

    2006-01-01

    We find an unexpected iterative structure within the two-loop five-gluon amplitude in N=4 supersymmetric Yang-Mills theory. Specifically, we show that a subset of diagrams contributing to the full amplitude, including a two-loop pentagon-box integral with nontrivial dependence on five kinematical variables, satisfies an iterative relation in terms of one-loop scalar box diagrams. The implications of this result for the possible iterative structure of the full two-loop amplitude are discussed

  6. Extending two Higgs doublet models for two-loop neutrino mass generation and one-loop neutrinoless double beta decay

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Zhen, E-mail: liu-zhen@sjtu.edu.cn; Gu, Pei-Hong, E-mail: peihong.gu@sjtu.edu.cn

    2017-02-15

    We extend some two Higgs doublet models, where the Yukawa couplings for the charged fermion mass generation only involve one Higgs doublet, by two singlet scalars respectively carrying a singly electric charge and a doubly electric charge. The doublet and singlet scalars together can mediate a two-loop diagram to generate a tiny Majorana mass matrix of the standard model neutrinos. Remarkably, the structure of the neutrino mass matrix is fully determined by the symmetric Yukawa couplings of the doubly charged scalar to the right-handed leptons. Meanwhile, a one-loop induced neutrinoless double beta decay can arrive at a testable level even if the electron neutrino has an extremely small Majorana mass. We also study other experimental constraints and implications including some rare processes and Higgs phenomenology.

  7. Extending two Higgs doublet models for two-loop neutrino mass generation and one-loop neutrinoless double beta decay

    Directory of Open Access Journals (Sweden)

    Zhen Liu

    2017-02-01

    Full Text Available We extend some two Higgs doublet models, where the Yukawa couplings for the charged fermion mass generation only involve one Higgs doublet, by two singlet scalars respectively carrying a singly electric charge and a doubly electric charge. The doublet and singlet scalars together can mediate a two-loop diagram to generate a tiny Majorana mass matrix of the standard model neutrinos. Remarkably, the structure of the neutrino mass matrix is fully determined by the symmetric Yukawa couplings of the doubly charged scalar to the right-handed leptons. Meanwhile, a one-loop induced neutrinoless double beta decay can arrive at a testable level even if the electron neutrino has an extremely small Majorana mass. We also study other experimental constraints and implications including some rare processes and Higgs phenomenology.

  8. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-14

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  9. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-01

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  10. Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites

    DEFF Research Database (Denmark)

    Frederiksson, Per; Gudmundson, Peter; Mikkelsen, Lars Pilgaard

    2009-01-01

    A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements...... of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due...... to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories....

  11. Correlated random-phase approximation from densities and in-medium matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)

    2016-07-01

    The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.

  12. Short-distance matrix elements for $D$-meson mixing for 2+1 lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Chia Cheng [Univ. of Illinois, Champaign, IL (United States)

    2015-01-01

    We study the short-distance hadronic matrix elements for D-meson mixing with partially quenched Nf = 2+1 lattice QCD. We use a large set of the MIMD Lattice Computation Collaboration's gauge configurations with a2 tadpole-improved staggered sea quarks and tadpole-improved Lüscher-Weisz gluons. We use the a2 tadpole-improved action for valence light quarks and the Sheikoleslami-Wohlert action with the Fermilab interpretation for the valence charm quark. Our calculation covers the complete set of five operators needed to constrain new physics models for D-meson mixing. We match our matrix elements to the MS-NDR scheme evaluated at 3 GeV. We report values for the Beneke-Buchalla-Greub-Lenz-Nierste choice of evanescent operators.

  13. Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions

    Energy Technology Data Exchange (ETDEWEB)

    Harris, Frank E., E-mail: harris@qtp.ufl.edu [Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA and Quantum Theory Project, University of Florida, P.O. Box 118435, Gainesville, Florida 32611 (United States)

    2016-05-28

    Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance r{sub ij}. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.

  14. Lattice calculation of hadronic weak matrix elements: the ΔI = 1/2 rule

    International Nuclear Information System (INIS)

    Bernard, C.

    1984-01-01

    A lattice Monte Carlo technique for calculating the matrix elements of weak operators is described. Emphasis is placed on the ΔI = 1/2 rule, which is such a large effect that the significant errors associated with current lattice methods (statistics, finite size, finite lattice spacing, extrapolations in quark mass, etc.) should not disguise the important qualitative features. A detailed exposition of the analytic bases for the calculation is given, and an attempt is made to avoid the questionable phenomenological assumptions (such as some of those inherent in the Penguin approach) which were necessary when matrix elements could not be calculated. The current state of the calculation-in-progress is described. This work is being done in collaboration with A. Soni, T. Draper, G. Hockney, and M. Rushton

  15. Current matrix element in HAL QCD's wavefunction-equivalent potential method

    Science.gov (United States)

    Watanabe, Kai; Ishii, Noriyoshi

    2018-04-01

    We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wavefunction-equivalent potentials proposed by the HAL QCD collaboration. As a first step, a non-relativistic field theory with two-channel coupling is considered as the original theory, with which a wavefunction-equivalent HAL QCD potential is obtained in a closed analytic form. The external field method is used to derive the formula by demanding that the result should agree with the original theory. With this formula, the matrix element is obtained by sandwiching the effective current operator between the left and right eigenfunctions of the effective Hamiltonian associated with the HAL QCD potential. In addition to the naive one-body current, the effective current operator contains an additional two-body term emerging from the degrees of freedom which has been integrated out.

  16. On the estimation of matrix elements for optical transitions in semiconductors

    International Nuclear Information System (INIS)

    Hassan, A.R.

    1992-09-01

    A semi-empirical method is used to calculate the numerical values of the interband momentum matrix elements of the allowed optical transitions in semiconductors. This method is based on the evaluation of the ratio of the two-photon and one-photon absorption coefficients and the compare the result with the corresponding experimental values in a number of semiconductors both for direct and indirect transition processes. The numerical values of the momentum matrix elements are compared with the convenient theoretical calculations available. The result is found to agree fairly well with the corresponding values computed using the k-vector · p-vector perturbation theory. (author). 19 refs, 2 figs, 2 tabs

  17. Study of the Matrix Effect on the Plasma Characterization of Heavy Elements in Soil Sediments

    Directory of Open Access Journals (Sweden)

    Tawfik W.

    2007-01-01

    Full Text Available Laser-induced breakdown spectroscopy (LIBS has been applied to perform a study of the matrix effect on the plasma characterization of soil sediment targets. The plasma is generated by focusing a pulsed Nd: YAG laser on the target in air at atmospheric pressure. The plasma emission spectrum was detected using a portable Echelle spectrometer (Mechelle 7500 — Multichannel Instruments, Stockholm, Sweden with intensified CCD camera. Spectroscopic analysis of plasma evolution of laser produced plasmas has been characterized in terms of their spectra, and electron temperature. Four heavy elements V, Pb, Mn and Co were determined in the obtained spectra. The LTE and optically thin plasma conditions were verified for the produced plasma. The electron temperature and density were determined using the emission intensity and stark broadening, respectively, of the spectral lines of the heavy elements in the soil sediments. The electron temperature does not change with concentration. For environmental applications, the obtained results showed the capability of the proposed LIBS setup with the portable Mechelle 7500 spectrometer to be applied in-situ for real-time measurements of the variation of the matrix elemental composition of soil sediments by following up only a single element as a marker for the composition of the soil sediment without need of analysis of the other elements.

  18. Large momentum expansion of two-loop self-energy diagrams with arbitrary masses

    International Nuclear Information System (INIS)

    Davydychev, A.I.; Smirnov, V.A.; Tausk, J.B.

    1993-01-01

    For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the coefficients of the expansion are calculated analytically. For some two-loop diagrams occurring in the Standard Model, comparison with results of numerical integration shows that our expansion works well in the region above the highest physical threshold. (orig.)

  19. Determination of the two-loop Lamb shift in lithiumlike bismuth

    International Nuclear Information System (INIS)

    Sapirstein, J.; Cheng, K. T.

    2001-01-01

    The energy levels of lithiumlike bismuth are shown to be accurately described in a representation-independent manner when all diagrams involving one and two photons, with the exception of the two-loop Lamb shift, are evaluated. Comparison with the experimental value of the 2p 3/2 -2s 1/2 splitting then shows that, assuming three-photon effects are negligible, the contribution of the two-loop Lamb shift is 0.175(39) eV

  20. New class of two-loop neutrino mass models with distinguishable phenomenology

    Science.gov (United States)

    Cao, Qing-Hong; Chen, Shao-Long; Ma, Ernest; Yan, Bin; Zhang, Dong-Ming

    2018-04-01

    We discuss a new class of neutrino mass models generated in two loops, and explore specifically three new physics scenarios: (A) doubly charged scalar, (B) dark matter, and (C) leptoquark and diquark, which are verifiable at the 14 TeV LHC Run-II. We point out how the different Higgs insertions will distinguish our two-loop topology with others if the new particles in the loop are in the simplest representations of the SM gauge group.

  1. Higgs-Boson Two-Loop Contributions to Electric Dipole Moments in the MSSM

    CERN Document Server

    Pilaftsis, Apostolos

    1999-01-01

    The complete set of Higgs-boson two-loop contributions to electric dipole moments of the electron and neutron is calculated in the minimal supersymmetric standard model. The electric dipole moments are induced by CP-violating trilinear couplings of the `CP-odd' and charged Higgs bosons to the scalar top and bottom quarks. Numerical estimates of the individual two-loop contributions to electric dipole moments are given.

  2. Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

    Energy Technology Data Exchange (ETDEWEB)

    Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence RI 02912 (United States)

    2016-03-14

    We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

  3. Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

    International Nuclear Information System (INIS)

    Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia

    2016-01-01

    We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

  4. Reactor calculation in coarse mesh by finite element method applied to matrix response method

    International Nuclear Information System (INIS)

    Nakata, H.

    1982-01-01

    The finite element method is applied to the solution of the modified formulation of the matrix-response method aiming to do reactor calculations in coarse mesh. Good results are obtained with a short running time. The method is applicable to problems where the heterogeneity is predominant and to problems of evolution in coarse meshes where the burnup is variable in one same coarse mesh, making the cross section vary spatially with the evolution. (E.G.) [pt

  5. Heavy flavor operator matrix elements at O({alpha}{sub s}{sup 3})

    Energy Technology Data Exchange (ETDEWEB)

    Bierenbaum, Isabella; Buemlein, Johannes; Klein, Sebastian

    2008-12-15

    The heavy quark effects in deep.inelastic scattering in the asymptotic regime Q{sup 2}>>m{sup 2} can be described by heavy flavor operator matrix elements. Complete analytic expressions for these objects are currently known to NLO. We present first results for fixed moments at NNLO. This involves a recalculation of fixed moments of the corresponding NNLO anomalous dimensions, which we thereby confirm. (orig.)

  6. Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Hasselhuhn, A.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); IHES, Bures-sur-Yvette (France)

    2017-05-15

    Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=m{sup 2}{sub c}/m{sup 2}{sub b}∝1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived earlier (I. Bierenbaum, J: Bluemlein, S. Klein, 2009). We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A{sup (3)}{sub gq}. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A{sub gg}. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.

  7. Three-loop contributions to the gluonic massive operator matrix elements at general values of N

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Hasselhuhn, Alexander [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); De Freitas, Abilio; Round, Mark; Schneider, Carsten; Wissbrock, Fabian [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Klein, Sebastian [RWTH Aachen Univ. (Germany). Inst. fuer Theoretische Physik E

    2012-12-15

    Recent results on the calculation of 3-loop massive operator matrix elements in case of one and two heavy quark masses are reported. They concern the O(n{sub f}T{sup 2}{sub F}C{sub F,A}) and O(T{sup 2}{sub F}C{sub F,A}) gluonic corrections, two-mass quarkonic moments, and ladder- and Benz-topologies. We also discuss technical aspects of the calculations.

  8. K-M matrix elements and decays of the B meson to J/Psi

    International Nuclear Information System (INIS)

    Wilson, Richard

    2002-01-01

    This talk discusses some of the last work on B meson decays of the CLEO collaboration, which work is, in fact, improvements in precision of much earlier work of the same collaboration. New theoretical developments have enabled us to present much improved numbers on the matrix elements Vcb, and Vub. Also some recent work on the decay of B mesons to J/Psi plus other particles will be briefly presented

  9. Matrix elements and transition probabilities of interaction of electromagnetic field with a hydrogen-like atom

    International Nuclear Information System (INIS)

    Rajput, B.S.

    1977-01-01

    Using the reduced expansions of second quantized electromagnetic vector potential operator in terms of irreducible representations of Pioncare group in the interaction Hamiltonian, the exact matrix elements of interaction of electromagnetic field with a hydrogenic atom have been derived and the contributions of transitions for different combinations of angular momentum quantum numbers to the transition probabilities of various lines in Lyman-, Balmer-, and Paschen-series have been computed. (author)

  10. Quenching of the Gamow-Teller matrix element in closed LS-shell-plus-one nuclei

    International Nuclear Information System (INIS)

    Towner, I.S.

    1989-06-01

    It is evident that nuclear Gamow-Teller matrix elements determined from β-decay and charge-exchange reactions are significantly quenched compared to simple shell-model estimates based on one-body operators and free-nucleon coupling constants. Here we discuss the theoretical origins of this quenching giving examples from light nuclei near LS-closed shells, such as 16 0 and 40 Ca. (Author) 12 refs., 2 tabs

  11. Off-diagonal helicity density matrix elements for vector mesons produced at LEP

    International Nuclear Information System (INIS)

    Anselmino, M.; Bertini, M.; Quintairos, P.

    1997-05-01

    Final state q q-bar interactions may give origin to non zero values of the off-diagonal element ρ 1 of the helicity density matrix of vector mesons produced in e + e - annihilations, as confirmed by recent OPAL data on φ and D * 's. Predictions are given for ρ1,-1 of several mesons produced at large z and small PT, collinear with the parent jet; the values obtained for θ and D * are in agreement with data. (author)

  12. Nucleon scalar matrix elements with N{sub f}=2+1+1 twisted mass fermions

    Energy Technology Data Exchange (ETDEWEB)

    Dinter, Simon; Drach, Vincent; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2011-12-15

    We investigate scalar matrix elements of the nucleon using N{sub f}=2+1+1 flavors of maximally twisted mass fermions at a fixed value of the lattice spacing of a{approx}0.078 fm. We compute disconnected contributions to the relevant three-point functions using an efficient noise reduction technique. Using these methods together with an only multiplicative renormalization applicable for twisted mass fermions, allows us to obtain accurate results in the light and strange sector. (orig.)

  13. Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses

    Directory of Open Access Journals (Sweden)

    J. Ablinger

    2017-08-01

    Full Text Available Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=mc2/mb2∼1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element Agq(3. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element Agg. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.

  14. Separation of soft and collinear infrared limits of QCD squared matrix elements

    CERN Document Server

    Nagy, Zoltan; Trócsányi, Z L; Trocsanyi, Zoltan; Somogyi, Gabor; Trocsanyi, Zoltan

    2007-01-01

    We present a simple way of separating the overlap between the soft and collinear factorization formulae of QCD squared matrix elements. We check its validity explicitly for single and double unresolved emissions of tree-level processes. The new method makes possible the definition of helicity-dependent subtraction terms for regularizing the real contributions in computing radiative corrections to QCD jet cross sections. This implies application of Monte Carlo helicity summation in computing higher order corrections.

  15. Matrix elements and few-body calculations within the unitary correlation operator method

    International Nuclear Information System (INIS)

    Roth, R.; Hergert, H.; Papakonstantinou, P.

    2005-01-01

    We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges. (orig.)

  16. Matrix elements and few-body calculations within the unitary correlation operator method

    International Nuclear Information System (INIS)

    Roth, R.; Hergert, H.; Papakonstantinou, P.; Neff, T.; Feldmeier, H.

    2005-01-01

    We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges

  17. Energy diffusion in strongly driven quantum chaotic systems: the role of correlations of the matrix elements

    International Nuclear Information System (INIS)

    Elyutin, P V; Rubtsov, A N

    2008-01-01

    The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule (FGR) is about or exceeds the frequency of perturbation. For this case, the models of the Hamiltonian with random non-correlated matrix elements demonstrate that the energy evolution retains its diffusive character, but the rate of diffusion increases slower than the square of the magnitude of perturbation, thus destroying the quantum-classical correspondence for the energy diffusion and the energy absorption in the classical limit ℎ → 0. The numerical calculation carried out for a model built from the first principles (the quantum analog of the Pullen-Edmonds oscillator) demonstrates that the evolving energy distribution, apart from the diffusive component, contains a ballistic one with the energy dispersion that is proportional to the square of time. This component originates from the chains of matrix elements with correlated signs and vanishes if the signs of matrix elements are randomized. The presence of the ballistic component formally extends the applicability of the FGR to the non-perturbative domain and restores the quantum-classical correspondence

  18. Matching NLO parton shower matrix element with exact phase space case of $W\\to l\

    CERN Document Server

    Nanava, G; Was, Z

    2010-01-01

    In practical applications PHOTOS Monte Carlo is often used for simulation of QED effects in decay of intermediate particles and resonances. Generated in such a way that samples of events cover the whole bremsstrahlung phase space. With the help of selection cuts, experimental acceptance can be then taken into account. The program is based on exact multiphoton phase space. To evaluate the program precision it is necessary to control its matrix element. Generally it is obtained using iteration of the universal multidimensional kernel. In some cases it is however obtained from the exact first order matrix element. Then, as a consequence, all terms necessary for non-leading logarithms are taken into account. In the present paper we will focus on the decays W -> l nu and gamma^* -> pi^+ pi^-. The Born level cross sections for both processes approach zero in some points of the phase space. Process dependent, compensating weight is constructed to implement exact matrix element, but it will be recommended for use onl...

  19. A generalized Talmi-Moshinsky transformation for few-body and direct interaction matrix elements

    International Nuclear Information System (INIS)

    Tobocman, W.

    1981-01-01

    A set of basis states for use in evaluating matrix elements of few-body system operators is suggested. These basis states are products of harmonic oscillator wave functions having as arguments a set of Jacobi coordinates for the system. We show that these harmonic oscillator functions can be chosen in a manner that allows such a product to be expanded as a finite sum of the corresponding products for any other set of Jacobi coordinates. This result is a generalization of the Talmi-Moshinsky transformation for two equal-mass particles to a system of any number of particles of arbitrary masses. With the help of our method the multidimensional integral which must be performed to evaluate a few-body matrix element can be transformed into a sum of products of three dimensional integrals. The coefficients in such an expansion are generalized Talmi-Moshinsky coefficients. The method is tested by calculation of a matrix element for knockout scattering for a simple three-body-system. The results indicate that the method is a viable calculational tool. (orig.)

  20. Effect of the Heat Treatment on the Graphite Matrix of Fuel Element for HTGR

    International Nuclear Information System (INIS)

    Lee, Chungyong; Lee, Seungjae; Suh, Jungmin; Jo, Youngho; Lee, Youngwoo; Cho, Moonsung

    2013-01-01

    In this paper, the cylinder-formed fuel element for the block type reactor is focused on, which consists of the large part of graphite matrix. One of the most important properties of the graphite matrix is the mechanical strength for the high reliability because the graphite matrix should be enabled to protect the TRISO particles from the irradiation environment and the impact from the outside. In this study, the three kinds of candidate graphites and Phenol as a binder were chosen and mixed with each other, formed and heated for the compressive strength test. The objective of this research is to optimize the kinds and composition of the mixed graphite and the forming process by evaluating the compressive strength before/after heat treatment (carbonization of binder). In this study, the effect of heat treatment on graphite matrix was studied in terms of the density and the compressive strength. The size (diameter and length) of pellet is increased by heat treatment. Due to additional weight reduction and swelling (length and diameter) of samples the density of graphite pellet is decreased from about 2.0 to about 1.7g/cm 3 . From the mechanical test results, the compressive strength of graphite pellets was related to the various conditions such as the contents of binder, the kinds of graphite and the heat treatment. Both the green pellet and the heat treated pellet, the compressive strength of G+S+P pellets is relatively higher than that of R+S+P pellets. To optimize fuel element matrix, the effect of Phenol and other binders, graphite composition and the heat treatment on the mechanical properties will be deeply investigated for further study

  1. A Data Matrix Method for Improving the Quantification of Element Percentages of SEM/EDX Analysis

    Science.gov (United States)

    Lane, John

    2009-01-01

    A simple 2D M N matrix involving sample preparation enables the microanalyst to peer below the noise floor of element percentages reported by the SEM/EDX (scanning electron microscopy/ energy dispersive x-ray) analysis, thus yielding more meaningful data. Using the example of a 2 3 sample set, there are M = 2 concentration levels of the original mix under test: 10 percent ilmenite (90 percent silica) and 20 percent ilmenite (80 percent silica). For each of these M samples, N = 3 separate SEM/EDX samples were drawn. In this test, ilmenite is the element of interest. By plotting the linear trend of the M sample s known concentration versus the average of the N samples, a much higher resolution of elemental analysis can be performed. The resulting trend also shows how the noise is affecting the data, and at what point (of smaller concentrations) is it impractical to try to extract any further useful data.

  2. Analysis of smart beams with piezoelectric elements using impedance matrix and inverse Laplace transform

    International Nuclear Information System (INIS)

    Li, Guo-Qing; Miao, Xing-Yuan; Hu, Yuan-Tai; Wang, Ji

    2013-01-01

    A comprehensive study on smart beams with piezoelectric elements using an impedance matrix and the inverse Laplace transform is presented. Based on the authors’ previous work, the dynamics of some elements in beam-like smart structures are represented by impedance matrix equations, including a piezoelectric stack, a piezoelectric bimorph, an elastic straight beam or a circular curved beam. A further transform is applied to the impedance matrix to obtain a set of implicit transfer function matrices. Apart from the analytical solutions to the matrices of smart beams, one computation procedure is proposed to obtained the impedance matrices and transfer function matrices using FEA. By these means the dynamic solution of the elements in the frequency domain is transformed to that in Laplacian s-domain and then inversely transformed to time domain. The connections between the elements and boundary conditions of the smart structures are investigated in detail, and one integrated system equation is finally obtained using the symbolic operation of TF matrices. A procedure is proposed for dynamic analysis and control analysis of the smart beam system using mode superposition and a numerical inverse Laplace transform. The first example is given to demonstrate building transfer function associated impedance matrices using both FEA and analytical solutions. The second example is to verify the ability of control analysis using a suspended beam with PZT patches under close-loop control. The third example is designed for dynamic analysis of beams with a piezoelectric stack and a piezoelectric bimorph under various excitations. The last example of one smart beam with a PPF controller shows the applicability to the control analysis of complex systems using the proposed method. All results show good agreement with the other results in the previous literature. The advantages of the proposed methods are also discussed at the end of this paper. (paper)

  3. X-ray microanalysis of elements present in the matrix of cnidarian nematocysts.

    Science.gov (United States)

    Tardent, P; Zierold, K; Klug, M; Weber, J

    1990-01-01

    The composition and concentration of elements, in particular those of metallic cations, present in the intracapsular matrix and the wall of nematocysts of various cnidarian species have been recorded by means of X-ray microanalysis performed on 100nm thick cryosections. The predominant cation detected in the nematocyst matrix of the hydrozoan Podocoryne carnea (medusa), the scyphozoan Aurelia aurita (scyphopolyp) and the anthozoan Calliactis parasitica (tentacles and acontia) is K(+). Mg(2+) prevails in tentacular cysts of Anthopleura elegantissima, Actinia equina and Anemonia viridis, whereas, the acrorhagial cysts of A. elegantissima and A. equina contain Ca(2+) instead of Mg(2+). The acrorhagial cysts of A. viridis contain Mg(2+) like those of the tentacles. In the tentacular nematocysts of Podocoryne carnea polyps (Hydrozoa) on the other hand ambiguous element contents were found indicating that the cysts of this species has no preference for a particular cation. The high values of sulfur recorded in the matrix and particularly the wall of all the cysts are reflecting the presence of numerous protein disulfide bonds within the structural components (wall, shaft, tubule) of the nematocysts.

  4. Dimensional Behavior of Matrix Graphite Compacts during Heat Treatments for HTGR Fuel Element Fabrication

    International Nuclear Information System (INIS)

    Lee, Young-Woo; Yeo, Seunghwan; Cho, Moon Sung

    2015-01-01

    The carbonization is a process step where the binder that is incorporated during the matrix graphite powder preparation step is evaporated and the residue of the binder is carbonized during the heat treatment at about 1073 K. This carbonization step is followed by the final high temperature heat treatment where the carbonized compacts are heat treated at 2073-2173 K in vacuum for a relatively short time (about 2 hrs). In order to develop a fuel compact fabrication technology, and for fuel matrix graphite to meet the required material properties, it is essential to investigate the relationship among the process parameters of the matrix graphite powder preparation, the fabrication parameters of fuel element green compact and the heat treatments conditions, which has a strong influence on the further steps and the material properties of fuel element. In this work, the dimensional changes of green compacts during the carbonization and final heat treatment are evaluated when compacts have different densities from different pressing conditions and different final heat treatment temperatures are employed, keeping other process parameters constant, such as the binder content, carbonization time, temperature and atmosphere (two hours ant 1073K and N2 atmosphere). In this work, the dimensional variations of green compacts during the carbonization and final heat treatment are evaluated when compacts have different densities from different pressing conditions and different final heat treatment temperatures are employed

  5. On the possibility to measure 0νββ-decay nuclear matrix element for 48Ca

    International Nuclear Information System (INIS)

    Rodin, Vadim

    2011-01-01

    As shown in Ref. [2], the Fermi part M F 0ν of the total 0νββ-decay nuclear matrix element M 0ν can be related to the single Fermi transition matrix element between the isobaric analog state (IAS) of the ground state of the initial nucleus and the ground state of the final nucleus. The latter matrix element could be measured in charge-exchange reactions. Here we discuss a possibility of such a measurement for 48 Ca and estimate the cross-section of the reaction 48 Ti(n,p) 48 Sc(IAS).

  6. Relation between the 2{nu}{beta}{beta} and 0{nu}{beta}{beta} nuclear matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Vogel, Petr [Kellogg Radiation Laboratory, Caltech, Pasadena, CA 91125 (United States); Simkovic, Fedor [Department of Nuclear Physics and Biophysics, Comenius University, Mlynska dolina F1, SK-84248 Bratislava (Slovakia)

    2011-12-16

    A formal relation between the GT part of the nuclear matrix elements M{sub GT}{sup 0{nu}} of 0{nu}{beta}{beta} decay and the closure matrix elements M{sub cl}{sup 2{nu}} of 2{nu}{beta}{beta} decay is established. This relation is based on the integral representation of these quantities in terms of their dependence on the distance r between the two nucleons undergoing transformation. We also discuss the difficulties in determining the correct values of the closure 2{nu}{beta}{beta} decay matrix elements.

  7. Two-loop mass splittings in electroweak multiplets: Winos and minimal dark matter

    Science.gov (United States)

    McKay, James; Scott, Pat

    2018-03-01

    The radiatively-induced splitting of masses in electroweak multiplets is relevant for both collider phenomenology and dark matter. Precision two-loop corrections of O (MeV ) to the triplet mass splitting in the wino limit of the minimal supersymmetric standard model can affect particle lifetimes by up to 40%. We improve on previous two-loop self-energy calculations for the wino model by obtaining consistent input parameters to the calculation via two-loop renormalization-group running, and including the effect of finite light quark masses. We also present the first two-loop calculation of the mass splitting in an electroweak fermionic quintuplet, corresponding to the viable form of minimal dark matter (MDM). We place significant constraints on the lifetimes of the charged and doubly-charged fermions in this model. We find that the two-loop mass splittings in the MDM quintuplet are not constant in the large-mass limit, as might naively be expected from the triplet calculation. This is due to the influence of the additional heavy fermions in loop corrections to the gauge boson propagators.

  8. SQED two-loop beta function in the context of Implicit regularization

    International Nuclear Information System (INIS)

    Cherchiglia, Adriano Lana; Sampaio, Marcos; Nemes, Maria Carolina

    2013-01-01

    Full text: In this work we present the state-of-art for Implicit Regularization (IReg) in the context of supersymmetric theories. IReg is a four-dimensional regularization technique in momentum space which disentangles, in a consistent way at arbitrary order, the divergencies, regularization dependent and finite parts of any Feynman amplitude. Since it does not resort to modifications on the physical space-time dimensions of the underlying quantum field theoretical model, it can be consistently applied to supersymmetric theories. First we describe the technique and present previous results for supersymmetric models: the two-loop beta function for the Wess-Zumino model (both in the component and superfield formalism); the two-loop beta function for Super Yang-Mills (in the superfield formalism using the background field technique). After, we present our calculation of the two-loop beta function for massless and massive SQED using the superfield formalism with and without resorting to the background field technique. We find that only in the second case the two-loop divergence cancels out. We argue it is due to an anomalous Jacobian under the rescaling of the fields in the path-integral which is necessary for the application of the supersymmetric background field technique. We find, however, that in both cases the two-loop coefficients of beta function are non-null. Finally we briefly discuss the anomaly puzzle in the context of our technique. (author)

  9. IMPACT OF MATRIX INVERSION ON THE COMPLEXITY OF THE FINITE ELEMENT METHOD

    Directory of Open Access Journals (Sweden)

    M. Sybis

    2016-04-01

    Full Text Available Purpose. The development of a wide construction market and a desire to design innovative architectural building constructions has resulted in the need to create complex numerical models of objects having increasingly higher computational complexity. The purpose of this work is to show that choosing a proper method for solving the set of equations can improve the calculation time (reduce the complexity by a few levels of magnitude. Methodology. The article presents an analysis of the impact of matrix inversion algorithm on the deflection calculation in the beam, using the finite element method (FEM. Based on the literature analysis, common methods of calculating set of equations were determined. From the found solutions the Gaussian elimination, LU and Cholesky decomposition methods have been implemented to determine the effect of the matrix inversion algorithm used for solving the equations set on the number of computational operations performed. In addition, each of the implemented method has been further optimized thereby reducing the number of necessary arithmetic operations. Findings. These optimizations have been performed on the use of certain properties of the matrix, such as symmetry or significant number of zero elements in the matrix. The results of the analysis are presented for the division of the beam to 5, 50, 100 and 200 nodes, for which the deflection has been calculated. Originality. The main achievement of this work is that it shows the impact of the used methodology on the complexity of solving the problem (or equivalently, time needed to obtain results. Practical value. The difference between the best (the less complex and the worst (the most complex is in the row of few orders of magnitude. This result shows that choosing wrong methodology may enlarge time needed to perform calculation significantly.

  10. On- and off-resonance radiation-atom-coupling matrix elements involving extended atomic wave functions

    Science.gov (United States)

    Komninos, Yannis; Mercouris, Theodoros; Nicolaides, Cleanthes A.

    2014-01-01

    In continuation of our earlier works, we present results concerning the computation of matrix elements of the multipolar Hamiltonian (MPH) between extended wave functions that are obtained numerically. The choice of the MPH is discussed in connection with the broader issue of the form of radiation-atom (or -molecule) interaction that is appropriate for the systematic solution of various problems of matter-radiation interaction. We derive analytic formulas, in terms of the sine-integral function and spherical Bessel functions of various orders, for the cumulative radial integrals that were obtained and calculated by Komninos, Mercouris, and Nicolaides [Phys. Rev. A 71, 023410 (2005), 10.1103/PhysRevA.71.023410]. This development allows the much faster and more accurate computation of such matrix elements, a fact that enhances the efficiency with which the time-dependent Schrödinger equation is solved nonperturbatively, in the framework of the state-specific expansion approach. The formulas are applicable to the general case where a pair of orbitals with angular parts |ℓ1,m1> and |ℓ2,m2> are coupled radiatively. As a test case, we calculate the matrix elements of the electric field and of the paramagnetic operators for on- and off-resonance transitions, between hydrogenic circular states of high angular momentum, whose quantum numbers are chosen so as to satisfy electric dipole and electric quadrupole selection rules. Because of the nature of their wave function (they are nodeless and the large centrifugal barrier keeps their overwhelming part at large distances from the nucleus), the validity of the electric dipole approximation in various applications where the off-resonance couplings must be considered becomes precarious. For example, for the transition from the circular state with n = 20 to that with n = 21, for which ≈400 a.u., the dipole approximation starts to fail already at XUV wavelengths (λ <125nm).

  11. Kaon matrix elements and CP violation from quenched lattice QCD: The 3-flavor case

    International Nuclear Information System (INIS)

    Blum, T.; Wingate, M.; Chen, P.; Christ, N.; Cristian, C.; Fleming, G.; Mawhinney, R.; Siegert, G.; Wu, L.; Zhestkov, Y.; Dawson, C.; Soni, A.; Ohta, S.; Vranas, P.

    2003-01-01

    We report the results of a calculation of the K→ππ matrix elements relevant for the ΔI=1/2 rule and ε ' /ε in quenched lattice QCD using domain wall fermions at a fixed lattice spacing a -1 ∼2 GeV. Working in the three-quark effective theory, where only the u, d, and s quarks enter and which is known perturbatively to next-to-leading order, we calculate the lattice K→π and K→|0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K→ππ matrix elements, which we then normalize to continuum values through a nonperturbative renormalization technique. For the ratio of isospin amplitudes vertical bar A 0 vertical bar/vertical bar A 2 vertical bar we find a value of 25.3±1.8 (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10%-20% below the experimental values. For ε ' /ε, using known central values for standard model parameters, we calculate (-4.0±2.3)x10 -4 (statistical error only) compared to the current experimental average of (17.2±1.8)x10 -4 . Because we find a large cancellation between the I=0 and I=2 contributions to ε ' /ε, the result may be very sensitive to the approximations employed. Among these are the use of quenched QCD, lowest order chiral perturbation theory, and continuum perturbation theory below 1.3 GeV. We also calculate the kaon B parameter B K and find B K,MS (2 GeV)=0.532(11). Although currently unable to give a reliable systematic error, we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities

  12. Measurement of the CKM matrix element vertical stroke Vts vertical stroke 2

    International Nuclear Information System (INIS)

    Unverdorben, Christopher Gerhard

    2015-03-01

    This is the first direct measurement of the CKM matrix element vertical stroke V ts vertical stroke, using data collected by the ATLAS detector in 2012 at √(s)= 8 TeV pp-collisions with a total integrated luminosity of 20.3 fb -1 . The analysis is based on 112 171 reconstructed t anti t candidate events in the lepton+jets channel, having a purity of 90.0 %. 183 t anti t→W + W - b anti s decays are expected (charge conjugation implied), which are available for the extraction of the CKM matrix element vertical stroke V ts vertical stroke 2 . To identify these rare decays, several observables are examined, such as the properties of jets, tracks and of b-quark identification algorithms. Furthermore, the s-quark hadrons K 0 s are considered, reconstructed by a kinematic fit. The best observables are combined in a multivariate analysis, called ''boosted decision trees''. The responses from Monte Carlo simulations are used as templates for a fit to data events yielding a significance value of 0.7σ for t→s+W decays. An upper limit of vertical stroke V ts vertical stroke 2 <1.74 % at 95 % confidence level is set, including all systematic and statistical uncertainties. So this analysis, using a direct measurement of the CKM matrix element vertical stroke V ts vertical stroke 2 , provides the best direct limit on vertical stroke V ts vertical stroke 2 up to now.

  13. Structure of the two-neutrino double-β decay matrix elements within perturbation theory

    Science.gov (United States)

    Štefánik, Dušan; Šimkovic, Fedor; Faessler, Amand

    2015-06-01

    The two-neutrino double-β Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It is found that this model reproduces the main features of realistic calculation within the quasiparticle random-phase approximation with isospin symmetry restoration concerning the dependence of the two-neutrino double-β decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-β decay matrix elements on the like-nucleon pairing, particle-particle T =0 and T =1 , and particle-hole proton-neutron interactions is obtained. It is found that double-β decay matrix elements do not depend on the mean field part of Hamiltonian and that they are governed by a weak violation of both SU(2) and SU(4) symmetries by the particle-particle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-β decay transition through a single state of intermediate nucleus. The energy position of this state relative to energies of initial and final ground states is given by a combination of strengths of residual interactions. Further, energy-weighted Fermi and Gamow-Teller sum rules connecting Δ Z =2 nuclei are discussed. It is proposed that these sum rules can be used to study the residual interactions of the nuclear Hamiltonian, which are relevant for charge-changing nuclear transitions.

  14. Relativistic atomic matrix elements of rq for arbitrary states in the quantum-defect approximation

    International Nuclear Information System (INIS)

    Owono Owono, L.C.; Owona Angue, M.L.C.; Kwato Njock, M.G.; Oumarou, B.

    2004-01-01

    Recurrence relations used in the calculation of matrix elements of r q for arbitrary q and states of the relativistic one-electron atom with a point-like ionic core are obtained with Dirac and quasirelativistic effective radial Hamiltonians. The phenomenological and supersymmetry-inspired quantum-defect approaches introduced in previous works to model the electron-core interactions are employed. The formulas worked out on the basis of a hypervirial inspired method may be viewed as a generalization to off-diagonal cases of our recently reported results on the evaluation of expectation values of r q

  15. Closed form for two-photon free-free transition matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Karule, Erna E-mail: karule@latnet.lv

    2000-08-01

    Two-photon free-free transitions happen in the multiphoton ionization with more than one excess photon and in Bremsstrahlung. Up to now, the configuration space free-free transition amplitudes have not been written in closed form. We propose a modified Coulomb Green's function (CGF) Sturm ian expansion which allows one to obtain expressions for two-photon radial transition matrix elements in the closed form which are easy to continue analytically to calculate free-free transitions in H.

  16. Neutron-proton matrix element ratios of 21+ states in 58,60,62,64Ni

    International Nuclear Information System (INIS)

    Antalik, R.

    1989-01-01

    The neutron-proton matrix element ratios (η) for 2 1 + states of even Ni isotopes are investigated within the framework of the shell model quasiparticle random-phase approximation. The special attention is devoted to the dependence of η ratios on the radial neutron and proton ground-state density-distribution differences (Δ np ). This dependence is found to be about 0.5Δ np . The theoretical η ratios are 14-23% greater than the hydrodynamical limit. The theoretical Δ np dependence of η ratios enable us to understand the empirical η ratio results. 20 refs.; 2 figs.; 2 tabs

  17. Number-conserving random phase approximation with analytically integrated matrix elements

    International Nuclear Information System (INIS)

    Kyotoku, M.; Schmid, K.W.; Gruemmer, F.; Faessler, A.

    1990-01-01

    In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem

  18. Differential cross sections and spin density matrix elements for the reaction gamma p -> p omega

    Energy Technology Data Exchange (ETDEWEB)

    M. Williams, D. Applegate, M. Bellis, C.A. Meyer

    2009-12-01

    High-statistics differential cross sections and spin density matrix elements for the reaction gamma p -> p omega have been measured using the CLAS at Jefferson Lab for center-of-mass (CM) energies from threshold up to 2.84 GeV. Results are reported in 112 10-MeV wide CM energy bins, each subdivided into cos(theta_CM) bins of width 0.1. These are the most precise and extensive omega photoproduction measurements to date. A number of prominent structures are clearly present in the data. Many of these have not previously been observed due to limited statistics in earlier measurements.

  19. Elimination of matrix effect in quantitative analysis of elements using x-ray fluorescence

    International Nuclear Information System (INIS)

    Sampaio, R.V.

    1973-07-01

    The emission-transmission method of Leroux and Mahmud, an experimental technique for compensating matrix effects in photon excited X-ray fluorescence analysis, was used to determine the concentration of lead and antimony in pellets of galalith. The effect of interfering elements was studied by adding various concentrations of mercury and tin to the respective pellets. To illustrate possible environmental applications, a number of pellets was prepared from leaves of almond trees located in different regions of Rio de Janeiro. Lead concentrations were determined for the dried leaf material and showed values ranging from 50 to 145 parts per million [pt

  20. Spin Density Matrix Elements in exclusive production of ω mesons at Hermes

    Directory of Open Access Journals (Sweden)

    Marianski B.

    2014-03-01

    Full Text Available Spin density matrix elements have been determined for exclusive ω meson production on hydrogen and deuterium targets, in the kinematic region of 1.0 < Q2 < 10.0 GeV2, 3.0 < W < 6.3 GeV and –t' < 0.2 GeV2. The data, from which SDMEs are determined, were accumulated with the HERMES forward spectrometer during the running period of 1996 to 2007 using the 27.6 GeV electron or positron beam of HERA. A sizable contribution of unnatural parity exchange amplitudes is found for exclusive ω meson production.

  1. The matrix element for radiative Bhabha scattering in the forward direction

    International Nuclear Information System (INIS)

    Kleiss, R.

    1993-09-01

    We present an approximation to the matrix element for the process e + e - →e + e - γ, appropriate to the situation where one or both of the fermions are scattered over very small angles. The leading terms in the situation where all scattering angles are small contains not only terms quadratic in the electron mass, but also quartic and even sextic terms must be included. Special attention is devoted to the numerical stability of the resultant expression. Its relation to several existing formulae is discussed. (orig.)

  2. The O(αs3TF2) contributions to the gluonic operator matrix element

    International Nuclear Information System (INIS)

    Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; Manteuffel, A. von; Round, M.; Schneider, C.

    2014-01-01

    The O(α s 3 T F 2 C F (C A )) contributions to the transition matrix element A gg,Q relevant for the variable flavor number scheme at 3-loop order are calculated. The corresponding graphs contain two massive fermion lines of equal mass leading to terms given by inverse binomially weighted sums beyond the usual harmonic sums. In x-space two root-valued letters contribute in the iterated integrals in addition to those forming the harmonic polylogarithms. We outline technical details needed in the calculation of graphs of this type, which are as well of importance in the case of two different internal massive lines

  3. Spatially dependent burnup implementation into the nodal program based on the finite element response matrix method

    International Nuclear Information System (INIS)

    Yoriyaz, H.

    1986-01-01

    In this work a spatial burnup scheme and feedback effects has been implemented into the FERM ( 'Finite Element Response Matrix' )program. The spatially dependent neutronic parameters have been considered in three levels: zonewise calculation, assembly wise calculation and pointwise calculation. Flux and power distributions and the multiplication factor were calculated and compared with the results obtained by CITATIOn program. These comparisons showed that processing time in the Ferm code has been hundred of times shorter and no significant difference has been observed in the assembly average power distribution. (Author) [pt

  4. Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (I)-Formalism

    Institute of Scientific and Technical Information of China (English)

    DAI Lian-Rong; PAN Feng

    2001-01-01

    The tensor algebraic method is used to derive general one- and two-body operator matrix elements within the Un representations, which are useful in the unitary group approach to the configuration interaction problems of quantum many-body systems.

  5. Two-Loop Correction to the Higgs Boson Mass in the MRSSM

    International Nuclear Information System (INIS)

    Stöckinger, Dominik; Diessner, Philip; Kotlarski, Wojciech; Kalinowski, Jan

    2015-01-01

    We present the impact of two-loop corrections on the mass of the lightest Higgs boson in the minimal R-symmetric supersymmetric standard model (MRSSM). These shift the Higgs boson mass up by typically 5 GeV or more. The dominant corrections arise from strong interactions, and from the gluon and its N=2 superpartners, the sgluon and Dirac gluino, and these corrections further increase with large Dirac gluino mass. The two-loop contributions governed purely by Yukawa couplings and the MRSSM λ, Λ parameters are smaller. We also update our earlier analysis which showed that the MRSSM can accommodate the measured Higgs and W boson masses. Including the two-loop corrections increases the parameter space where the theory prediction agrees with the measurement.

  6. Two-loop renormalization in the standard model, part I. Prolegomena

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)

    2006-12-15

    In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)

  7. N ≥ 4 Supergravity Amplitudes from Gauge Theory at Two Loops

    International Nuclear Information System (INIS)

    Boucher-Veronneau, Camille

    2012-01-01

    We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.

  8. Two-loop corrections for nuclear matter in the Walecka model

    International Nuclear Information System (INIS)

    Furnstahl, R.J.; Perry, R.J.; Serot, B.D.; Department of Physics, The Ohio State University, Columbus, Ohio 43210; Physics Department and Nuclear Theory Center, Indiana University, Bloomington, Indiana 47405)

    1989-01-01

    Two-loop corrections for nuclear matter, including vacuum polarization, are calculated in the Walecka model to study the loop expansion as an approximation scheme for quantum hadrodynamics. Criteria for useful approximation schemes are discussed, and the concepts of strong and weak convergence are introduced. The two-loop corrections are evaluated first with one-loop parameters and mean fields and then by minimizing the total energy density with respect to the scalar field and refitting parameters to empirical nuclear matter saturation properties. The size and nature of the corrections indicate that the loop expansion is not convergent at two-loop order in either the strong or weak sense. Prospects for alternative approximation schemes are discussed

  9. The two-loop master integrals for qq-bar→VV

    International Nuclear Information System (INIS)

    Gehrmann, Thomas; Manteuffel, Andreas von; Tancredi, Lorenzo; Weihs, Erich

    2014-01-01

    We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes for vector boson pair production at hadron colliders, qq-bar→VV, and thus to compute this process to next-to-next-to-leading order accuracy in QCD. The master integrals are derived using the method of differential equations, employing a canonical basis for the integrals. We obtain analytical results for all integrals, expressed in terms of multiple polylogarithms. We optimize our results for numerical evaluation by employing functions which are real valued for physical scattering kinematics and allow for an immediate power series expansion

  10. Color ferromagnetic vacuum states in QCD and two-loop energy densities

    International Nuclear Information System (INIS)

    Nielsen, H.B.; Ninomiya, M.

    1979-12-01

    Two-loop energy densities of color ferromagnetic states are obtained using the β-function calculated to two-loop approximation and the exact formula for the energy density of such a state. This is used to derive bounds on the MIT bag constant correcting the previous bound in one-loop approximation. For a constant field color ferromagnetic ansatz state the bound on the QCD scale parameter Λsub(p) 3 -vacuum ansatz with two-loop and instanton correction gives Λsub(p)<= 0.16 GeV. Tt is stressed that the 'perturbative vacuum', which is identified with the inside bag state is a somewhat ill defined concept due to a path-dependence in the integral giving the energy density. (Auth.)

  11. Validity of the M-3Y force equivalent G-matrix element for the calculations of nuclear structure in the s-d shell

    International Nuclear Information System (INIS)

    Song Hong-qiu; Wang Zixing; Cai Yanhuang; Huang Weizhi

    1987-01-01

    The matrix elements of the M-3Y force are adopted as the equivalent G-matrix elements and the folded diagram method is used to calculate the spectra of 18 O and 18 F. The results show that the matrix elements of the M-3Y force as the equivalent G-matrix elements are suitable for microscopic calculations of the nuclei in the s-d shell

  12. Development of a diffuse element matrix in 'planar' technology. A particular application: logical gate with coupled emitter

    International Nuclear Information System (INIS)

    Rousseau, P.

    1968-01-01

    In a first part, after a brief recall concerning 'planar' technology we discuss the various parasitic elements associated with integrated circuits components. Mathematical formulae of these elements are derived. In a second part, we present a matrix of 22 transistors and 12 resistors which has been realized. This matrix enables the integration of the major part of nuclear circuits. Some of the obtained circuits are shown, particularly an emitter coupled logic gate which presents good electrical behaviour. (author) [fr

  13. Second level semi-degenerate fields in W{sub 3} Toda theory: matrix element and differential equation

    Energy Technology Data Exchange (ETDEWEB)

    Belavin, Vladimir [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky Avenue 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Moscow Institute of Physics and Technology,Dolgoprudnyi, 141700 Moscow region (Russian Federation); Cao, Xiangyu [LPTMS, CNRS (UMR 8626), Université Paris-Saclay,15 rue Georges Clémenceau, 91405 Orsay (France); Estienne, Benoit [LPTHE, CNRS and Université Pierre et Marie Curie, Sorbonne Universités,4 Place Jussieu, 75252 Paris Cedex 05 (France); Santachiara, Raoul [LPTMS, CNRS (UMR 8626), Université Paris-Saclay,15 rue Georges Clémenceau, 91405 Orsay (France)

    2017-03-02

    In a recent study we considered W{sub 3} Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl{sub 3}. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

  14. Massive 3-loop ladder diagrams for quarkonic local operator matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes; Hasselhuhn, Alexander; Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [Technische Hochschule Aachen (Germany). Inst. fuer Theoretische Physik

    2012-06-15

    3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with {xi} element of {l_brace}1,1/2,2{r_brace} emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q{sup 2} >> m{sup 2}.

  15. Massive 3-loop ladder diagrams for quarkonic local operator matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstrasse 69, A-4040 Linz (Austria); Bluemlein, Johannes, E-mail: johannes.bluemlein@desy.de [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Hasselhuhn, Alexander [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Klein, Sebastian [Research Institut fuer Theoretische Physik E, RWTH Aachen University, D-52056 Aachen (Germany); Schneider, Carsten [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstrasse 69, A-4040 Linz (Austria); Wissbrock, Fabian [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)

    2012-11-01

    3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with {xi} Element-Of {l_brace}1,1/2,2{r_brace} emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q{sup 2} Much-Greater-Than m{sup 2}.

  16. Two-Loop Self-Energy Correction in a Strong Coulomb Nuclear Field

    International Nuclear Information System (INIS)

    Yerokhin, V.A.; Indelicato, P.; Shabaev, V.M.

    2005-01-01

    The two-loop self-energy correction to the ground-state energy levels of hydrogen-like ions with nuclear charges Z ≥ 10 is calculated without the Zα expansion, where α is the fine-structure constant. The data obtained are compared with the results of analytical calculations within the Zα expansion; significant disagreement with the analytical results of order α 2 (Zα) 6 has been found. Extrapolation is used to obtain the most accurate value for the two-loop self-energy correction for the 1s state in hydrogen

  17. Exact two-loop vacuum polarization correction to the Lamb shift in hydrogenlike ions

    International Nuclear Information System (INIS)

    Plunien, G.; Beier, T.; Soff, G.

    1998-01-01

    We present a calculation scheme for the two-loop vacuum polarization correction of order α 2 to the Lamb shift of hydrogenlike high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in (Zα). By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuumpolarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell electron states in hydrogenlike lead and uranium are presented. (orig.)

  18. Two loop effective Kahler potential of (non)-renormalizable supersymmetric models

    International Nuclear Information System (INIS)

    Groot Nibbelink, S.; Nyawelo, T.S.

    2005-10-01

    We perform a supergraph computation of the effective Kahler potential at one and two loops for general four dimensional N=1 supersymmetric theories described by arbitrary Kahler potential, superpotential and gauge kinetic function. We only insist on gauge invariance of the Kahler potential and the superpotential as we heavily rely on its consequences in the quantum theory. However, we do not require gauge invariance for the gauge kinetic functions, so that our results can also be applied to anomalous theories that involve the Green-Schwarz mechanism. We illustrate our two loop results by considering a few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum Electrodynamics. (author)

  19. Validity of M-3Y force equivalent G-matrix elements for calculations of the nuclear structure in heavy mass region

    International Nuclear Information System (INIS)

    Cheng Lan; Huang Weizhi; Zhou Baosen

    1996-01-01

    Using the matrix elements of M-3Y force as the equivalent G-matrix elements, the spectra of 210 Pb, 206 Pb, 206 Hg and 210 Po are calculated in the framework of the Folded Diagram Method. The results show that such equivalent matrix elements are suitable for microscopic calculations of the nuclear structure in heavy mass region

  20. Measurement of single top quark production at D0 using a matrix element method

    International Nuclear Information System (INIS)

    Mitrevski, Jovan Pavle

    2007-01-01

    Until now, the top quark has only been observed produced in pairs, by the strong force. According to the standard model, it can also be produced singly, via an electroweak interaction. Top quarks produced this way provide powerful ways to test the charged-current electroweak interactions of the top quark, to measure |V tb |, and to search for physics beyond the standard model. This thesis describes the application of the matrix element analysis technique to the search for single top quark production with the D0 detector using 0.9 fb -1 of Run II data. From a comparison of the matrix element discriminants between data and the background model, assuming a Standard Model s-channel to t-channel cross section ratio of σ s /σ t = 0.44, we measure the single top quark production cross section: σ(p(bar p) → tb + X, tqb + X) = 4.8 -1.4 +1.6 pb. This result has a p-value of 0.08%, corresponding to a 3.2 standard deviation Gaussian equivalent significance

  1. Diagrammatic technique for calculating matrix elements of collective operators in superradiance

    International Nuclear Information System (INIS)

    Lee, C.T.

    1975-01-01

    Adopting the so-called ''genealogical construction,'' one can express the eigenstates of collective operators corresponding to a specified mode for an N-atom system in terms of those for an (N-1) -atom system. Using these Dicke states as bases and using the Wigner-Eckart theorem, a matrix element of a collective operator of an arbitrary mode can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME is obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups is then introduced. This gives a simple and systematic way of calculating the RME. This method is especially useful when the cooperation number r is close to N/2, where almost exact asymptotic expressions can be obtained easily. The result shows explicitly the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes. This clears up the chief difficulty encountered in the Dicke-Schwendimann approach to the problem of N two-level atoms, spread over large regions, interacting with a multimode radiation field

  2. Reorientation-effect measurement of the matrix element in 10Be

    Science.gov (United States)

    Orce, J. N.; Drake, T. E.; Djongolov, M. K.; Navrátil, P.; Triambak, S.; Ball, G. C.; Al Falou, H.; Churchman, R.; Cross, D. S.; Finlay, P.; Forssén, C.; Garnsworthy, A. B.; Garrett, P. E.; Hackman, G.; Hayes, A. B.; Kshetri, R.; Lassen, J.; Leach, K. G.; Li, R.; Meissner, J.; Pearson, C. J.; Rand, E. T.; Sarazin, F.; Sjue, S. K. L.; Stoyer, M. A.; Sumithrarachchi, C. S.; Svensson, C. E.; Tardiff, E. R.; Teigelhoefer, A.; Williams, S. J.; Wong, J.; Wu, C. Y.

    2012-10-01

    The highly-efficient and segmented TIGRESS γ-ray spectrometer at TRIUMF has been used to perform a reorientation-effect Coulomb-excitation study of the 21+ state at 3.368 MeV in 10Be. This is the first Coulomb-excitation measurement that enables one to obtain information on diagonal matrix elements for such a high-lying first excited state from γ-ray data. With the availability of accurate lifetime data, a value of -0.110±0.087 eb is determined for the diagonal matrix element, which assuming the rotor model, leads to a negative spectroscopic quadrupole moment of QS(21+)=-0.083±0.066 eb. This result is in agreement with both no-core shell-model calculations performed in this work with the CD-Bonn 2000 two-nucleon potential and large shell-model spaces, and Green's function Monte Carlo predictions with two- plus three-nucleon potentials.

  3. A new program for calculating matrix elements of one-particle operators in jj-coupling

    International Nuclear Information System (INIS)

    Pyper, N.C.; Grant, I.P.; Beatham, N.

    1978-01-01

    The aim of this paper is to calculate the matrix elements of one-particle tensor operators occurring in atomic and nuclear theory between configuration state functions representing states containing any number of open shells in jj-coupling. The program calculates the angular part of these matrix elements. The program is essentially a new version of RDMEJJ, written by J.J. Chang. The aims of this version are to eliminate inconsistencies from RDMEJJ, to modify its input requirements for consistency with MCP75, and to modify its output so that it can be stored in a discfile for access by other compatible programs. The program assumes that the configurational states are built from a common orthonormal set of basis orbitals. The number of electrons in a shell having j>=9/2 is restricted to be not greater than 2 by the available CFP routines . The present version allows up to 40 orbitals and 50 configurational states with <=10 open shells; these numbers can be changed by recompiling with modified COMMON/DIMENSION statements. The user should ensure that the CPC library subprograms AAGD, ACRI incorporate all current updates and have been converted to use double precision floating point arithmetic. (Auth.)

  4. An experimentalist's guide to the matrix element in angle resolved photoemission

    International Nuclear Information System (INIS)

    Moser, Simon

    2017-01-01

    Highlights: • An introduction to the art of angle resolved photoemission is presented. • Matrix element effects are described by a nearly free electron final state model. • ARPES spectral weight of a Bloch band can be calculated from the Fourier transform of its Wannier orbital. • Experimental handedness and improper polarization introduce dichroism. • Instructive showcases from modern ARPES are discussed in detail. - Abstract: Angle resolved photoemission spectroscopy (ARPES) is commonly known as a powerful probe of the one-electron removal spectral function in ordered solid state. With increasing efficiency of light sources and spectrometers, experiments over a wide range of emission angles become more and more common. Consequently, the angular variation of ARPES spectral weight – often times termed “matrix element effect” – enters as an additional source of information. In this tutorial, we develop a simple but instructive free electron final state approach based on the three-step model to describe the intensity distribution in ARPES. We find a compact expression showing that the ARPES spectral weight of a given Bloch band is essentially determined by the momentum distribution (the Fourier transform) of its associated Wannier orbital – times a polarization dependent pre-factor. While the former is giving direct information on the symmetry and shape of the electronic wave function, the latter can give rise to surprising geometric effects. We discuss a variety of modern and instructive experimental showcases for which this simplistic formalism works astonishingly well and discuss the limits of this approach.

  5. Precision Measurement of the Neutron Twist-3 Matrix Element dn2: Probing Color Forces

    Energy Technology Data Exchange (ETDEWEB)

    Posik, Matthew; Flay, David; Parno, Diana; Allada, Kalyan; Armstrong, Whitney; Averett, Todd; Benmokhtar, Fatiha; Bertozzi, William; Camsonne, Alexandre; Canan, Mustafa; Cates, Gordon; Chen, Chunhua; Chen, Jian-Ping; Choi, Seonho; Chudakov, Eugene; Cusanno, Francesco; Dalton, Mark; Deconinck, Wouter; De Jager, Cornelis; Deng, Xiaoyan; Deur, Alexandre; Dutta, Chiranjib; El Fassi, Lamiaa; Franklin, Gregg; Friend, Megan; Gao, Haiyan; Garibaldi, Franco; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Golge, Serkan; Gomez, Javier; Guo, Lei; Hansen, Jens-Ole; Higinbotham, Douglas; Holmstrom, Timothy; Huang, J; Hyde, Charles; Ibrahim Abdalla, Hassan; Jiang, Xiaodong; Jin, Ge; Katich, Joseph; Kelleher, Aidan; Kolarkar, Ameya; Korsch, Wolfgang; Kumbartzki, Gerfried; LeRose, John; Lindgren, Richard; Liyanage, Nilanga; Long, Elena; Lukhanin, Oleksandr; Mamyan, Vahe; McNulty, Dustin; Meziani, Zein-Eddine; Michaels, Robert; Mihovilovic, Miha; Moffit, Bryan; Muangma, Navaphon; Nanda, Sirish; Narayan, Amrendra; Nelyubin, Vladimir; Norum, Blaine; Nuruzzaman, nfn; Oh, Yongseok; Peng, Jen-chieh; Qian, Xin; Qiang, Yi; Rakhman, Abdurahim; Riordan, Seamus; Saha, Arunava; Sawatzky, Bradley; Hashemi Shabestari, Mitra; Shahinyan, Albert; Sirca, Simon; Solvignon-Slifer, Patricia; Subedi, Ramesh; Sulkosky, Vincent; Tobias, William; Troth, Wolfgang; Wang, Diancheng; Wang, Y; Wojtsekhowski, Bogdan; Yan, X; Yao, Huan; Ye, Yunxiu; Ye, Zhihong; Yuan, Lulin; Zhan, X; Zhang, Y; Zhang, Y -W; Zhao, Bo; Zheng, Xiaochao

    2014-07-01

    Double-spin asymmetries and absolute cross sections were measured at large Bjorken x (0.25 lte x lte 0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized 3He target. In this dedicated experiment, the spin structure function g2 on 3He was determined with precision at large x, and the neutron twist-three matrix element dn2 was measured at ?Q2? of 3.21 and 4.32 GeV2/c2, with an absolute precision of about 10?5. Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at ?Q2?= 5 GeV2/c2. Combining dn2 and a newly extracted twist-four matrix element, fn2, the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 60 MeV/fm in magnitude.

  6. Double Beta Decay and Neutrino Masses Accuracy of the Nuclear Matrix Elements

    International Nuclear Information System (INIS)

    Faessler, Amand

    2005-01-01

    The neutrinoless double beta decay is forbidden in the standard model of the electroweak and strong interaction but allowed in most Grand Unified Theories (GUT's). Only if the neutrino is a Majorana particle (identical with its antiparticle) and if it has a mass, the neutrinoless double beta decay is allowed. Apart of one claim that the neutrinoless double beta decay in 76 Ge is measured, one has only upper limits for this transition probability. But even the upper limits allow to give upper limits for the electron Majorana neutrino mass and upper limits for parameters of GUT's and the minimal R-parity violating supersymmetric model. One further can give lower limits for the vector boson mediating mainly the right-handed weak interaction and the heavy mainly right-handed Majorana neutrino in left-right symmetric GUT's. For that one has to assume that the specific mechanism is the leading one for the neutrinoless double beta decay and one has to be able to calculate reliably the corresponding nuclear matrix elements. In the present contribution, one discusses the accuracy of the present status of calculating the nuclear matrix elements and the corresponding limits of GUT's and supersymmetric parameters

  7. An experimentalist's guide to the matrix element in angle resolved photoemission

    Energy Technology Data Exchange (ETDEWEB)

    Moser, Simon, E-mail: skmoser@lbl.gov [Advanced Light Source (ALS), Berkeley, CA 94720 (United States); Institute of Physics (IPHYS), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne (Switzerland)

    2017-01-15

    Highlights: • An introduction to the art of angle resolved photoemission is presented. • Matrix element effects are described by a nearly free electron final state model. • ARPES spectral weight of a Bloch band can be calculated from the Fourier transform of its Wannier orbital. • Experimental handedness and improper polarization introduce dichroism. • Instructive showcases from modern ARPES are discussed in detail. - Abstract: Angle resolved photoemission spectroscopy (ARPES) is commonly known as a powerful probe of the one-electron removal spectral function in ordered solid state. With increasing efficiency of light sources and spectrometers, experiments over a wide range of emission angles become more and more common. Consequently, the angular variation of ARPES spectral weight – often times termed “matrix element effect” – enters as an additional source of information. In this tutorial, we develop a simple but instructive free electron final state approach based on the three-step model to describe the intensity distribution in ARPES. We find a compact expression showing that the ARPES spectral weight of a given Bloch band is essentially determined by the momentum distribution (the Fourier transform) of its associated Wannier orbital – times a polarization dependent pre-factor. While the former is giving direct information on the symmetry and shape of the electronic wave function, the latter can give rise to surprising geometric effects. We discuss a variety of modern and instructive experimental showcases for which this simplistic formalism works astonishingly well and discuss the limits of this approach.

  8. Three loop contributions to the matrix elements in the variable flavor number scheme

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes; Hasselhuhn, Alexander [DESY (Germany); Schneider, Carsten [RISC, JKU Linz (Austria)

    2012-07-01

    The variable flavor number scheme may be used to describe parton distributions in the transition region in which one heavy quark gradually becomes a light flavor. We present first three-loop results to the massive operator matrix elements A{sub gg} and A{sub gq} for the contributions due to bubble topologies {proportional_to}T{sub F}{sup 2} n{sub f} at general values of the Mellin variable N. The calculation has been performed using higher transcendental functions and by applying modern summation technologies encoded in the package Sigma. These massive operator matrix elements describe the universal contributions in the matching of different flavor sectors, which are the logarithmic and constant contributions in the ratio of m{sup 2}{sub H}/Q{sup 2}, with Q{sup 2} the virtuality and m{sub H} the respective heavy quark mass. The framework allows to derive heavy quark parton distributions which are of relevance for calculating specific processes at hadron-hadron colliders.

  9. Measurement of the top quark mass in the dilepton final state using the matrix element method

    Energy Technology Data Exchange (ETDEWEB)

    Grohsjean, Alexander [Ludwig Maximilian Univ., Munich (Germany)

    2008-12-15

    The top quark, discovered in 1995 by the CDF and D0 experiments at the Fermilab Tevatron Collider, is the heaviest known fundamental particle. The precise knowledge of its mass yields important constraints on the mass of the yet-unobserved Higgs boson and allows to probe for physics beyond the Standard Model. The first measurement of the top quark mass in the dilepton channel with the Matrix Element method at the D0 experiment is presented. After a short description of the experimental environment and the reconstruction chain from hits in the detector to physical objects, a detailed review of the Matrix Element method is given. The Matrix Element method is based on the likelihood to observe a given event under the assumption of the quantity to be measured, e.g. the mass of the top quark. The method has undergone significant modifications and improvements compared to previous measurements in the lepton+jets channel: the two undetected neutrinos require a new reconstruction scheme for the four-momenta of the final state particles, the small event sample demands the modeling of additional jets in the signal likelihood, and a new likelihood is designed to account for the main source of background containing tauonic Z decay. The Matrix Element method is validated on Monte Carlo simulated events at the generator level. For the measurement, calibration curves are derived from events that are run through the full D0 detector simulation. The analysis makes use of the Run II data set recorded between April 2002 and May 2008 corresponding to an integrated luminosity of 2.8 fb-1. A total of 107 t$\\bar{t}$ candidate events with one electron and one muon in the final state are selected. Applying the Matrix Element method to this data set, the top quark mass is measured to be mtopRun IIa = 170.6 ± 6.1(stat.)-1.5+2.1(syst.)GeV; mtopRun IIb = 174.1 ± 4.4(stat.)-1.8+2.5(syst.)GeV; m

  10. Lepton mixing matrix element U13 and new assignments of universal texture for quark and lepton mass matrices

    International Nuclear Information System (INIS)

    Matsuda, Koichi; Nishiura, Hiroyuki

    2004-01-01

    We reanalyze the mass matrix model of quarks and leptons that gives a unified description of quark and lepton mass matrices with the same texture form. By investigating possible types of assignment for the texture components of the lepton mass matrix, we find that a different assignment for neutrinos than for charged leptons can also lead to consistent values of the Maki-Nakagawa-Sakata-Pontecorv (MNSP) lepton mixing matrix. We also find that the predicted value for the lepton mixing matrix element U 13 of the model depends on the assignment. A proper assignment will be discriminated by future experimental data for U 13

  11. Two-loop anomalous dimensions for four-Fermi operators in supersymmetric theories

    Directory of Open Access Journals (Sweden)

    Junji Hisano

    2017-09-01

    Full Text Available We derive two-loop anomalous dimensions for four-Fermi operators in supersymmetric theories using the effective Kähler potential. We introduce the general forms in generic gauge theories and apply our results to the flavor-changing operators in (minimal supersymmetric standard models.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-12-10

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

  13. The SU(2|3) dynamic two-loop form factors

    International Nuclear Information System (INIS)

    Brandhuber, A.; Kostacińska, M.; Penante, B.; Travaglini, G.; Young, D.

    2016-01-01

    We compute two-loop form factors of operators in the SU(2|3) closed subsector of N = 4 supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators Tr(X[Y,Z]) and Tr(ψψ) for which we compute the four possible two-loop form factors, and corresponding remainder functions, with external states 〈X̄ȲZ̄| and 〈ψ̄ψ̄|. Interestingly, the maximally transcendental part of the two-loop remainder of 〈X̄ȲZ̄|Tr(X[Y,Z])|0〉 turns out to be identical to that of the corresponding known quantity for the half-BPS operator Tr(X"3). We also find a surprising connection between the terms subleading in transcendentality and certain a priori unrelated remainder densities introduced in the study of the spin chain Hamiltonian in the SU(2) sector. Next, we use our calculation to resolve the mixing, recovering anomalous dimensions and eigenstates of the dilatation operator in the SU(2|3) sector at two loops. We also speculate on potential connections between our calculations in N = 4 super Yang-Mills and Higgs + multi-gluon amplitudes in QCD in an effective Lagrangian approach.

  14. The SU(2|3) dynamic two-loop form factors

    Energy Technology Data Exchange (ETDEWEB)

    Brandhuber, A.; Kostacińska, M. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom); Penante, B. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom); Institut für Physik und IRIS Adlershof, Humboldt Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); Travaglini, G.; Young, D. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)

    2016-08-23

    We compute two-loop form factors of operators in the SU(2|3) closed subsector of N = 4 supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators Tr(X[Y,Z]) and Tr(ψψ) for which we compute the four possible two-loop form factors, and corresponding remainder functions, with external states 〈X̄ȲZ̄| and 〈ψ̄ψ̄|. Interestingly, the maximally transcendental part of the two-loop remainder of 〈X̄ȲZ̄|Tr(X[Y,Z])|0〉 turns out to be identical to that of the corresponding known quantity for the half-BPS operator Tr(X{sup 3}). We also find a surprising connection between the terms subleading in transcendentality and certain a priori unrelated remainder densities introduced in the study of the spin chain Hamiltonian in the SU(2) sector. Next, we use our calculation to resolve the mixing, recovering anomalous dimensions and eigenstates of the dilatation operator in the SU(2|3) sector at two loops. We also speculate on potential connections between our calculations in N = 4 super Yang-Mills and Higgs + multi-gluon amplitudes in QCD in an effective Lagrangian approach.

  15. Two-loop calculation of the effective potential for the Wess-Zumino model

    International Nuclear Information System (INIS)

    Fogleman, G.; Starkmann, G.D.; Viswanathan, K.S.; Simon Fraser Univ., Burnaby, British Columbia

    1983-01-01

    The effective potential for the supersymmetric Wess-Zumino model is computed off-shell to two loops. A renormalization procedure which preserves positivity of the kinetic terms in the effective action is implemented. Supersymmetry is not broken to this order. (orig.)

  16. The complete two-loop integrated jet thrust distribution in soft-collinear effective theory

    International Nuclear Information System (INIS)

    Manteuffel, Andreas von; Schabinger, Robert M.; Zhu, Hua Xing

    2014-01-01

    In this work, we complete the calculation of the soft part of the two-loop integrated jet thrust distribution in e + e − annihilation. This jet mass observable is based on the thrust cone jet algorithm, which involves a veto scale for out-of-jet radiation. The previously uncomputed part of our result depends in a complicated way on the jet cone size, r, and at intermediate stages of the calculation we actually encounter a new class of multiple polylogarithms. We employ an extension of the coproduct calculus to systematically exploit functional relations and represent our results concisely. In contrast to the individual contributions, the sum of all global terms can be expressed in terms of classical polylogarithms. Our explicit two-loop calculation enables us to clarify the small r picture discussed in earlier work. In particular, we show that the resummation of the logarithms of r that appear in the previously uncomputed part of the two-loop integrated jet thrust distribution is inextricably linked to the resummation of the non-global logarithms. Furthermore, we find that the logarithms of r which cannot be absorbed into the non-global logarithms in the way advocated in earlier work have coefficients fixed by the two-loop cusp anomalous dimension. We also show that in many cases one can straightforwardly predict potentially large logarithmic contributions to the integrated jet thrust distribution at L loops by making use of analogous contributions to the simpler integrated hemisphere soft function

  17. The light-cone gauge at two loops: The scalar anomalous dimension

    International Nuclear Information System (INIS)

    Capper, D.M.; Suzuki, A.T.; Jones, D.R.T.

    1985-01-01

    We demonstrate that the light-cone gauge is a feasible tool for multi-loop computations by using it to evaluate the two-loop scalar anomalous dimension, γsup((2)), in a general gauge theory. In the special case of supersymmetry we obtain agreement with previous results which were derived using nonlight-cone techniques. (orig.)

  18. A two-loop four-gluon helicity amplitude in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, L.

    2000-01-06

    The authors present the two-loop pure gauge contribution to the gluon-gluon scattering amplitude with maximal helicity violation. The construction of the amplitude does not rely directly on Feynman diagrams, but instead uses its analytic properties 4--2{epsilon} dimensions. The authors evaluate the loop integrals appearing in the amplitude through order({epsilon}{sup 0})in terms of polylogarithms.

  19. Computation of Groebner bases for two-loop propagator type integrals

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    2004-01-01

    The Groebner basis technique for calculating Feynman diagrams proposed in (Acta Phys. Pol. B 29(1998) 2655) is applied to the two-loop propagator type integrals with arbitrary masses and momentum. We describe the derivation of Groebner bases for all integrals with 1PI topologies and present explicit content of the Groebner bases

  20. Computation of Groebner bases for two-loop propagator type integrals

    Energy Technology Data Exchange (ETDEWEB)

    Tarasov, O.V. [DESY Zeuthen, Theory Group, Deutsches Elektronen Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)]. E-mail: tarasov@ifh.de

    2004-11-21

    The Groebner basis technique for calculating Feynman diagrams proposed in (Acta Phys. Pol. B 29(1998) 2655) is applied to the two-loop propagator type integrals with arbitrary masses and momentum. We describe the derivation of Groebner bases for all integrals with 1PI topologies and present explicit content of the Groebner bases.

  1. Application of 't Hooft's renormalization scheme to two-loop calculations 230

    International Nuclear Information System (INIS)

    Vladimirov, A.A.

    1975-01-01

    The advantages of the Hooft scheme for asymptotic calculations in the renormalization group have been demonstrated. Two-loop calculations have been carried out in three renormalized models: in scalar electrodynamics, in a pseudoscalar Yukawa theory and in the Weiss-Zumino supersymmetrical model [ru

  2. Single top quark production and Vtb CKM matrix element measurement in high energy e+e- collisions

    International Nuclear Information System (INIS)

    Dokholyan, N.V.; Jikia, G.V.

    1993-01-01

    The new method of determination of CKM mixing matrix element V tb has been proposed. It has been shown, that at the future colliders one will measure the tb-mixing element with the accuracy 12 - 28%. 16 refs., 6 figs., 1 tab

  3. Overcoming Matrix Effects in a Complex Sample: Analysis of Multiple Elements in Multivitamins by Atomic Absorption Spectroscopy

    Science.gov (United States)

    Arnold, Randy J.; Arndt, Brett; Blaser, Emilia; Blosser, Chris; Caulton, Dana; Chung, Won Sog; Fiorenza, Garrett; Heath, Wyatt; Jacobs, Alex; Kahng, Eunice; Koh, Eun; Le, Thao; Mandla, Kyle; McCory, Chelsey; Newman, Laura; Pithadia, Amit; Reckelhoff, Anna; Rheinhardt, Joseph; Skljarevski, Sonja; Stuart, Jordyn; Taylor, Cassie; Thomas, Scott; Tse, Kyle; Wall, Rachel; Warkentien, Chad

    2011-01-01

    A multivitamin tablet and liquid are analyzed for the elements calcium, magnesium, iron, zinc, copper, and manganese using atomic absorption spectrometry. Linear calibration and standard addition are used for all elements except calcium, allowing for an estimate of the matrix effects encountered for this complex sample. Sample preparation using…

  4. Analytic two-loop results for self-energy- and vertex-type diagrams with one non-zero mass

    International Nuclear Information System (INIS)

    Fleischer, J.; Kotikov, A.V.; Veretin, O.L.

    1999-01-01

    For a large class of two-loop self-energy- and vertex-type diagrams with only one non-zero mass (m) and the vertices also with only one non-zero external momentum squared (q 2 ) the first few expansion coefficients are calculated by the large mass expansion. This allows us to 'guess' the general structure of these coefficients and to verify them in terms of certain classes of 'basis elements', which are essentially harmonic sums. Since for this case with only one non-zero mass the large mass expansion and the Taylor series in terms of q 2 are identical, this approach yields analytic expressions of the Taylor coefficients, from which the diagram can be easily evaluated numerically in a large domain of the complex q 2 -plane by well known methods. It is also possible to sum the Taylor series and present the results in terms of polylogarithms

  5. Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Raab, Clemens; Wissbrock, Fabian

    2014-02-01

    We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a N , a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.

  6. Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC)

    2014-02-15

    We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a{sup N}, a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.

  7. Matrix elements for the anti B{yields}X{sub s}{gamma} decay at NNLO

    Energy Technology Data Exchange (ETDEWEB)

    Schutzmeier, Thomas Paul

    2009-12-17

    In the context of the indirect search for non-standard physics in the flavour sector of the Standard Model (SM), one of the most interesting processes is the rare inclusive anti B{yields} X{sub s}{gamma} decay. On the one hand, being a flavour-changing neutral current, this B decay is sensitive to new physics, as it is loop-suppressed in the SM. On the other hand, it is only mildly affected by non-perturbative effects, and thus allows for precise theoretical predictions in the framework of renormalization-group improved perturbation theory. Accurate measurements as well as precise theoretical predictions with a good control over both perturbative and non-perturbative contributions have to be provided in order to derive stringent constraints on the parameter space of physics beyond the SM. On the experimental side, an outstanding accuracy in the measurement of the anti B{yields}X{sub s}{gamma} decay rate has been achieved, which is mainly due the specialized experiments BaBar and Belle at the so-called B factories. To match the small experimental uncertainty, higher order computations within an effective low-energy theory of the SM are mandatory. In fact, next-to-next-to-leading order (NNLO) QCD corrections are required to provide a prediction for the decay rate with the same precision as the measurement. The NNLO evaluation of the anti B{yields}X{sub s}{gamma} decay rate has been pursued by various groups over the last decade. The project was completed to a large extent and a first estimate at this level of perturbation theory was obtained in 2006. This prediction, however, lacks important contributions from yet unknown matrix elements, that were estimated from results which are only partially known to date. In this work, we provide a framework for the systematic study of the missing matrix elements at the NNLO. As main results of this thesis, we determine fermionic corrections to the charm quark mass dependent matrix elements of four-quark operators in the

  8. Matrix elements for the anti B→Xsγ decay at NNLO

    International Nuclear Information System (INIS)

    Schutzmeier, Thomas Paul

    2009-01-01

    In the context of the indirect search for non-standard physics in the flavour sector of the Standard Model (SM), one of the most interesting processes is the rare inclusive anti B→ X s γ decay. On the one hand, being a flavour-changing neutral current, this B decay is sensitive to new physics, as it is loop-suppressed in the SM. On the other hand, it is only mildly affected by non-perturbative effects, and thus allows for precise theoretical predictions in the framework of renormalization-group improved perturbation theory. Accurate measurements as well as precise theoretical predictions with a good control over both perturbative and non-perturbative contributions have to be provided in order to derive stringent constraints on the parameter space of physics beyond the SM. On the experimental side, an outstanding accuracy in the measurement of the anti B→X s γ decay rate has been achieved, which is mainly due the specialized experiments BaBar and Belle at the so-called B factories. To match the small experimental uncertainty, higher order computations within an effective low-energy theory of the SM are mandatory. In fact, next-to-next-to-leading order (NNLO) QCD corrections are required to provide a prediction for the decay rate with the same precision as the measurement. The NNLO evaluation of the anti B→X s γ decay rate has been pursued by various groups over the last decade. The project was completed to a large extent and a first estimate at this level of perturbation theory was obtained in 2006. This prediction, however, lacks important contributions from yet unknown matrix elements, that were estimated from results which are only partially known to date. In this work, we provide a framework for the systematic study of the missing matrix elements at the NNLO. As main results of this thesis, we determine fermionic corrections to the charm quark mass dependent matrix elements of four-quark operators in the effective theory at NNLO. For the first time, the

  9. Measurement of the Top Quark Mass Using the Matrix Element Technique in Dilepton Final States

    CERN Document Server

    Abazov, Victor Mukhamedovich

    2016-08-18

    We present a measurement of the top quark mass in ppbar collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7 fb-1. The matrix element technique is applied to ttbar events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton + jets final state of ttbar decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain a top quark mass of mt = 173.93 +- 1.84 GeV.

  10. Nucleon distribution apmlitudes and proton decay matrix elements on the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Braun, Vladimir M.; Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (GB). School of Physics] (and others)

    2008-11-15

    Baryon distribution amplitudes (DAs) are crucial for the theory of hard exclusive reactions. We present a calculation of the first few moments of the leading-twist nucleon DA within lattice QCD. In addition we deal with the normalization of the next-to-leading (twist-four) DAs. The matrix elements determining the latter quantities are also responsible for proton decay in Grand Unified Theories. Our lattice evaluation makes use of gauge field configurations generated with two flavors of clover fermions. The relevant operators are renormalized nonperturbatively with the final results given in the MS scheme. We find that the deviation of the leading-twist nucleon DA from its asymptotic form is less pronounced than sometimes claimed in the literature. (orig.)

  11. Quadrupole corrections to matrix elements of transitions in resonant reactions of muonic molecule formation

    International Nuclear Information System (INIS)

    Faifman, M.P.; Strizh, T.A.; Armour, E.A.G.; Harston, M.R.

    1996-01-01

    The calculated resonant formation rates of the muonic molecules DDμ and DTμ are presented. The approach developed earlier for calculating the transition matrix elements in the dipole approximation has been extended to include the quadrupole terms in the multipole expansion of the interaction operator. The calculated dependence of the DTμ formation rates on the energies of the incident Tμ muonic atoms shows that the effect of including the quadrupole correction is to reduce the magnitude of the peak rates by about 20-30% at the different temperatures, compared to those calculated in the dipole approximation. The dependence on temperature for the DDμ formation rates is obtained with the differences between the presented and previous calculations being less than 5%. (orig.)

  12. Improved method for eliminating center-of-mass coordinates from matrix elements in oscillator basis

    International Nuclear Information System (INIS)

    Richardson, R.H.; Shapiro, J.Y.

    1986-01-01

    This paper presents a concise, efficient method of reducing potential energy matrix elements to relative coordinates, when one is using an oscillator basis. It is especially suited to computer calculations. One nice feature of the method is its modular form, which allows a wide range of calculations. Separate FORTRAN subroutines have been written which calculate and store tables of the one-dimensional brackets of an equation that is presented and the single particle brackets from the isotropic to the axially symmetric oscillator equations. The tables are used by other subroutines which calculate the modified brackets and the brackets with spin. The methods developed here are a substantial improvement over what has been done heretofore, and open up new possibilities for performing nuclear structure calculations

  13. HELAC-Onia: an automatic matrix element generator for heavy quarkonium physics

    CERN Document Server

    Shao, Hua-Sheng

    2013-01-01

    By the virtues of the Dyson-Schwinger equations, we upgrade the published code \\mtt{HELAC} to be capable to calculate the heavy quarkonium helicity amplitudes in the framework of NRQCD factorization, which we dub \\mtt{HELAC-Onia}. We rewrote the original \\mtt{HELAC} to make the new program be able to calculate helicity amplitudes of multi P-wave quarkonium states production at hadron colliders and electron-positron colliders by including new P-wave off-shell currents. Therefore, besides the high efficiencies in computation of multi-leg processes within the Standard Model, \\mtt{HELAC-Onia} is also sufficiently numerical stable in dealing with P-wave quarkonia (e.g. $h_{c,b},\\chi_{c,b}$) and P-wave color-octet intermediate states. To the best of our knowledge, it is a first general-purpose automatic quarkonium matrix elements generator based on recursion relations on the market.

  14. Grassmann integral and Balian–Brézin decomposition in Hartree–Fock–Bogoliubov matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Mizusaki, Takahiro, E-mail: mizusaki@isc.senshu-u.ac.jp [Institute of Natural Sciences, Senshu University, 3-8-1 Kanda-Jinbocho, Chiyoda-ku, Tokyo 101-8425 (Japan); Oi, Makito [Institute of Natural Sciences, Senshu University, 3-8-1 Kanda-Jinbocho, Chiyoda-ku, Tokyo 101-8425 (Japan); Chen, Fang-Qi [Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Sun, Yang [Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China)

    2013-08-09

    We present a new formula to calculate matrix elements of a general unitary operator with respect to Hartree–Fock–Bogoliubov states allowing multiple quasi-particle excitations. The Balian–Brézin decomposition of the unitary operator [R. Balian, E. Brézin, Il Nuovo Cimento B 64 (1969) 37] is employed in the derivation. We found that this decomposition is extremely suitable for an application of Fermion coherent state and Grassmann integrals in the quasi-particle basis. The resultant formula is compactly expressed in terms of the Pfaffian, and shows the similar bipartite structure to the formula that we have previously derived in the bare-particles basis [T. Mizusaki, M. Oi, Phys. Lett. B 715 (2012) 219].

  15. Extraction of the CKM matrix element Vus from the hyperon semileptonic decays

    International Nuclear Information System (INIS)

    Sharma, N.; Dahiya, H.; Chatley, P.K.

    2010-01-01

    The chiral constituent quark model with configuration mixing (χCQM config ), which is successful in explaining the weak vector and axial-vector form factors for the strangeness-changing as well as strangeness-nonchanging hyperon semileptonic decays at Q 2 =0, has been extended to determine the CKM matrix element V us for the strangeness-changing decays. The implications of the effect of the SU(3) symmetry breaking, Q 2 -dependence and radiative corrections on the form factors and V us have also been investigated. It is found that the results with SU(3) symmetry breaking show considerable improvement over the SU(3) symmetric results when compared with the existing experimental data. The inclusion of the Q 2 -dependence and radiative corrections in form factors have only a small effect on the prediction of V us as is expected from the theory. (orig.)

  16. Massive 3-loop ladder diagrams for quarkonic local operator matrix elements

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Blümlein, Johannes; Hasselhuhn, Alexander; Klein, Sebastian; Schneider, Carsten; Wißbrock, Fabian

    2012-01-01

    3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with ξ∈{1,1/2,2} emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q 2 ≫m 2 .

  17. Minimizing matrix effect by femtosecond laser ablation and ionization in elemental determination.

    Science.gov (United States)

    Zhang, Bochao; He, Miaohong; Hang, Wei; Huang, Benli

    2013-05-07

    Matrix effect is unavoidable in direct solid analysis, which usually is a leading cause of the nonstoichiometric effect in quantitative analysis. In this research, experiments were carried out to study the overall characteristics of atomization and ionization in laser-solid interaction. Both nanosecond (ns) and femtosecond (fs) lasers were applied in a buffer-gas-assisted ionization source coupled with an orthogonal time-of-flight mass spectrometer. Twenty-nine solid standards of ten different matrices, including six metals and four dielectrics, were analyzed. The results indicate that the fs-laser mode offers more stable relative sensitivity coefficients (RSCs) with irradiance higher than 7 × 10(13) W·cm(-2), which could be more reliable in the determination of element composition of solids. The matrix effect is reduced by half when the fs-laser is employed, owing to the fact that the fs-laser ablation and ionization (fs-LAI) incurs an almost heat-free ablation process and creates a dense plasma for the stable ionization.

  18. Numerical Methods Application for Reinforced Concrete Elements-Theoretical Approach for Direct Stiffness Matrix Method

    Directory of Open Access Journals (Sweden)

    Sergiu Ciprian Catinas

    2015-07-01

    Full Text Available A detailed theoretical and practical investigation of the reinforced concrete elements is due to recent techniques and method that are implemented in the construction market. More over a theoretical study is a demand for a better and faster approach nowadays due to rapid development of the calculus technique. The paper above will present a study for implementing in a static calculus the direct stiffness matrix method in order capable to address phenomena related to different stages of loading, rapid change of cross section area and physical properties. The method is a demand due to the fact that in our days the FEM (Finite Element Method is the only alternative to such a calculus and FEM are considered as expensive methods from the time and calculus resources point of view. The main goal in such a method is to create the moment-curvature diagram in the cross section that is analyzed. The paper above will express some of the most important techniques and new ideas as well in order to create the moment curvature graphic in the cross sections considered.

  19. The muon magnetic moment in the 2HDM: complete two-loop result

    International Nuclear Information System (INIS)

    Cherchiglia, Adriano; Kneschke, Patrick; Stöckinger, Dominik; Stöckinger-Kim, Hyejung

    2017-01-01

    We study the 2HDM contribution to the muon anomalous magnetic moment a μ and present the complete two-loop result, particularly for the bosonic contribution. We focus on the Aligned 2HDM, which has general Yukawa couplings and contains the type I, II, X, Y models as special cases. The result is expressed with physical parameters: three Higgs boson masses, Yukawa couplings, two mixing angles, and one quartic potential parameter. We show that the result can be split into several parts, each of which has a simple parameter dependence, and we document their general behavior. Taking into account constraints on parameters, we find that the full 2HDM contribution to a μ can accommodate the current experimental value, and the complete two-loop bosonic contribution can amount to (2⋯4)×10 −10 , more than the future experimental uncertainty.

  20. Local integrand representations of all two-loop amplitudes in planar SYM

    International Nuclear Information System (INIS)

    Bourjaily, Jacob L.; Trnka, Jaroslav

    2015-01-01

    We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and manifestly divergent terms — in a way that renders all infrared-safe observables (including ratio functions) calculable without any need for regulation. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a MATHEMATICA package which implements these results, available as part of this work’s source files on the arXiv.

  1. Resummed two-loop calculation of the disjoining pressure of a symmetric electrolyte soap film

    International Nuclear Information System (INIS)

    Dean, D.S.; Horgan, R.R.

    2004-01-01

    In this paper we consider the calculation of the disjoining pressure of a symmetric electrolytic soap film correct to two loops in perturbation theory. We show that the disjoining pressure is finite when the loop expansion is resummed using a cumulant expansion and requires no short distance cutoff in order to give a finite result. The loop expansion is resummed in terms of an expansion in g=l B /l D where l D is the Debye length and l B is the Bjerrum length. We show that there there is a nonanalytic contribution of order g ln(g). We also show that the two-loop correction is greater than the one-loop term at large film thicknesses suggesting a nonperturbative correction to the one-loop result in this limit

  2. Matching the $D^{6}R^{4}$ interaction at two-loops

    CERN Document Server

    D'Hoker, Eric; Pioline, Boris; Russo, Rodolfo

    2015-01-01

    The coefficient of the $D^6 {\\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \\leq 3$ and $d \\leq 4$ is included.

  3. Low-energy effective action in two-dimensional SQED: a two-loop analysis

    Science.gov (United States)

    Samsonov, I. B.

    2017-07-01

    We study two-loop quantum corrections to the low-energy effective actions in N=(2,2) and N=(4,4) SQED on the Coulomb branch. In the latter model, the low-energy effective action is described by a generalized Kähler potential which depends on both chiral and twisted chiral superfields. We demonstrate that this generalized Kähler potential is one-loop exact and corresponds to the N=(4,4) sigma-model with torsion presented by Roček, Schoutens and Sevrin [1]. In the N=(2,2) SQED, the effective Kähler potential is not protected against higher-loop quantum corrections. The two-loop quantum corrections to this potential and the corresponding sigma-model metric are explicitly found.

  4. Automatic calculation of massive two-loop self-energies with XLOOPS

    International Nuclear Information System (INIS)

    Franzkowski, J.

    1997-01-01

    Within the program package XLOOPS it is possible to calculate self-energies up to the two-loop level for arbitrary massive particles. The program package -written in MAPLE (Char et al., Maple V Language Reference Manual (Springer, 1991); Char et al., Maple V Library Reference Manual (Springer, 1991)) - is designed to deal with the full tensor structure of the occurring integrals. This means that applications are not restricted to those cases where the reduction to scalars via equivalence theorem is allowed. The algorithms handle two-loop integrals analytically if this is possible. For those topologies where no analytic result for the general mass case is available, the diagrams are reduced to integral representations which encounter at most at two-fold integration. These integral representations are numerically stable and can be performed easily using VEGAS (Lepage, J. Comp. Phys. 27 (1978) 192; Lepage, Cornell Univ. Preprint CLNS-80/447 (1980)). (orig.)

  5. BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis

    Energy Technology Data Exchange (ETDEWEB)

    Bianchi, Marco S. [Institut für Physik, Humboldt-Universität zu Berlin,Newtonstraße 15, 12489 Berlin (Germany); Griguolo, Luca [Dipartimento di Fisica e Scienze della Terra, Università di Parmaand INFN Gruppo Collegato di Parma,Viale G.P. Usberti 7/A, 43100 Parma (Italy); Leoni, Matias [Physics Department, FCEyN-UBA & IFIBA-CONICETCiudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina); Penati, Silvia [Dipartimento di Fisica, Università di Milano-Bicoccaand INFN, Sezione di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Seminara, Domenico [Dipartimento di Fisica, Università di Firenzeand INFN Sezione di Firenze,via G. Sansone 1, 50019 Sesto Fiorentino (Italy)

    2014-06-19

    We study a family of circular BPS Wilson loops in N=6 super Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar and fermionic couplings depend on two deformation parameters and these operators can be considered as the ABJ(M) counterpart of the DGRT latitudes defined in N=4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the appearance of framing-like phases and propose a general relation with cohomologically equivalent bosonic operators. We make an all-loop proposal for computing the Bremsstrahlung function associated to the 1/2-BPS cusp in terms of these generalized Wilson loops. When applied to our two-loop result it reproduces the known expression. Finally, we comment on the generalization of this proposal to the bosonic 1/6-BPS case.

  6. Two-Loop Master Integrals for $\\gamma^{*} \\to 3$ Jets the Non-Planar Topologies

    CERN Document Server

    Gehrmann, T

    2001-01-01

    The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in $\\e=(4-d)/2$, where $d$ is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.

  7. Heavy-quark production in gluon fusion at two loops in QCD

    International Nuclear Information System (INIS)

    Czakon, M.

    2007-07-01

    We present the two-loop virtual QCD corrections to the production of heavy quarks in gluon fusion. The results are exact in the limit when all kinematical invariants are large compared to the mass of the heavy quark up to terms suppressed by powers of the heavy-quark mass. Our derivation uses a simple relation between massless and massive QCD scattering amplitudes as well as a direct calculation of the massive amplitude at two loops. The results presented here together with those obtained previously for quark-quark scattering form important parts of the next-to-next-to-leading order QCD corrections to heavy-quark production in hadron-hadron collisions. (orig.)

  8. Neutrinoless double-β decay matrix elements in large shell-model spaces with the generator-coordinate method

    Science.gov (United States)

    Jiao, C. F.; Engel, J.; Holt, J. D.

    2017-11-01

    We use the generator-coordinate method (GCM) with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-β decay of 48Ca, 76Ge, and 82Se. We work in one major shell for the first isotope, in the f5 /2p g9 /2 space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter β , but also the triaxiality angle γ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-09-14

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

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

    International Nuclear Information System (INIS)

    Martini, Till; Uwer, Peter

    2015-01-01

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

  11. Two-loop Higgs mass calculations beyond the MSSM with SARAH and SPheno

    Energy Technology Data Exchange (ETDEWEB)

    Nickel, Kilian [Physikalisches Institut, Universitaet Bonn (Germany); Staub, Florian [Theory Division, CERN, Geneva (Switzerland); Goodsell, Mark [LPTHE, UPMC Univ. Paris 06 (France)

    2015-07-01

    We present a recent extension to the Mathematica package SARAH which allows for Higgs mass calculations at the two-loop level in a wide range of supersymmetric models beyond the MSSM. These calculations are based on the effective potential approach. For the numerical evaluation Fortran code for SPheno is generated by SARAH. This allows to predict the Higgs mass in more complicated SUSY theories with a similar precision as most state-of-the-art spectrum generators do for the MSSM.

  12. Uncertainty of the two-loop RG upper bound on the Higgs mass

    International Nuclear Information System (INIS)

    Pirogov, Yu.F.; Zenin, O.V.

    2003-01-01

    A modified criterion of the SM perturbative consistency is proposed. It is based on the analytic properties of the two-loop SM running couplings. Under the criterion adopted, the Higgs mass up to 380 GeV might not give rise to strong coupling prior to the Planck scale. This means that the light Higgs boson is possibly preferred for reasons other than the SM perturbative consistency, i.e., for reasons beyond the SM

  13. Two-loop finiteness of self-energies in higher-derivative SQED3

    Directory of Open Access Journals (Sweden)

    E.A. Gallegos

    2015-09-01

    Full Text Available In the N=1 superfield formalism, two higher-derivative kinetic operators (Lee–Wick operators are implemented into the standard three dimensional supersymmetric quantum electrodynamics (SQED3 for improving its ultraviolet behavior. It is shown in particular that the ghosts associated with these Lee–Wick operators allow to remove all ultraviolet divergences in the scalar and gauge self-energies at two-loop level.

  14. Uncertainty of the two-loop RG upper bound on the Higgs mass

    International Nuclear Information System (INIS)

    Pirogov, Yu.F.; Zenin, O.V.

    2003-01-01

    A modified criterion of the standard model perturbative consistency is proposed. It is based on the analytic properties of the two-loop standard model running couplings. Under the criterion adopted, the Higgs mass up to 380 GeV might not give rise to the strong coupling prior to the Planck scale. This means that light Higgs boson is possibly preferred for reasons other than the standard model perturbative consistency, i.e., for reasons beyond the standard model [ru

  15. Two-loop QED corrections to the Altarelli-Parisi splitting functions

    Energy Technology Data Exchange (ETDEWEB)

    Florian, Daniel de [International Center for Advanced Studies (ICAS), UNSAM,Campus Miguelete, 25 de Mayo y Francia (1650) Buenos Aires (Argentina); Sborlini, Germán F.R.; Rodrigo, Germán [Instituto de Física Corpuscular, Universitat de València,Consejo Superior de Investigaciones Científicas,Parc Científic, E-46980 Paterna, Valencia (Spain)

    2016-10-11

    We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.

  16. Two-loop current–current operator contribution to the non-leptonic QCD penguin amplitude

    Directory of Open Access Journals (Sweden)

    G. Bell

    2015-11-01

    Full Text Available The computation of direct CP asymmetries in charmless B decays at next-to-next-to-leading order (NNLO in QCD is of interest to ascertain the short-distance contribution. Here we compute the two-loop penguin contractions of the current–current operators Q1,2 and provide a first estimate of NNLO CP asymmetries in penguin-dominated b→s transitions.

  17. Two-loop effective potential for Wess-Zumino model using superfields

    International Nuclear Information System (INIS)

    Santos, R.P. dos; Srivastava, P.P.

    1989-01-01

    For the case of several interacting chiral superfields the propagators for the unconstrained superfield potentials in the 'shifted' theory, where the supersymmetry is explicity broken, are derived in a compact form. They are used to compute the one-loop effective potential in the general case, while a superfield calculation of the renormalized effective potential to two loops for the Wess-Zumino models is performed. (authors) [pt

  18. CHIRON: a package for ChPT numerical results at two loops

    Energy Technology Data Exchange (ETDEWEB)

    Bijnens, Johan [Lund University, Department of Astronomy and Theoretical Physics, Lund (Sweden)

    2015-01-01

    This document describes the package CHIRON which includes two libraries, chiron itself and jbnumlib.chiron is a set of routines useful for two-loop numerical results in chiral perturbation theory (ChPT). It includes programs for the needed one- and two-loop integrals as well as routines to deal with the ChPT parameters. The present version includes everything needed for the masses, decay constants and quark-antiquark vacuum-expectation-values. An added routine calculates consistent values for the masses and decay constants when the pion and kaon masses are varied. In addition a number of finite volume results are included: one-loop tadpole integrals, two-loop sunset integrals and the results for masses and decay constants. The numerical routine library jbnumlib contains the numerical routines used in chiron. Many are to a large extent simple C++ versions of routines in the CERNLIB numerical library. Notable exceptions are the dilogarithm and the Jacobi theta function implementations. This paper describes what is included in CHIRON v0.50. (orig.)

  19. Two-loop renormalization in the standard model, part II. Renormalization procedures and computational techniques

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

    2006-12-15

    In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, are discussed in part III where numerical results, e.g. for the complex poles of the unstable gauge bosons, are shown. An attempt is made to define the running of the electromagnetic coupling constant at the two-loop level. (orig.)

  20. Two-Loop Gluon to Gluon-Gluon Splitting Amplitudes in QCD

    International Nuclear Information System (INIS)

    Bern, Z.

    2004-01-01

    Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g → gg splitting amplitudes in QCD, N = 1, and N = 4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The ε-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/ε pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula

  1. The matrix elements of the potential energy operator between the Sp(2,R) basis generating functions. Near-magic nuclei

    International Nuclear Information System (INIS)

    Filippov, G.F.; Ovcharenko, V.I.; Teryoshin, Yu.V.

    1980-01-01

    For near-magnetic nuclei, the matrix elements of the central exchange nucleon-nucleon interaction potential energy operator between the generating functions of the total basis of the Sn are obtained. The basis states are highest weigt vectorsp(2,R) irreducible representatio of the SO(3) irredicible representation and in addition, have a definite O(A-1) symmetry. The Sp(2,R) basis generating matrix elements simplify essentially the problem of calculating the spectrum of collective excitations of the atomic nucleus over an intrinsic function of definite O(A-1) symmetry

  2. Regularization independent analysis of the origin of two loop contributions to N=1 Super Yang-Mills beta function

    Energy Technology Data Exchange (ETDEWEB)

    Fargnoli, H.G.; Sampaio, Marcos; Nemes, M.C. [Federal University of Minas Gerais, ICEx, Physics Department, P.O. Box 702, Belo Horizonte, MG (Brazil); Hiller, B. [Coimbra University, Faculty of Science and Technology, Physics Department, Center of Computational Physics, Coimbra (Portugal); Baeta Scarpelli, A.P. [Setor Tecnico-Cientifico, Departamento de Policia Federal, Lapa, Sao Paulo (Brazil)

    2011-05-15

    We present both an ultraviolet and an infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out, whilst the beta function receives contributions of infrared modes. (orig.)

  3. Regularization independent analysis of the origin of two loop contributions to N=1 Super Yang-Mills beta function

    International Nuclear Information System (INIS)

    Fargnoli, H.G.; Sampaio, Marcos; Nemes, M.C.; Hiller, B.; Baeta Scarpelli, A.P.

    2011-01-01

    We present both an ultraviolet and an infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out, whilst the beta function receives contributions of infrared modes. (orig.)

  4. Micromechanics of deformation of metallic-glass-matrix composites from in situ synchrotron strain measurements and finite element modeling

    International Nuclear Information System (INIS)

    Ott, R.T.; Sansoz, F.; Molinari, J.F.; Almer, J.; Ramesh, K.T.; Hufunagel, T.C.

    2005-01-01

    In situ X-ray scattering and finite element modeling (FEM) were used to examine the micromechanics of deformation of in situ formed metallic-glass-matrix composites consisting of Ta-rich particles dispersed in an amorphous matrix. The strain measurements show that under uniaxial compression the second-phase particles yield at an applied stress of approx. 325 MPa. After yielding, the particles do not strain harden significantly; we show that this is due to an increasingly hydrostatic stress state arising from the lateral constraint on deformation of the particles imposed by the elastic matrix. Shear band initiation in the matrix is not due to the difference in elastic properties between the matrix and the particles. Rather, the development of a plastic misfit strain causes stress concentrations around the particles, resulting in localized yielding of the matrix by shear band formation at an applied stress of approx. 1450 MPa, considerably lower than the macroscopic yield stress of the composite (approx. 1725 MPa). Shear bands do not propagate at the lower stress because the yield criterion of the matrix is only satisfied in the region immediately around the particles. At the higher stresses, the yield criterion is satisfied in large regions of the matrix, allowing extensive shear band propagation and significant macroscopic plastic deformation. However, the presence of the particles makes the stress state highly inhomogeneous, which may partially explain why fracture is suppressed in the composite, allowing the development of large plastic strains

  5. Dynamic-stiffness matrix of embedded and pile foundations by indirect boundary-element method

    International Nuclear Information System (INIS)

    Wolf, J.P.; Darbre, G.R.

    1984-01-01

    The boundary-integral equation method is well suited for the calculation of the dynamic-stiffness matrix of foundations embedded in a layered visco-elastic halfspace (or a transmitting boundary of arbitrary shape), which represents an unbounded domain. It also allows pile groups to be analyzed, taking pile-soil-pile interaction into account. The discretization of this boundary-element method is restricted to the structure-soil interface. All trial functions satisfy exactly the field equations and the radiation condition at infinity. In the indirect boundary-element method distributed source loads of initially unknown intensities act on a source line located in the excavated part of the soil and are determined such that the prescribed boundary conditions on the structure-soil interface are satisfied in an average sense. In the two-dimensional case the variables are expanded in a Fourier integral in the wave number domain, while in three dimensions, Fourier series in the circumferential direction and bessel functions of the wave number domain, while in three dimensions, Fourier series in the circumferential direction and Bessel functions of the wave number in the radial direction are selected. Accurate results arise with a small number of parameters of the loads acting on a source line which should coincide with the structure-soil interface. In a parametric study the dynamic-stiffness matrices of rectangular foundations of various aspect ratios embedded in a halfplane and in a layer built-in at its base are calculated. For the halfplane, the spring coefficients for the translational directions hardly depend on the embedment, while the corresponding damping coefficients increase for larger embedments, this tendency being more pronounced in the horizontal direction. (orig.)

  6. Generating matrix elements of the hamiltonian of the algebraic version of resonating group method on intrinsic wave functions with various oscillator lengths

    International Nuclear Information System (INIS)

    Badalov, S.A.; Filippov, G.F.

    1986-01-01

    The receipts to calculate the generating matrix elements of the algebraic version of resonating group method (RGM) are given for two- and three-cluster nucleon systems, the center of mass motion being separeted exactly. For the Hamiltonian with Gaussian nucleon-nucleon potential dependence the generating matrix elements of the RGM algebraic version can be written down explictly if matrix elements of the corresponding system on wave functions of the Brink cluster model are known

  7. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L =1

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-01

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  8. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1.

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-21

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  9. K →π matrix elements of the chromomagnetic operator on the lattice

    Science.gov (United States)

    Constantinou, M.; Costa, M.; Frezzotti, R.; Lubicz, V.; Martinelli, G.; Meloni, D.; Panagopoulos, H.; Simula, S.; ETM Collaboration

    2018-04-01

    We present the results of the first lattice QCD calculation of the K →π matrix elements of the chromomagnetic operator OCM=g s ¯ σμ νGμ νd , which appears in the effective Hamiltonian describing Δ S =1 transitions in and beyond the standard model. Having dimension five, the chromomagnetic operator is characterized by a rich pattern of mixing with operators of equal and lower dimensionality. The multiplicative renormalization factor as well as the mixing coefficients with the operators of equal dimension have been computed at one loop in perturbation theory. The power divergent coefficients controlling the mixing with operators of lower dimension have been determined nonperturbatively, by imposing suitable subtraction conditions. The numerical simulations have been carried out using the gauge field configurations produced by the European Twisted Mass Collaboration with Nf=2 +1 +1 dynamical quarks at three values of the lattice spacing. Our result for the B parameter of the chromomagnetic operator at the physical pion and kaon point is BCMOK π=0.273 (69 ) , while in the SU(3) chiral limit we obtain BCMO=0.076 (23 ) . Our findings are significantly smaller than the model-dependent estimate BCMO˜1 - 4 , currently used in phenomenological analyses, and improve the uncertainty on this important phenomenological quantity.

  10. Phenomenological renormalization of free nucleon-nucleon interaction. [Sussex matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Prakash, M; Waghmare, Y R [Indian Inst. of Tech., Kanpur. Dept. of Physics; Mehrotra, I [Allahabad Univ. (India). Dept. of Physics

    1976-08-01

    Low-lying spectra of /sup 6/Li, /sup 18/F, /sup 18/O, /sup 42/Sc, /sup 42/Ca, /sup 58/Ni and /sup 92/Zr are studied with Sussex matrix elements (SME) and their central, spin-orbit and tensor components. It is observed that major contribution to level energies comes from the central part, while the tensor part provides the finer details of spectra, particularly for T = 0 levels. The spin-orbit part does not make any appreciable contribution to level energies. A phenomenological renormalization fo the SME is carried out to improve the agreement with the experimental results. It turns out that some of the low-lying T = 0 levels can be satisfactorily described if the SME in the /sup 3/S/sub 1/ relative state are made (1+..cap alpha..) times their bare interaction value, where ..cap alpha.. is a constant to be determined from a comparison with experimental level energies. Similarly, for T = 1 levels, better agreement with the experimental results is obtained if a delta-function-plus-quadrupole interaction is added to the SME.

  11. Investigation of Product Performance of Al-Metal Matrix Composites Brake Disc using Finite Element Analysis

    International Nuclear Information System (INIS)

    Fatchurrohman, N; Marini, C D; Suraya, S; Iqbal, AKM Asif

    2016-01-01

    The increasing demand of fuel efficiency and light weight components in automobile sectors have led to the development of advanced material parts with improved performance. A specific class of MMCs which has gained a lot of attention due to its potential is aluminium metal matrix composites (Al-MMCs). Product performance investigation of Al- MMCs is presented in this article, where an Al-MMCs brake disc is analyzed using finite element analysis. The objective is to identify the potentiality of replacing the conventional iron brake disc with Al-MMCs brake disc. The simulation results suggested that the MMCs brake disc provided better thermal and mechanical performance as compared to the conventional cast iron brake disc. Although, the Al-MMCs brake disc dissipated higher maximum temperature compared to cast iron brake disc's maximum temperature. The Al-MMCs brake disc showed a well distributed temperature than the cast iron brake disc. The high temperature developed at the ring of the disc and heat was dissipated in circumferential direction. Moreover, better thermal dissipation and conduction at brake disc rotor surface played a major influence on the stress. As a comparison, the maximum stress and strain of Al-MMCs brake disc was lower than that induced on the cast iron brake disc. (paper)

  12. Quarkonium polarization and the long distance matrix elements hierarchies using jet substructure

    Science.gov (United States)

    Dai, Lin; Shrivastava, Prashant

    2017-08-01

    We investigate the quarkonium production mechanisms in jets at the LHC, using the fragmenting jet functions (FJF) approach. Specifically, we discuss the jet energy dependence of the J /ψ production cross section at the LHC. By comparing the cross sections for the different NRQCD production channels (1S0[8], 3S1[8], 3PJ[8], and 3cripts>S1[1]), we find that at fixed values of energy fraction z carried by the J /ψ , if the normalized cross section is a decreasing function of the jet energy, in particular for z >0.5 , then the depolarizing 1S0[8] must be the dominant channel. This makes the prediction made in [Baumgart et al., J. High Energy Phys. 11 (2014) 003, 10.1007/JHEP11(2014)003] for the FJF's also true for the cross section. We also make comparisons between the long distance matrix elements extracted by various groups. This analysis could potentially shed light on the polarization properties of the J /ψ production in high pT region.

  13. Automated evaluation of matrix elements between contracted wavefunctions: A Mathematica version of the FRODO program

    Science.gov (United States)

    Angeli, C.; Cimiraglia, R.

    2013-02-01

    A symbolic program performing the Formal Reduction of Density Operators (FRODO), formerly developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme, has been rewritten in Mathematica. New version : A program summaryProgram title: FRODO Catalogue identifier: ADV Y _v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVY_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3878 No. of bytes in distributed program, including test data, etc.: 170729 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which the Mathematica computer algebra system can be installed Operating system: Linux Classification: 5 Catalogue identifier of previous version: ADV Y _v1_0 Journal reference of previous version: Comput. Phys. Comm. 171(2005)63 Does the new version supersede the previous version?: No Nature of problem. In order to improve on the CAS-SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICFs) which are obtained by application of the excitation operators to the reference CAS-SCF wavefunction. The previous formulation of such matrix elements in the MuPAD computer algebra system, has been rewritten using Mathematica. Solution method: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICFs and in the electronic Hamiltonian expressed in the second quantization formalism. Reasons for new version: Some years ago we published in this journal a couple of papers [1, 2

  14. Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

    International Nuclear Information System (INIS)

    Ablinger, J.; Schneider, C.; Manteuffel, A. von

    2015-09-01

    Three loop ladder and V-topology diagrams contributing to the massive operator matrix element A Qg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

  15. A measurement of the top quark mass with a matrix element method

    Energy Technology Data Exchange (ETDEWEB)

    Gibson, Adam Paul [Univ. of California, Berkeley, CA (United States)

    2006-01-01

    The authors present a measurement of the mass of the top quark. The event sample is selected from proton-antiproton collisions, at 1.96 TeV center-of-mass energy, observed with the CDF detector at Fermilab's Tevatron. They consider a 318 pb-1 dataset collected between March 2002 and August 2004. They select events that contain one energetic lepton, large missing transverse energy, exactly four energetic jets, and at least one displaced vertex b tag. The analysis uses leading-order t$\\bar{t}$ and background matrix elements along with parameterized parton showering to construct event-by-event likelihoods as a function of top quark mass. From the 63 events observed with the 318 pb-1 dataset they extract a top quark mass of 172.0 ± 2.6(stat) ± 3.3(syst) GeV/c2 from the joint likelihood. The mean expected statistical uncertainty is 3.2 GeV/c2 for m $\\bar{t}$ = 178 GTeV/c2 and 3.1 GeV/c2 for m $\\bar{t}$ = 172.5 GeV/c2. The systematic error is dominated by the uncertainty of the jet energy scale.

  16. Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

    Science.gov (United States)

    Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

    2016-05-01

    Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

  17. Study on thermal conductivity of HTR spherical fuel element matrix graphite

    International Nuclear Information System (INIS)

    Zhang Kaihong; Liu Xiaoxue; Zhao Hongsheng; Li Ziqiang; Tang Chunhe

    2014-01-01

    Taking the spherical fuel element matrix graphite ball samples as an example, this paper introduced the principle and method of laser thermal conductivity meter, as well as the specific heat capacity, and analyzed the effects of different test methods and sampling methods on the thermal conductivities at 1000 ℃ of graphite material. The experimental results show that the thermal conductivities of graphite materials tested by synchronous thermal analyzer combining with laser thermal conductivity meter were different from that directly by laser thermal conductivity meter, the former was more reliable and accurate than the later; When sampling from different positions, central samples had higher thermal conductivities than edging samples, which was related to the material density and porosity at the different locations; the thermal conductivities had obvious distinction between samples from different directions, which was because the layer structure of polycrystalline graphite preferred orientation under pressure, generally speaking, the thermal conductivities perpendicular to the molding direction were higher than that parallel to the molding direction. Besides this, the test results show that the thermal conductivities of all the graphite material samples were greater than 30 W/(m (K), achieving the thermal performance index of high temperature gas cooled reactor. (authors)

  18. Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers

    Energy Technology Data Exchange (ETDEWEB)

    Bury, Marcin; Hameren, Andreas van; Kutak, Krzysztof; Sapeta, Sebastian [Polish Academy of Sciences, Institute of Nuclear Physics, Cracow (Poland); Jung, Hannes [Polish Academy of Sciences, Institute of Nuclear Physics, Cracow (Poland); DESY, Hamburg (Germany); Serino, Mirko [Polish Academy of Sciences, Institute of Nuclear Physics, Cracow (Poland); Ben Gurion University of the Negev, Department of Physics, Beersheba (Israel)

    2018-02-15

    A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the Cascade package for the full TMD parton shower, final state shower and hadronization from Pythia where events in HEPMC format are produced. We have determined a full set of TMD parton densities and developed an initial state TMD parton shower, including all flavors following the TMD distribution. As an example of application we have calculated the azimuthal de-correlation of high p{sub t} dijets as measured at the LHC and found very good agreement with the measurement when including initial state TMD parton showers together with conventional final state parton showers and hadronization. (orig.)

  19. Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Blümlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Schneider, Carsten [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Wißbrock, Fabian [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)

    2014-08-15

    We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version of the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators, new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∼30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N∈C. Integrals with a power-like divergence in N-space ∝a{sup N},a∈R,a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.

  20. Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Blümlein, Johannes; Raab, Clemens; Schneider, Carsten; Wißbrock, Fabian

    2014-01-01

    We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version of the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators, new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∼30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N∈C. Integrals with a power-like divergence in N-space ∝a N ,a∈R,a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions

  1. Matrix elements of four-quark operators relevant to life time difference ΔΓBs from QCD sum rules

    International Nuclear Information System (INIS)

    Huang, C.S.; Zhang Ailin; Zhu, S.L.

    2001-01-01

    We extract the matrix elements of four-quark operators O L,S relevant to the B s and anti B s life time difference from QCD sum rules. We find that the vacuum saturation approximation works reasonably well, i.e., within 10%. We discuss the implications of our results and compare them with a recent lattice QCD determination. (orig.)

  2. Study of color-octet matrix elements through J/ψ production in e{sup +}e{sup -} annihilation

    Energy Technology Data Exchange (ETDEWEB)

    Li, Yi-Jie; Xu, Guang-Zhi; Zhang, Pan-Pan; Liu, Kui-Yong [Liaoning University, Department of Physics, Shenyang (China); Zhang, Yu-Jie [Beihang University, School of Physics, Beijing (China); CAS Center for Excellence in Particle Physics, Beijing (China)

    2017-09-15

    In this paper, the color-octet long distance matrix elements are studied through the inclusive J/ψ production in e{sup +}e{sup -} annihilation within the framework of non-relativistic QCD factorization. The calculations are up-to next-to-leading order with the radiative and relativistic corrections in the energy region of the B-factory and the near-threshold region of 4.6-5.6 GeV. A constraint of the long distance matrix elements (left angle {sup 1}S{sub 0}{sup 8} right angle, left angle {sup 3}P{sub 0}{sup 8} right angle) is obtained. Through our estimation, the P-wave color-octet matrix element (left angle 0 vertical stroke {sup 3}P{sup 8}{sub 0} vertical stroke 0 right angle) should be of the order of 0.008m{sub c}{sup 2} GeV{sup 3} or less. The constrained region is not compatible with the values of the long distance matrix elements fitted at hadron colliders. (orig.)

  3. An approximate method for calculating electron-phonon matrix element of a disordered transition metal and relevant comments on superconductivity

    International Nuclear Information System (INIS)

    Zhang, L.

    1981-08-01

    A method based on the tight-binding approximation is developed to calculate the electron-phonon matrix element for the disordered transition metals. With the method as a basis the experimental Tsub(c) data of the amorphous transition metal superconductors are re-analysed. Some comments on the superconductivity of the disordered materials are given

  4. A new Eulerian-Lagrangian finite element simulator for solute transport in discrete fracture-matrix systems

    Energy Technology Data Exchange (ETDEWEB)

    Birkholzer, J.; Karasaki, K. [Lawrence Berkeley National Lab., CA (United States). Earth Sciences Div.

    1996-07-01

    Fracture network simulators have extensively been used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful fracture network simulator with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The fracture network simulator used in TRIPOLY features a mixed Lagrangian-Eulerian solution scheme for the transport in fractures, combined with an adaptive gridding technique to account for sharp concentration fronts. The fracture-matrix interaction is calculated with an efficient method which has been successfully used in the past for dual-porosity models. Discrete fractures and matrix blocks are treated as two different systems, and the interaction is modeled by introducing sink/source terms in both systems. It is assumed that diffusive transport in the matrix can be approximated as a one-dimensional process, perpendicular to the adjacent fracture surfaces. A direct solution scheme is employed to solve the coupled fracture and matrix equations. The newly developed combination of the fracture network simulator and the fracture-matrix interaction module allows for detailed studies of spreading processes in fractured porous rock. The authors present a sample application which demonstrate the codes ability of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size and shape.

  5. Plasma-related matrix effects in inductively coupled plasma--atomic emission spectrometry by group I and group II matrix-elements

    International Nuclear Information System (INIS)

    Chan, George C.-Y.; Chan, W.-T.

    2003-01-01

    The effects of Na, K, Ca and Ba matrices on the plasma excitation conditions in inductively coupled plasma-atomic emission spectrometry (ICP-AES) were studied. Normalized relative intensity was used to indicate the extent of the plasma-related matrix effects. The group I matrices have no effects on the plasma excitation conditions. In contrast, the group II matrices depress the normalized relative intensities of some spectral lines. Specifically, the Group II matrices have no effects on the normalized relative intensity of atomic lines of low upper energy level (soft lines), but reduce the normalized relative intensity of some ionic lines and atomic lines of high energy level (hard lines). The Group II matrices seem to shift the Saha balance of the analytes only; no shift in the Boltzmann balance was observed experimentally. Moreover, for some ionic lines with sum of ionization and excitation potentials close to the ionization potential of argon (15.75 eV), the matrix effect is smaller than other ionic lines of the same element. The reduced matrix effects may be attributed qualitatively to charge transfer excitation mechanism of these ionic lines. Charge transfer reaction renders ionic emission lines from the quasi-resonant levels similar in characteristics of atomic lines. The contribution of charge transfer relative to excitation by other non-specific excitation mechanisms (via Saha balance and Boltzmann balance) determines the degree of atomic behavior of a quasi-resonant level. A significant conclusion of this study is that plasma-related matrix effect depends strongly on the excitation mechanism of a spectral line. Since, in general, more than one excitation mechanism may contribute to the overall excitation of an emission line, the observed matrix effects reflect the sum of the effects due to individual excitation mechanisms. Excitation mechanisms, in addition to the often-used total excitation energy, should be considered in matrix effect studies

  6. Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

    International Nuclear Information System (INIS)

    Bajnok, Zoltán; Balog, János; Correa, Diego H.; Hegedűs, Árpád; Massolo, Fidel I. Schaposnik; Tóth, Gábor Zsolt

    2014-01-01

    The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in http://dx.doi.org/10.1007/JHEP08(2012)134http://dx.doi.org/10.1007/JHEP10(2013)135 to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension

  7. Local integrands for two-loop all-plus Yang-Mills amplitudes

    International Nuclear Information System (INIS)

    Badger, Simon; Mogull, Gustav; Peraro, Tiziano

    2016-01-01

    We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.

  8. Reggeon field theory at D = 2 in two-loop approximation

    International Nuclear Information System (INIS)

    Eremyan, Sh.S.; Nazaryan, A.E.

    1982-01-01

    A general method of constructing an explicit representation is developed for the pomeron propagator in the presence of additional parameters, such as the pomeron production threshold xi 0 , momentum transfer K vector or the intercept shift delta 0 . The method is shown to be applicable in both one-loop and two-loop approximations. The obtained general formulae allow to consider the pomeron propagator in both asymptotic region and the region of the perturbation theory applicability. Besides, they provide the smooth matching of both these regions. The observed values are calculated, and the results connected with asymptotically high energies are discussed

  9. The two-loop symbol of all multi-Regge regions

    International Nuclear Information System (INIS)

    Bargheer, Till; Schomerus, Volker; Papathanasiou, Georgios

    2015-12-01

    We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N= 4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.

  10. Local integrands for two-loop all-plus Yang-Mills amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Badger, Simon; Mogull, Gustav; Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh, James Clerk Maxwell Building,Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)

    2016-08-09

    We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.

  11. The two-loop symbol of all multi-Regge regions

    International Nuclear Information System (INIS)

    Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker

    2016-01-01

    We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.

  12. A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

    International Nuclear Information System (INIS)

    Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O’Connell, Donal

    2015-01-01

    We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

  13. New perturbative upper bound on MH from fermionic Higgs decays at two loops

    International Nuclear Information System (INIS)

    Durand, L.; Kniehl, B.A.; Riesselmann, K.

    1993-09-01

    We present the dominant two-loop O (G F 2 M H 4 ) electroweak corrections to the fermionic decay widths of a high-mass Higgs boson in the Standard Model. The corrections are negative and quite significant, and are larger in magnitude than the one-loop electroweak corrections for M H > or ∼400 GeV. This indicates the onset of a breakdown of perturbation theory in the Higgs sector of the Standard Model at this surprisingly low value of the Higgs boson mass. (orig.)

  14. Electroweak two-loop corrections to the effective weak mixing angle

    International Nuclear Information System (INIS)

    Awramik, Malgorzata; Czakon, Michal; Freitas, Ayres

    2006-01-01

    Recently exact results for the complete electroweak two-loop contributions to the effective weak mixing angle were published. This paper illustrates the techniques used for this computation, in particular the methods for evaluating the loop diagrams and the proper definition of Z-pole observables at next-to-next-to-leading order. Numerical results are presented in terms of simple parametrization formulae and compared in detail with a previous result of an expansion up to next-to-leading order in the top-quark mass. Finally, an estimate of the remaining theoretical uncertainties from unknown higher-order corrections is given

  15. A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

    Energy Technology Data Exchange (ETDEWEB)

    Badger, Simon; Mogull, Gustav; Ochirov, Alexander [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); O’Connell, Donal [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 (United States)

    2015-10-09

    We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

  16. New two-loop contribution to electric dipole moment in supersymmetric theories

    CERN Document Server

    Chang, Darwin; Pilaftsis, Apostolos; Chang, Darwin; Keung, Wai-Yee; Pilaftsis, Apostolos

    1999-01-01

    We calculate a new type of two-loop contributions to the electric dipole moments of the electron and neutron in supersymmetric theories. The new contributions are originated from the potential CP violation in the trilinear couplings of the Higgs bosons to the scalar-top or the scalar-bottom quarks. These couplings were previously very weakly constrained. The electric dipole moments are induced through a mechanism analogous to that due to Barr and Zee. We find observable effects for a sizeable portion of the parameter space related to the third generation scalar-quarks in the minimal supersymmetric standard model which cannot be excluded by earlier considerations.

  17. Reduction of the N-component scalar model at the two-loop level

    International Nuclear Information System (INIS)

    Jakovac, A.

    1996-01-01

    Dimensional reduction of high temperature field theories improves IR features of their perturbative treatment. A crucial question is the following: What three-dimensional theory is representing the full system the most faithful way? A careful investigation of the induced three-dimensional counterterm structure of the finite temperature 4D O(N) symmetric scalar theory at the two-loop level leads to proposing the presence of nonlocal operators in the effective theory. A three-dimensional matching process is applied for the construction of the optimal local, superrenormalizable approximation. copyright 1996 The American Physical Society

  18. Description of the two-loop RELAP5 model of the L-Reactor at the Savannah River Site

    International Nuclear Information System (INIS)

    Cozzuol, J.M.; Davis, C.B.

    1989-12-01

    A two-loop RELAP5 input model of the L-Reactor at the Savannah River Site (SRS) was developed to support thermal-hydraulic analysis of SRS reactors. The model was developed to economically evaluate potential design changes. The primary simplifications in the model were in the number of loops and the detail in the moderator tank. The six loops in the reactor were modeled with two loops, one representing a single loop and the other representing five combined loops. The model has undergone a quality assurance review. This report describes the two-loop model, its limitations, and quality assurance. 29 refs., 18 figs., 10 tabs

  19. The NUMEN project: NUclear Matrix Elements for Neutrinoless double beta decay

    Science.gov (United States)

    Cappuzzello, F.; Agodi, C.; Cavallaro, M.; Carbone, D.; Tudisco, S.; Lo Presti, D.; Oliveira, J. R. B.; Finocchiaro, P.; Colonna, M.; Rifuggiato, D.; Calabretta, L.; Calvo, D.; Pandola, L.; Acosta, L.; Auerbach, N.; Bellone, J.; Bijker, R.; Bonanno, D.; Bongiovanni, D.; Borello-Lewin, T.; Boztosun, I.; Brunasso, O.; Burrello, S.; Calabrese, S.; Calanna, A.; Chávez Lomelí, E. R.; D'Agostino, G.; De Faria, P. N.; De Geronimo, G.; Delaunay, F.; Deshmukh, N.; Ferreira, J. L.; Fisichella, M.; Foti, A.; Gallo, G.; Garcia-Tecocoatzi, H.; Greco, V.; Hacisalihoglu, A.; Iazzi, F.; Introzzi, R.; Lanzalone, G.; Lay, J. A.; La Via, F.; Lenske, H.; Linares, R.; Litrico, G.; Longhitano, F.; Lubian, J.; Medina, N. H.; Mendes, D. R.; Moralles, M.; Muoio, A.; Pakou, A.; Petrascu, H.; Pinna, F.; Reito, S.; Russo, A. D.; Russo, G.; Santagati, G.; Santopinto, E.; Santos, R. B. B.; Sgouros, O.; da Silveira, M. A. G.; Solakci, S. O.; Souliotis, G.; Soukeras, V.; Spatafora, A.; Torresi, D.; Magana Vsevolodovna, R.; Yildirim, A.; Zagatto, V. A. B.

    2018-05-01

    The article describes the main achievements of the NUMEN project together with an updated and detailed overview of the related R&D activities and theoretical developments. NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the fact that the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave functions in the two types of processes and the formal similarity of the transition operators. First experimental results obtained at the INFN-LNS laboratory for the 40Ca(18O,18Ne)40Ar reaction at 270MeV give an encouraging indication on the capability of the proposed technique to access relevant quantitative information. The main experimental tools for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer. The former is used for the acceleration of the required high resolution and low emittance heavy-ion beams and the latter is the large acceptance magnetic spectrometer for the detection of the ejectiles. The use of the high-order trajectory reconstruction technique, implemented in MAGNEX, allows to reach the experimental resolution and sensitivity required for the accurate measurement of the DCE cross sections at forward angles. However, the tiny values of such cross sections and the resolution requirements demand beam intensities much larger than those manageable with the present facility. The on-going upgrade of the INFN-LNS facilities in this perspective is part of the NUMEN project and will be discussed in the article.

  20. Two-loop renormalization group analysis of supersymmetric SO(10) models with an intermediate scale

    International Nuclear Information System (INIS)

    Bastero-Gil, M.; Brahmachari, B.

    1996-03-01

    Two-loop evolutions of the gauge couplings in a class of intermediate scale supersymmetric SO(10) models including the effect of third generation Yukawa couplings are studied. The unification scale, the intermediate scale and the value of the unification gauge coupling in these models are calculated and the gauge boson mediated proton decay rates are estimated. In some cases the predicted proton lifetime turns out to be in the border-line of experimental limit. The predictions of the top quark mass, the mass ratio m b (m b )/m τ (m τ ) from the two-loop evolution of Yukawa couplings and the mass of the left handed neutrino via see-saw mechanism are summarized. The lower bounds on the ratio of the VEVs of the two low energy doublets (tan β) from the requirement of the perturbative unitarity of the top quark Yukawa coupling up to the grand unification scale are also presented. All the predictions have been compared with those of the one-step unified theory. (author). 33 refs, 5 figs, 1 tab

  1. The impact of two-loop effects on the scenario of MSSM Higgs alignment without decoupling

    Energy Technology Data Exchange (ETDEWEB)

    Haber, Howard E.; Stefaniak, Tim [University of California, Santa Cruz Institute for Particle Physics (SCIPP) and Department of Physics, Santa Cruz, CA (United States); Heinemeyer, Sven [Campus of International Excellence UAM+CSIC, Madrid (Spain); Universidad Autonoma de Madrid, Instituto de Fisica Teorica, (UAM/CSIC), Madrid (Spain); Instituto de Fisica de Cantabria (CSIC-UC), Santander (Spain)

    2017-11-15

    In multi-Higgs models, the properties of one neutral scalar state approximate those of the Standard Model (SM) Higgs boson in a limit where the corresponding scalar field is roughly aligned in field space with the scalar doublet vacuum expectation value. In a scenario of alignment without decoupling, a SM-like Higgs boson can be accompanied by additional scalar states whose masses are of a similar order of magnitude. In the Minimal Supersymmetric Standard Model (MSSM), alignment without decoupling can be achieved due to an accidental cancellation of tree-level and radiative loop-level effects. In this paper we assess the impact of the leading two-loop O(α{sub s}h{sub t}{sup 2}) corrections on the Higgs alignment condition in the MSSM. These corrections are sizable and important in the relevant regions of parameter space and furthermore give rise to solutions of the alignment condition that are not present in the approximate one-loop description. We provide a comprehensive numerical comparison of the alignment condition obtained in the approximate one-loop and two-loop approximations, and discuss its implications for phenomenologically viable regions of the MSSM parameter space. (orig.)

  2. Testing SUSY at the LHC: Electroweak and Dark matter fine tuning at two-loop order

    CERN Document Server

    Cassel, S; Ross, G G

    2010-01-01

    In the framework of the Constrained Minimal Supersymmetric Standard Model (CMSSM) we evaluate the electroweak fine tuning measure that provides a quantitative test of supersymmetry as a solution to the hierarchy problem. Taking account of current experimental constraints we compute the fine tuning at two-loop order and determine the limits on the CMSSM parameter space and the measurements at the LHC most relevant in covering it. Without imposing the LEPII bound on the Higgs mass, it is shown that the fine tuning computed at two-loop has a minimum $\\Delta=8.8$ corresponding to a Higgs mass $m_h=114\\pm 2$ GeV. Adding the constraint that the SUSY dark matter relic density should be within present bounds we find $\\Delta=15$ corresponding to $m_h=114.7\\pm 2$ GeV and this rises to $\\Delta=17.8$ ($m_h=115.9\\pm 2$ GeV) for SUSY dark matter abundance within 3$\\sigma$ of the WMAP constraint. We extend the analysis to include the contribution of dark matter fine tuning. In this case the overall fine tuning and Higgs mas...

  3. Two-loop scale-invariant scalar potential and quantum effective operators

    CERN Document Server

    Ghilencea, D.M.

    2016-11-29

    Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\\sigma$). Its vev $\\langle\\sigma\\rangle$ generates the DR subtraction scale ($\\mu\\sim\\langle\\sigma\\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\\mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\\mu$=fixed scale). These operators have the form: $\\phi^6/\\sigma^2$, $\\phi^8/\\sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $\\langle\\sigma\\rangle\\gg \\langle\\phi\\rangle$, where such hierarchy is arranged by {\\it one} initial, classical tuning. These operators emerge at the quantum...

  4. Infrared divergences and harmonic anomalies in the two-loop superstring effective action

    CERN Document Server

    Pioline, Boris

    2015-01-01

    We analyze the pertubative contributions to the $D^4 R^4$ and $D^6 R^4$ couplings in the low-energy effective action of type II string theory compactified on a torus $T^d$, with particular emphasis on two-loop corrections. In general, it is necessary to introduce an infrared cut-off $\\Lambda$ to separate local interactions from non-local effects due to the exchange of massless states. We identify the degenerations of the genus-two Riemann surface which are responsible for power-like dependence on $\\Lambda$, and give an explicit prescription for extracting the $\\Lambda$-independent effective couplings. These renormalized couplings are then shown to be eigenmodes of the Laplace operator with respect to the torus moduli, up to computable anomalous source terms arising in the presence of logarithmic divergences, in precise agreement with predictions from U-duality. Our results for the two-loop $D^6 R^4$ contribution also probe essential properties of the Kawazumi-Zhang invariant

  5. Infrared divergences and harmonic anomalies in the two-loop superstring effective action

    Energy Technology Data Exchange (ETDEWEB)

    Pioline, Boris [CERN PH-TH,Case C01600, CERN, CH-1211 Geneva 23 (Switzerland); Sorbonne Universités,UPMC Université Paris 6, UMR 7589, F-75005 Paris (France); Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589,Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris cedex 05 (France); Russo, Rodolfo [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom)

    2015-12-16

    We analyze the pertubative contributions to the D{sup 4}R{sup 4} and D{sup 6}R{sup 4} couplings in the low-energy effective action of type II string theory compactified on a torus T{sup d}, with particular emphasis on two-loop corrections. In general, it is necessary to introduce an infrared cut-off Λ to separate local interactions from non-local effects due to the exchange of massless states. We identify the degenerations of the genus-two Riemann surface which are responsible for power-like dependence on Λ, and give an explicit prescription for extracting the Λ-independent effective couplings. These renormalized couplings are then shown to be eigenmodes of the Laplace operator with respect to the torus moduli, up to computable anomalous source terms arising in the presence of logarithmic divergences, in precise agreement with predictions from U-duality. Our results for the two-loop D{sup 6}R{sup 4} contribution also probe essential properties of the Kawazumi-Zhang invariant.

  6. Dynamical symmetry breaking of λφ4 theory in the two loop effective potential

    International Nuclear Information System (INIS)

    Yang Jifeng; Ruan Jianhong

    2002-01-01

    The two loop effective potential of massless λφ 4 theory is presented in several regularization and renormalization prescriptions and the dynamical symmetry breaking solution is obtained in the strong-coupling situation in several prescriptions except the Coleman-Weinberg prescription. The beta function in the broken phase becomes negative and the UV fixed point turns out to be a strong-coupling one, and its numeric value varies with the renormalization prescriptions, a detail which is different from the asymptotic-free solution in the one loop case. The symmetry-breaking phase is shown to be an entirely strong-coupling phase. The reason for the relevance of the renormalization prescriptions is shown to be due to the nonperturbative nature of the effective potential. We also reanalyze the two loop effective potential by adopting a differential equation approach based on the understanding that all the quantum field theories are ill-defined formulations of the 'low-energy' effective theories of a complete underlying theory. The relevance of the prescriptions of fixing the local ambiguities to physical properties such as symmetry breaking is further emphasized. We also tentatively propose a rescaling insensitivity argument for fixing the quadratic ambiguities. Some detailed properties of the strongly coupled broken phase and related issues are discussed

  7. Two-loop corrections to the ρ parameter in Two-Higgs-Doublet models

    Energy Technology Data Exchange (ETDEWEB)

    Hessenberger, Stephan; Hollik, Wolfgang [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany)

    2017-03-15

    Models with two scalar doublets are among the simplest extensions of the Standard Model which fulfill the relation ρ = 1 at lowest order for the ρ parameter as favored by experimental data for electroweak observables allowing only small deviations from unity. Such small deviations Δρ originate exclusively from quantum effects with special sensitivity to mass splittings between different isospin components of fermions and scalars. In this paper the dominant two-loop electroweak corrections to Δρ are calculated in the CP-conserving THDM, resulting from the top-Yukawa coupling and the self-couplings of the Higgs bosons in the gauge-less limit. The on-shell renormalization scheme is applied. With the assumption that one of the CP-even neutral scalars represents the scalar boson observed by the LHC experiments, with standard properties, the two-loop non-standard contributions in Δρ can be separated from the standard ones. These contributions are of particular interest since they increase with mass splittings between non-standard Higgs bosons and can be additionally enhanced by tanβ and λ{sub 5}, an additional free coefficient of the Higgs potential, and can thus modify the one-loop result substantially. Numerical results are given for the dependence on the various non-standard parameters, and the influence on the calculation of electroweak precision observables is discussed. (orig.)

  8. Two-loop disorder effects on the nematic quantum criticality in d-wave superconductors

    International Nuclear Information System (INIS)

    Wang, Jing

    2015-01-01

    The gapless nodal fermions exhibit non-Fermi liquid behaviors at the nematic quantum critical point that is supposed to exist in some d-wave cuprate superconductors. This non-Fermi liquid state may be turned into a disorder-dominated diffusive metal if the fermions also couple to a disordered potential that generates a relevant perturbation in the sense of renormalization group theory. It is therefore necessary to examine whether a specific disorder is relevant or not. We study the interplay between critical nematic fluctuation and random chemical potential by performing renormalization group analysis. The parameter that characterizes the strength of random chemical potential is marginal at the one-loop level, but becomes marginally relevant after including the two-loop corrections. Thus even weak random chemical potential leads to diffusive motion of nodal fermions and the significantly critical behaviors of physical implications, since the strength flows eventually to large values at low energies. - Highlights: • The gapless nodal fermions exhibit non-Fermi liquid behaviors at the nematic QCP. • The strength of random chemical potential is marginal at the one-loop level. • The strength becomes marginally relevant after including the two-loop corrections. • The diffusive metallic state is induced by the marginally relevant disorder. • The behaviors of some physical observables are presented at the nematic QCP

  9. First determination of the quark mixing matrix element $V_{tb}$ from electroweak corrections to Z decays and implications for CKM matrix unitarity

    CERN Document Server

    Swain, J D

    1999-01-01

    We present a new method for the determination of the Cabibbo- Kobayashi-Maskawa quark mixing matrix element V/sub tb/ from electroweak loop corrections, in particular those affecting the process Z to bb. From a combined analysis of results from the LEP, SLC, Tevatron, and neutrino scattering experiments we determine V /sub tb/=0.77/sub -0.24//sup +18/. We comment briefly on the implications of this measurement for the mass of the top quark and Higgs boson, alpha /sub s/, and CKM unitarity. (19 refs).

  10. Continuous Modeling Technique of Fiber Pullout from a Cement Matrix with Different Interface Mechanical Properties Using Finite Element Program

    Directory of Open Access Journals (Sweden)

    Leandro Ferreira Friedrich

    Full Text Available Abstract Fiber-matrix interface performance has a great influence on the mechanical properties of fiber reinforced composite. This influence is mainly presented during fiber pullout from the matrix. As fiber pullout process consists of fiber debonding stage and pullout stage which involve complex contact problem, numerical modeling is a best way to investigate the interface influence. Although many numerical research works have been conducted, practical and effective technique suitable for continuous modeling of fiber pullout process is still scarce. The reason is in that numerical divergence frequently happens, leading to the modeling interruption. By interacting the popular finite element program ANSYS with the MATLAB, we proposed continuous modeling technique and realized modeling of fiber pullout from cement matrix with desired interface mechanical performance. For debonding process, we used interface elements with cohesive surface traction and exponential failure behavior. For pullout process, we switched interface elements to spring elements with variable stiffness, which is related to the interface shear stress as a function of the interface slip displacement. For both processes, the results obtained are very good in comparison with other numerical or analytical models and experimental tests. We suggest using the present technique to model toughening achieved by randomly distributed fibers.

  11. Investigations on thermal properties, stress and deformation of Al/SiC metal matrix composite based on finite element method

    Directory of Open Access Journals (Sweden)

    K. A. Ramesh Kumar

    2014-09-01

    Full Text Available AlSiC is a metal matrix composite which comprises of aluminium matrix with silicon carbide particles. It is characterized by high thermal conductivity (180-200 W/m K, and its thermal expansion are attuned to match other important materials that finds enormous demand in industrial sectors. Although its application is very common, the physics behind the Al-SiC formation, functionality and behaviors are intricate owing to the temperature gradient of hundreds of degrees, over the volume, occurring on a time scale of a few seconds, involving multiple phases. In this study, various physical, metallurgical and numerical aspects such as equation of continuum for thermal, stress and deformation using finite element (FE matrix formulation, temperature dependent material properties, are analyzed. Modelling and simulation studies of Al/SiC composites are a preliminary attempt to view this research work from computational point of view.

  12. Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

    International Nuclear Information System (INIS)

    Itagaki, Masafumi; Sahashi, Naoki.

    1997-01-01

    The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

  13. Disintegration of graphite matrix from the simulative high temperature gas-cooled reactor fuel element by electrochemical method

    International Nuclear Information System (INIS)

    Tian Lifang; Wen Mingfen; Li Linyan; Chen Jing

    2009-01-01

    Electrochemical method with salt as electrolyte has been studied to disintegrate the graphite matrix from the simulative high temperature gas-cooled reactor fuel elements. Ammonium nitrate was experimentally chosen as the appropriate electrolyte. The volume average diameter of disintegrated graphite fragments is about 100 μm and the maximal value is less than 900 μm. After disintegration, the weight of graphite is found to increase by about 20% without the release of a large amount of CO 2 probably owing to the partial oxidation to graphite in electrochemical process. The present work indicates that the improved electrochemical method has the potential to reduce the secondary nuclear waste and is a promising option to disintegrate graphite matrix from high temperature gas-cooled reactor spent fuel elements in the head-end of reprocessing.

  14. 1ST-ORDER NONADIABATIC COUPLING MATRIX-ELEMENTS FROM MULTICONFIGURATIONAL SELF-CONSISTENT-FIELD RESPONSE THEORY

    DEFF Research Database (Denmark)

    Bak, Keld L.; Jørgensen, Poul; Jensen, H.J.A.

    1992-01-01

    A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response of a ref......A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response...... to the full configuration interaction limit. Comparisons are made with state-averaged MCSCF results for MgH2 and finite-difference configuration interaction by perturbation with multiconfigurational zeroth-order wave function reflected by interactive process (CIPSI) results for BH....

  15. On the evaluation of the U(3) content of the matrix elements of one-and two-body operators

    International Nuclear Information System (INIS)

    Vanagas, V.; Alcaras, J.A.C.

    1991-09-01

    An expression for the U(3) content of the matrix elements of one- and two-body operators in Elliott's basis is obtained. Three alternative ways of evaluating this content with increasing performance in computing time are presented. All of them allow an exact representation of that content in terms of integers, avoiding rounding errors in the computer codes. The role of dual bases in dealing with non-orthogonal bases is also clarified. (author)

  16. The transition matrix element Agq(N) of the variable flavor number scheme at O(α3s)

    International Nuclear Information System (INIS)

    Ablinger, J.; Hasselhuhn, A.; Schneider, C.; Manteuffel, A. von

    2014-01-01

    We calculate the massive operator matrix element A (3) gq (N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at O(α 3 s ). A fist independent recalculation is performed for the contributions ∝ N F of the 3-loop anomalous dimension γ (2) gq (N).

  17. Radiochemical separation and ICP-AES determination of some common metallic elements in ThO2 matrix

    International Nuclear Information System (INIS)

    Adya, V.C.; Hon, N.S.; Bangia, T.R.; Sastry, M.D.; Iyer, R.H.

    1997-01-01

    Radioactive tracer and also ICP-AES studies have been carried out to determine Al, Cd, Ca, Cr, Co, Cu, Mn, Mo and Pd in ThO 2 matrix after chemical separation. Di-2-ethyl-hexyl phosphoric acid/xylene/HNO 3 extraction system was used for quantitative separation of thorium. The recovery of elements as determined by tracers and ICP-AES was found to be quantitative within experimental error. (author). 3 refs., 1 tab

  18. Wigner Function:from Ensemble Average of Density Operator to Its One Matrix Element in Entangled Pure States

    Institute of Scientific and Technical Information of China (English)

    FAN Hong-Yi

    2002-01-01

    We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.

  19. SU(2) X SU(2) X U(1) basis for symmetric SO(6) representations: matrix elements of the generators

    International Nuclear Information System (INIS)

    Piepenbring, R.; Silvestre-Brac, B.; Szymanski, Z.

    1987-01-01

    Matrix elements of the group generators for the symmetric irreducible representations of SO(6) are explicitly calculated in a closed form employing thedecomposition chain SO(6) is contained in SU(2) X SU(2) X U(1) (which is different from the well known Wigner supermultiplet scheme). The relation to the Gel'fand Tsetlin method using SO(6) contained in SO(5) up to ... SO(2) is indicated. An example of a physical application is given

  20. The transition matrix element Agq(N) of the variable flavor number scheme at O(αs3)

    International Nuclear Information System (INIS)

    Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; Manteuffel, A. von; Round, M.; Schneider, C.; Wißbrock, F.

    2014-01-01

    We calculate the massive unpolarized operator matrix element A gq (3) (N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at O(α s 3 ). A first independent recalculation is performed for the contributions ∝N F of the 3-loop anomalous dimension γ gq (2) (N)

  1. A reduced scale two loop PWR core designed with particle swarm optimization technique

    International Nuclear Information System (INIS)

    Lima Junior, Carlos A. Souza; Pereira, Claudio M.N.A; Lapa, Celso M.F.; Cunha, Joao J.; Alvim, Antonio C.M.

    2007-01-01

    Reduced scale experiments are often employed in engineering projects because they are much cheaper than real scale testing. Unfortunately, designing reduced scale thermal-hydraulic circuit or equipment, with the capability of reproducing, both accurately and simultaneously, all physical phenomena that occur in real scale and at operating conditions, is a difficult task. To solve this problem, advanced optimization techniques, such as Genetic Algorithms, have been applied. Following this research line, we have performed investigations, using the Particle Swarm Optimization (PSO) Technique, to design a reduced scale two loop Pressurized Water Reactor (PWR) core, considering 100% of nominal power and non accidental operating conditions. Obtained results show that the proposed methodology is a promising approach for forced flow reduced scale experiments. (author)

  2. Two-loop integrals for CP-even heavy quarkonium production and decays: elliptic sectors

    Science.gov (United States)

    Chen, Long-Bin; Jiang, Jun; Qiao, Cong-Feng

    2018-04-01

    By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like {γ}^{\\ast}γ \\to Q\\overline{Q} , {e}+{e}-\\to γ +Q\\overline{Q} , and H/{Z}^0\\to γ +Q\\overline{Q} , heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.

  3. The Higgs Mass in the MSSM at two-loop order beyond minimal flavour violation

    CERN Document Server

    Goodsell, Mark D; Staub, Florian

    2016-01-01

    Soft supersymmetry-breaking terms provide a wealth of new potential sources of flavour violation, which lead to very tight constraints from precision experiments. This has posed a challenge to construct flavour models to both explain the structure of the Standard Model Yukawa couplings and how their consequent predictions for patterns in the soft supersymmetry-breaking terms do not violate these constraints. While such models have been studied in great detail, the impact of flavour violating soft terms on the Higgs mass at the two-loop level has been assumed to be small or negligible. In this letter, we show that large flavour violation in the up-squark sector can give a positive or negative shift to the SM-like Higgs of several GeV, without being in conflict with any other observation. We investigate in which regions of the parameter space these effects can be expected.

  4. A comprehensive coordinate space renormalization of quantum electrodynamics to two-loop order

    International Nuclear Information System (INIS)

    Haagensen, P.E.; Latorre, J.I.

    1993-01-01

    We develop a coordinate space renormalization of massless quantum electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all one- and two-loop 1PI diagrams, run renormalization group equations on them. and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle γ 5 problems

  5. Small-threshold behaviour of two-loop self-energy diagrams: two-particle thresholds

    International Nuclear Information System (INIS)

    Berends, F.A.; Davydychev, A.I.; Moskovskij Gosudarstvennyj Univ., Moscow; Smirnov, V.A.; Moskovskij Gosudarstvennyj Univ., Moscow

    1996-01-01

    The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of the diagram. By employing general formulae of asymptotic expansions of Feynman diagrams in momenta and masses, we construct an algorithm to derive analytic approximations to the diagrams. In such a way, we calculate several first coefficients of the expansion. Since no conditions on relative values of the small masses and the external momentum are imposed, the threshold irregularities are described analytically. Numerical examples, using diagrams occurring in the standard model, illustrate the convergence of the expansion below the first large threshold. (orig.)

  6. TLTA/6431, Two-Loop-Test-Apparatus, BWR/6 Simulator, Small-Break LOCA

    International Nuclear Information System (INIS)

    1992-01-01

    1 - Description of test facility: The Two-Loop-Test-Apparatus (TLTA) is a 1:624 volume scaled BWR/6 simulator. It was the predecessor of the better-scaled FIST facility. The facility is capable of full BWR system pressure and has a simulated core with a full size 8 x 8, full power single bundle of indirect electrically heated rods. All major BWR systems are simulated including lower plenum, guide tube, core region (bundle and bypass), upper plenum, steam separator, steam dome, annular downcomer, recirculation loops and ECC injection systems. The fundamental scaling consideration was to achieve real-time response. A number of the scaling compromises present in TLTA were corrected in the FIST configuration. These compromises include a number of regional volumes and component elevations. 2 - Description of test: 64.45 sqcm small break LOCA with activation of the full emergency core cooling system, but without activation of the automatic decompression system

  7. Probing the desert by the two-loop renormalization-group equations

    International Nuclear Information System (INIS)

    Tanimoto, M.; Suetake, Y.; Senba, K.

    1987-01-01

    We have reexamined the study of probing the desert with fermion masses, presented by Bagger, Dimopoulos, and Masso, by using the two-loop renormalization-group equations in the framework of the SU(3) x SU(2) x U(1) model with three generations and one Higgs doublet. The blow-up energy scale of the Yukawa coupling is found to be dependent on the Higgs quartic coupling λ. If the Yukawa coupling blows up between the electroweak scale M/sub W/ and the grand unified scale M/sub X/, the Higgs potential is destabilized for small values of λ at the electroweak scale M/sub W/, and becomes strongly coupled for large values of λ at M/sub W/. It is found that the Higgs-scalar mass as well as the fermion masses are important to probe the desert

  8. Dominant two-loop corrections to the MSSM finite temperature effective potential

    International Nuclear Information System (INIS)

    Espinosa, J.R.

    1996-04-01

    We show that two-loop corrections to the finite temperature effective potential in the MSSM can have a dramatic effect on the strength of the electroweak phase transition, making it more strongly first order. The change in the order parameter v/Tc can be as large as 75% of the one-loop daisy improved result. This effect can be decisive to widen the region in parameter space where erasure of the created baryons by sphaleron processes after the transition is suppressed and hence, where electroweak baryogenesis might be successful. We find an allowed region with tan β< or∼4.5 and a Higgs boson with standard couplings and mass below 80 GeV within the reach of LEP II. (orig.)

  9. Complete two-loop effective potential approximation to the lightest Higgs scalar boson mass in supersymmetry

    International Nuclear Information System (INIS)

    Martin, Stephen P.

    2003-01-01

    I present a method for accurately calculating the pole mass of the lightest Higgs scalar boson in supersymmetric extensions of the standard model, using a mass-independent renormalization scheme. The Higgs scalar self-energies are approximated by supplementing the exact one-loop results with the second derivatives of the complete two-loop effective potential in Landau gauge. I discuss the dependence of this approximation on the choice of renormalization scale, and note the existence of particularly poor choices, which fortunately can be easily identified and avoided. For typical input parameters, the variation in the calculated Higgs boson mass over a wide range of renormalization scales is found to be of the order of a few hundred MeV or less, and is significantly improved over previous approximations

  10. The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element

    Energy Technology Data Exchange (ETDEWEB)

    Kiefer, René; Schad, Ariane; Roth, Markus [Kiepenheuer-Institut für Sonnenphysik, Schöneckstraße 6, D-79104 Freiburg (Germany)

    2017-09-10

    Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and change over the course of activity cycles.

  11. Two-Loop Quark Self-Energy in a New Formalism; 2, Renormalization of the Quark Propagator in the Light-Cone Gauge

    CERN Document Server

    Leibbrandt, George; Leibbrandt, George; Williams, Jimmy D.

    2000-01-01

    The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the noncovariant light-cone gauge (lcg). (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n^*-prescription for the spurious poles of 1/qn, and the detailed analysis of the boundary singularities in five- and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Sigma_2 contains both covariant and noncovariant components, and is a local function of the external momentum p, even off the mass-shell, as all nonlocal divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Sigma_2 implies a quark mass counterterm of the form $\\delta m (lcg) = m\\tilde\\alpha_s C_F(3+\\tilde\\alpha_sW) + {\\rm O} (\\tilde\\alpha_s^3)$, the dimensional regulator epsilon, and on th...

  12. Two-loop quark self-energy in a new formalism; 2, Renormalization of the quark propagator in the light-cone gauge

    CERN Document Server

    Leibbrandt, G

    2000-01-01

    For pt.I see ibid., vol.440, p.537-602, 1995. The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the non-covariant light-cone gauge (LCG), n.A/sup a/(x)=0, n/sup 2/=0. (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n*/sub mu /-prescription for the spurious poles of (q.n)/sup -1/, and the detailed analysis of the boundary singularities in five- and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Sigma /sub 2/ contains both covariant and non-covariant components, and is a local function of the external momentum p, even off the mass-shell, as all non-local divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Sigma /sub 2/ implies a quark mass counterterm of the form delta m(LCG)=m alpha /sub...

  13. Adinkras from ordered quartets of BC4 Coxeter group elements and regarding another Gadget’s 1,358,954,496 matrix elements

    Science.gov (United States)

    Gates, S. James; Kang, Lucas; Kessler, David S.; Korotkikh, Vadim

    2018-04-01

    A Gadget, more precisely a scalar Gadget, is defined as a mathematical calculation acting over a domain of one or more adinkra graphs and whose range is a real number. A 2010 work on the subject of automorphisms of adinkra graphs, implied the existence of multiple numbers of Gadgets depending on the number of colors under consideration. For four colors, this number is two. In this work, we verify the existence of a second such Gadget and calculate (both analytically and via explicit computer-enabled algorithms) its 1,358,954,496 matrix elements over 36,864 minimal valise adinkras related to the Coxeter Group BC4.

  14. The Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix

    International Nuclear Information System (INIS)

    Kim, Jeong Soo; Kim, Moon Kyum

    2012-01-01

    In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.

  15. Consolidation effects on tensile properties of an elemental Al matrix composite

    Energy Technology Data Exchange (ETDEWEB)

    Tang, F. [Building 4515, MS 6064, Metals and Ceramics Division, Oak Ridge National Lab, Oak Ridge, TN 37831 (United States)]. E-mail: tangf@ornl.gov; Meeks, H. [Ceracon Inc., 5150 Fairoaks Blvd. 01-330, Carmichael, CA 95628 (United States); Spowart, J.E. [UES Incorporated, AFRL/MLLM Building 655, 2230 Tenth St. Suite 1, Wright-Patterson AFB, OH 45433 (United States); Gnaeupel-Herold, T. [NIST Center for Neutron Research, 100 Bureau Dr. Stop 8562, Gaithersburg, MD 20899-8562 (United States); Prask, H. [NIST Center for Neutron Research, 100 Bureau Dr. Stop 8562, Gaithersburg, MD 20899-8562 (United States); Anderson, I.E. [Materials and Engineering Physics Program, Ames Laboratory, Iowa State University, Ames, IA 50011 (United States)

    2004-11-25

    In a simplified composite design, an unalloyed Al matrix was reinforced by spherical Al-Cu-Fe alloy particles (30 vol.%), using either commercial purity (99.7%) or high purity (99.99%) fine powders (diameter < 10 {mu}m). This composite material was consolidated by either vacuum hot pressing (VHP) or quasi-isostatic forging. The spatial distribution of reinforcement particles in both VHP and forged samples was shown to be almost the same by quantitative characterization with a multi-scale area fraction analysis technique. The tensile properties of all composite samples were tested and the forged materials showed significantly higher strength, while the elastic modulus values of all composite materials were close to the upper bound of theoretical predictions. Neutron diffraction measurements showed that there were high compressive residual stresses in the Al matrix of the forged samples and relatively low Al matrix residual stresses (predominantly compressive) in the VHP samples. By tensile tests and neutron diffraction measurements of the forged samples after annealing, it was shown that the high compressive residual stresses in the Al matrix were relieved and that tensile strength was also reduced to almost the same level as that of the VHP samples. Therefore, it was deduced that increased compressive residual stresses and enhanced dislocation densities in the forged composites raised the tensile strength to higher values than those of the VHP composites.

  16. Models based on multichannel R-matrix theory for evaluating light element reactions

    International Nuclear Information System (INIS)

    Dodder, D.C.; Hale, G.M.; Nisley, R.A.; Witte, K.; Young, P.G.

    1975-01-01

    Multichannel R-matrix theory has been used as a basis for models for analysis and evaluation of light nuclear systems. These models have the characteristic that data predictions can be made utilizing information derived from other reactions related to the one of primary interest. Several examples are given where such an approach is valid and appropriate. (auth.)

  17. Standard error propagation in R-matrix model fitting for light elements

    International Nuclear Information System (INIS)

    Chen Zhenpeng; Zhang Rui; Sun Yeying; Liu Tingjin

    2003-01-01

    The error propagation features with R-matrix model fitting 7 Li, 11 B and 17 O systems were researched systematically. Some laws of error propagation were revealed, an empirical formula P j = U j c / U j d = K j · S-bar · √m / √N for describing standard error propagation was established, the most likely error ranges for standard cross sections of 6 Li(n,t), 10 B(n,α0) and 10 B(n,α1) were estimated. The problem that the standard error of light nuclei standard cross sections may be too small results mainly from the R-matrix model fitting, which is not perfect. Yet R-matrix model fitting is the most reliable evaluation method for such data. The error propagation features of R-matrix model fitting for compound nucleus system of 7 Li, 11 B and 17 O has been studied systematically, some laws of error propagation are revealed, and these findings are important in solving the problem mentioned above. Furthermore, these conclusions are suitable for similar model fitting in other scientific fields. (author)

  18. The extracellular matrix - the under-recognized element in lung disease?

    NARCIS (Netherlands)

    Burgess, Janette K.; Mauad, Thais; Tjin, Gavin; Karlsson, Jenny C.; Westergren-Thorsson, Gunilla

    2016-01-01

    The lung is composed of airways and lung parenchyma, and the extracellular matrix (ECM) contains the main building blocks of both components. The ECM provides physical support and stability to the lung, and as such it has in the past been regarded as an inert structure. More recent research has

  19. Evidence for two-loop interaction from IRIS and SDO observations of penumbral brightenings

    Science.gov (United States)

    Alissandrakis, C. E.; Koukras, A.; Patsourakos, S.; Nindos, A.

    2017-07-01

    Aims: We investigate small scale energy release events which can provide clues on the heating mechanism of the solar corona. Methods: We analyzed spectral and imaging data from the Interface Region Imaging Spectrograph (IRIS), images from the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatoty (SDO), and magnetograms from the Helioseismic and Magnetic Imager (HMI) aboard SDO. Results: We report observations of small flaring loops in the penumbra of a large sunspot on July 19, 2013. Our main event consisted of a loop spanning 15'', from the umbral-penumbral boundary to an opposite polarity region outside the penumbra. It lasted approximately 10 min with a two minute impulsive peak and was observed in all AIA/SDO channels, while the IRIS slit was located near its penumbral footpoint. Mass motions with an apparent velocity of 100 km s-1 were detected beyond the brightening, starting in the rise phase of the impulsive peak; these were apparently associated with a higher-lying loop. We interpret these motions in terms of two-loop interaction. IRIS spectra in both the C II and Si iv lines showed very extended wings, up to about 400 km s-1, first in the blue (upflows) and subsequently in the red wing. In addition to the strong lines, emission was detected in the weak lines of Cl I, O I and C I, as well as in the Mg II triplet lines. Absorption features in the profiles of the C II doublet, the Si iv doublet and the Mg II h and k lines indicate the existence of material with a lower source function between the brightening and the observer. We attribute this absorption to the higher loop and this adds further credibility to the two-loop interaction hypothesis. Tilts were detected in the absorption spectra, as well as in the spectra of Cl I, O I, and C I lines, possibly indicating rotational motions from the untwisting of magnetic flux tubes. Conclusions: We conclude that the absorption features in the C II, Si iv and Mg II profiles originate in a higher

  20. Study of electron-molecule collision via finite-element method and r-matrix propagation technique: Exact exchange

    International Nuclear Information System (INIS)

    Abdolsalami, F.; Abdolsalami, M.; Perez, L.; Gomez, P.

    1995-01-01

    The authors have applied the finite-element method to electron-molecule collision with the exchange effect implemented rigorously. All the calculations are done in the body-frame within the fixed-nuclei approximation, where the exact treatment of exchange as a nonlocal effect results in a set of coupled integro-differential equations. The method is applied to e-H 2 and e-N 2 scatterings and the cross sections obtained are in very good agreement with the corresponding results the authors have generated from the linear-algebraic approach. This confirms the significant difference observed between their results generated by linear-algebraic method and the previously published e-N 2 cross sections. Their studies show that the finite-element method is clearly superior to the linear-algebraic approach in both memory usage and CPU time especially for large systems such as e-N 2 . The system coefficient matrix obtained from the finite-element method is often sparse and smaller in size by a factor of 12 to 16, compared to the linear-algebraic technique. Moreover, the CPU time required to obtain stable results with the finite-element method is significantly smaller than the linear-algebraic approach for one incident electron energy. The usage of computer resources in the finite-element method can even be reduced much further when (1) scattering calculations involving multiple electron energies are performed in one computer run and (2) exchange, which is a short range effect, is approximated by a sparse matrix. 17 refs., 7 figs., 5 tabs

  1. Pole Mass of the W Boson at Two-Loop Order in the Pure $\\overline {MS}$ Scheme

    Energy Technology Data Exchange (ETDEWEB)

    Martin, Stephen P. [Northern Illinois U.

    2015-06-03

    I provide a calculation at full two-loop order of the complex pole squared mass of the W boson in the Standard Model in the pure MS¯ renormalization scheme, with Goldstone boson mass effects resummed. This approach is an alternative to earlier ones that use on-shell or hybrid renormalization schemes. The renormalization scale dependence of the real and imaginary parts of the resulting pole mass is studied. Both deviate by about ±4  MeV from their median values as the renormalization scale is varied from 50 to 200 GeV, but the theory error is likely larger. A surprising feature of this scheme is that the two-loop QCD correction has a larger scale dependence, but a smaller magnitude, than the two-loop non-QCD correction, unless the renormalization scale is chosen very far from the top-quark mass.

  2. Experimental tests for the Babu-Zee two-loop model of Majorana neutrino masses

    International Nuclear Information System (INIS)

    Sierra, Diego Aristizabal; Hirsch, Martin

    2006-01-01

    The smallness of the observed neutrino masses might have a radiative origin. Here we revisit a specific two-loop model of neutrino mass, independently proposed by Babu and Zee. We point out that current constraints from neutrino data can be used to derive strict lower limits on the branching ratio of flavour changing charged lepton decays, such as μ→eγ. Non-observation of Br(μ→eγ) at the level of 10 -13 would rule out singly charged scalar masses smaller than 590 GeV (5.04 TeV) in case of normal (inverse) neutrino mass hierarchy. Conversely, decay branching ratios of the non-standard scalars of the model can be fixed by the measured neutrino angles (and mass scale). Thus, if the scalars of the model are light enough to be produced at the LHC or ILC, measuring their decay properties would serve as a direct test of the model as the origin of neutrino masses

  3. Experimental tests for the Babu-Zee two-loop model of Majorana neutrino masses

    International Nuclear Information System (INIS)

    Aristizabal, D.

    2006-01-01

    Abstract: The smallness of the observed neutrino masses might have a radiative origin. Here we revisit a specific two-loop model of neutrino mass, independently proposed by Babu and Zee. We point out that current constraints from neutrino data can be used to derive strict lower limits on the branching ratio of flavour changing charged lepton decays, such as μ → e γ. Non-observation of Br(μ → e γ) at the level of 10 -13 would rule out singly charged scalar masses smaller than 590 GeV (5.04 TeV) in case of normal (inverse) neutrino mass hierarchy. Conversely, decay branching ratios of the non-standard scalars of the model can be fixed by the measured neutrino angles (and mass scale). Thus, if the scalars of the model are light enough to be produced at the LHC or ILC, measuring their decay properties would serve as a direct test of the model as the origin of neutrino masses. (author)

  4. Systematic classification of two-loop realizations of the Weinberg operator

    Energy Technology Data Exchange (ETDEWEB)

    Sierra, D. Aristizabal; Degee, A. [IFPA, Dep. AGO, Universite de Liege,Bat B5, Sart Tilman B-4000 Liege 1 (Belgium); Dorame, L.; Hirsch, M. [AHEP Group, Instituto de Fisica Corpuscular-C.S.I.C./Universitat de Valencia,Edificio Institutos de Paterna, Apt 22085, E-46071 Valencia (Spain)

    2015-03-09

    We systematically analyze the d=5 Weinberg operator at 2-loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2-loop models for which both, tree-level and 1-loop contributions, are guaranteed to be absent. And (ii) finite 2-loop diagrams, which correspond to the 1-loop generation of some particular vertex appearing in a given 1-loop neutrino mass model, thus being effectively 2-loop. From the large list of all possible 2-loop diagrams, the vast majority are infinite corrections to lower order neutrino mass models and only a moderately small number of diagrams fall into these two interesting classes. Moreover, all diagrams in class (i) are just variations of three basic diagrams, with examples discussed in the literature before. Similarly, we also show that class (ii) diagrams consists of only variations of these three plus two more basic diagrams. Finally, we show how our results can be consistently and readily used in order to construct two-loop neutrino mass models.

  5. Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops

    Energy Technology Data Exchange (ETDEWEB)

    Braathen, Johannes; Goodsell, Mark D. [LPTHE, UPMC University Paris 06, Sorbonne Universités,4 Place Jussieu, F-75252 Paris (France); LPTHE, CNRS,4 Place Jussieu, F-75252 Paris (France)

    2016-12-14

    We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently developed for the Standard Model and the MSSM, and we give compact, infra-red finite expressions in closed form for the tadpole equations. We also show that the results at this loop order are equivalent to (and are most easily obtained by) imposing an “on-shell” condition for the Goldstone bosons. Moreover, we extend the approach to show how the infra-red divergences in the calculation of the masses of neutral scalars (such as the Higgs boson) can be eliminated. For the mass computation, we specialise to the gaugeless limit and extend the effective potential computation to allow the masses to be determined without needing to solve differential equations for the loop functions — opening the door to fast, infra-red safe determinations of the Higgs mass in general theories.

  6. Two-loop conformal generators for leading-twist operators in QCD

    International Nuclear Information System (INIS)

    Braun, V.M.; Strohmaier, M.; Manashov, A.N.; Hamburg Univ.; Moch, S.

    2016-01-01

    QCD evolution equations in minimal subtraction schemes have a hidden symmetry: One can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer d=4-2ε space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in d=4-2ε effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD β-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.

  7. Two-loop beam and soft functions for rapidity-dependent jet vetoes

    Energy Technology Data Exchange (ETDEWEB)

    Gangal, Shireen [Theory Group, Deutsches Elektronen-Synchrotron (DESY),Notkestraße 85, D-22607 Hamburg (Germany); Gaunt, Jonathan R. [Nikhef Theory Group and VU University Amsterdam,De Boelelaan 1081, NL-1081 HV Amsterdam (Netherlands); Stahlhofen, Maximilian [PRISMA Cluster of Excellence, Institute of Physics, Johannes Gutenberg University,Staudingerweg 7, D-55128 Mainz (Germany); Tackmann, Frank J. [Theory Group, Deutsches Elektronen-Synchrotron (DESY),Notkestraße 85, D-22607 Hamburg (Germany)

    2017-02-06

    Jet vetoes play an important role in many analyses at the LHC. Traditionally, jet vetoes have been imposed using a restriction on the transverse momentum p{sub Tj} of jets. Alternatively, one can also consider jet observables for which p{sub Tj} is weighted by a smooth function of the jet rapidity y{sub j} that vanishes as |y{sub j}|→∞. Such observables are useful as they provide a natural way to impose a tight veto on central jets but a looser one at forward rapidities. We consider two such rapidity-dependent jet veto observables, T{sub Bj} and T{sub Cj}, and compute the required beam and dijet soft functions for the jet-vetoed color-singlet production cross section at two loops. At this order, clustering effects from the jet algorithm become important. The dominant contributions are computed fully analytically while corrections that are subleading in the limit of small jet radii are expressed in terms of finite numerical integrals. Our results enable the full NNLL{sup ′} resummation and are an important step towards N{sup 3}LL resummation for cross sections with a T{sub Bj} or T{sub Cj} jet veto.

  8. Fixation of actinide elements into zeolites/zeotypes and Flexcrete-cement matrix

    International Nuclear Information System (INIS)

    Amini, S.; Dyer, A.; Durrani, S.K.

    1993-01-01

    The leaching behavior of α-emitter radionuclides (uranium and americium) from zeolite-L and the zeotype (SAPO-34) in a Flexcrete-cement matrix were examined by static and dynamic methods using 0.005M CaCl 2 and synthetic ground water as leachants. The leaching rates of UO 2 2+ were found to be higher by about ten orders of magnitude than those of Am 3+ for both zeolite-L and SAPO-34 in the cement matrix. The static and dynamic leaching rates of UO 2 2+ for SAPO-34 in CaCl 2 and synthetic ground water were ten orders of magnitude lower than those for L. SAPO-34 showed good selectivity for uranium at pH 2-3.5 and L was usefully selective for Am 3+ . Distribution coefficients of Am 3+ and UO 2 2+ increased with equilibrium pH. (author) 20 refs.; 2 figs.; 4 tabs

  9. Off-diagonal helicity density matrix elements for vector mesons produced in polarized e+e- processes

    International Nuclear Information System (INIS)

    Anselmino, M.; Murgia, F.; Quintairos, P.

    1999-04-01

    Final state q q-bar interactions give origin to non zero values of the off-diagonal element ρ 1,-1 of the helicity density matrix of vector mesons produced in e + e - annihilations, as confirmed by recent OPAL data on φ, D * and K * 's. New predictions are given for ρ 1,-1 of several mesons produced at large x E and small p T - i.e. collinear with the parent jet - in the annihilation of polarized 3 + and 3 - , the results depend strongly on the elementary dynamics and allow further non trivial tests of the standard model. (author)

  10. (Quasi)Elastic Electron-Muon Large-Angle Scattering to a Two-Loop Approximation: Vertex Contributions

    CERN Document Server

    Bytev, V V; Shaikhatdenov, B G

    2002-01-01

    We consider a process of quasielastic e\\mu large-angle scattering at high energies with radiative corrections up to a two-loop level. The lowest order radiative correction arising both from one-loop virtual photon emission and a real soft emission are presented to a power accuracy. Two-loop level corrections are supposed to be of three gauge-invariant classes. One of them, so-called vertex contribution, is given in logarithmic approximation. Relation with the renormalization group approach is discussed.

  11. (Quasi)Elastic Electron-Muon Large-Angle Scattering to a Two-Loop Approximation Vertex Contributions

    CERN Document Server

    Bytev, V V; Shaikhatdenov, B G

    2002-01-01

    We consider a process of quasielastic e\\mu large-angle scattering at high energies with radiative corrections up to a two-loop level. The lowest order radiative correction arising both from one-loop virtual photon emission and a real soft emission are presented to a power accuracy. Two-loop level corrections are supposed to be of three gauge-invariant classes. One of them, so-called vertex contribution, is given in logarithmic approximation. Relation with the renormalization group approach is discussed.

  12. First unitarity-independent determination of the CKM matrix elements $V_{td}$, $V_{ts}$, and ${V_{tb}$ and the implications for unitarity

    OpenAIRE

    Swain, John; Taylor, Lucas

    1997-01-01

    The magnitudes of the CKM matrix elements $V_{td}$, $V_{ts}$, and $V_{tb}$ are determined for the first time without any assumptions of unitarity. The implications for the unitarity of the CKM matrix as a whole are discussed.

  13. 3-Loop massive O(T{sub 2}{sup F}) contributions to the DIS operator matrix element A{sub gg}

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Hasselhuhn, A.; Round, M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Inst. for Symbolic Computation (RISC); Manteuffel, A. von [Mainz Univ. (Germany). PRISMA Cluster of Excellence

    2014-09-15

    Contributions to heavy flavour transition matrix elements in the variable flavour number scheme are considered at 3-loop order. In particular a calculation of the diagrams with two equal masses that contribute to the massive operator matrix element A{sup (3)}{sub gg,Q} is performed. In the Mellin space result one finds finite nested binomial sums. In x-space these sums correspond to iterated integrals over an alphabet containing also square-root valued letters.

  14. Study of electron-molecule collisions via the finite-element method and R-matrix propagation technique: Model exchange

    International Nuclear Information System (INIS)

    Abdolsalami, F.; Abdolsalami, M.; Gomez, P.

    1994-01-01

    We have applied the finite-element method to electron-molecule collisions. All the calculations are done in the body frame within the fixed-nuclei approximation. A model potential, which is added to the static and polarization potential, has been used to represent the exchange effect. The method is applied to electron-H 2 scattering and the eigenphase sums and the cross sections obtained are in very good agreement with the corresponding results from the linear-algebraic approach. Finite-element calculations of the R matrix in the region where the static and exchange interactions are strong, however, has about one-half to one-fourth of the memory requirement of the linear-algebraic technique

  15. Determination of several trace elements in silicate rocks by an XRF method with background and matrix corrections

    International Nuclear Information System (INIS)

    Pascual, J.

    1987-01-01

    An X-ray fluorescence method for determining trace elements in silicate rock samples was studied. The procedure focused on the application of the pertinent matrix corrections. Either the Compton peak or the reciprocal of the mass absorption coefficient of the sample was used as internal standard for this purpose. X-ray tubes with W or Cr anodes were employed, and the W Lβ and Cr Kα Compton intensities scattered by the sample were measured. The mass absorption coefficients at both sides of the absorption edge for Fe (1.658 and 1.936 A) were calculated. The elements Zr, Y, Rb, Zn, Ni, Cr and V were determined in 15 international reference rocks covering wide ranges of concentration. Relative mean errors were in many cases less than 10%. (author)

  16. Naturalness made easy: two-loop naturalness bounds on minimal SM extensions

    Energy Technology Data Exchange (ETDEWEB)

    Clarke, Jackson D.; Cox, Peter [ARC Centre of Excellence for Particle Physics at the Terascale,School of Physics, University of Melbourne,Melbourne, 3010 (Australia)

    2017-02-24

    The main result of this paper is a collection of conservative naturalness bounds on minimal extensions of the Standard Model by (vector-like) fermionic or scalar gauge multiplets. Within, we advocate for an intuitive and physical concept of naturalness built upon the renormalisation group equations. In the effective field theory of the Standard Model plus a gauge multiplet with mass M, the low scale Higgs mass parameter is a calculable function of (MS)-bar input parameters defined at some high scale Λ{sub h}>M. If the Higgs mass is very sensitive to these input parameters, then this signifies a naturalness problem. To sensibly capture the sensitivity, it is shown how a sensitivity measure can be rigorously derived as a Bayesian model comparison, which reduces in a relevant limit to a Barbieri-Giudice-like fine-tuning measure. This measure is fully generalisable to any perturbative EFT. The interesting results of our two-loop renormalisation group study are as follows: for Λ{sub h}=Λ{sub Pl} we find “10% fine-tuning” bounds on the masses of various gauge multiplets of M

  17. Matrix units and Schur elements for the degenerate cyclotomic Hecke algebras

    OpenAIRE

    Zhao, Deke

    2011-01-01

    The paper uses the cellular basis of the (semi-simple) degenerate cyclotomic Hecke algebras to investigate these algebras exhaustively. As a consequence, we describe explicitly the "Young's seminormal form" and a orthogonal bases for Specht modules and determine explicitly the closed formula for the natural bilinear form on Specht modules and Schur elements for the degenerate cyclotomic Hekce algebras.

  18. Assessment of the influence of anthropogenic factors on elements of the ecological network in Vojvodina (Serbia using the Leopold matrix

    Directory of Open Access Journals (Sweden)

    Kicošev Vesna

    2015-01-01

    Full Text Available Salt steppes and marshes represent the most valuable ecosystems in the world, providing numerous ecosystem services that are extremely vulnerable to anthropogenic influences. These types of habitat in the territory of Serbia are most dominant in Banat and a significant portion of them is under protection or in the process of becoming protected. The section surrounding the protected areas of Slano Kopovo Special Nature Reserve, Rusanda Nature Park and Okanj Bara Special Nature Reserve with the non-building area of Novi Bečej, Kumane, Melenci, Elemir and Taraš cadastral municipalities, has been chosen for the analysis. The aim of this paper was to assess the influence of specific anthropogenic factors on the elements of an ecological network using the analytical method that can generate the required results in a manner suitable for presentation to various stakeholders. To achieve this aim, the Leopold matrix model, used for assessing anthropogenic influence on the environment, has been chosen. The specificity of this issue of protecting and preserving elements of an ecological network resulted in the need to isolate and evaluate the factors affecting the preservation of habitats and functionality of ecosystems, unlike the concept of Leopold matrix, which treats all factors as equally important in the process of evaluation. Evaluation results indicate significant effects of historical, perennial manner of using the area and other resources in the non-building area.

  19. BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

    OpenAIRE

    Caffo, Michele; Czyz, Henryk; Gunia, Michal; Remiddi, Ettore

    2008-01-01

    We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.

  20. Matrix equation decomposition and parallel solution of systems resulting from unstructured finite element problems in electromagnetics

    Energy Technology Data Exchange (ETDEWEB)

    Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)

    1996-12-31

    Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.

  1. Optimization of institutional streams of green construction using the elements of the theory of matrix games

    Directory of Open Access Journals (Sweden)

    Prokhin Egor Anatol’evich

    2016-10-01

    Full Text Available In the modern conditions innovatization of construction is of great necessity, though it is associated with a number of problems of first of all institutional genesis. The development of green construction in Russia is on its first stages, though its necessity is growing according to the tendency for energy efficiency and sustainable development. The innovative process of ecological construction has a network model and requires its optimization with the aim of further development by advancing the institutional platform. The author proposed a conceptual scheme for an institutional platform of the innovative process of green construction and conducted systematization of institutional structures. The unique role of innovative and ecological institutes is substantiated. The author recommends an optimization method for institutional interaction of the subjects using the stakeholder theory and the theory of matrix games aimed at activation of innovative green technologies. Practical application of the offered algorithms and methods will allow increasing the efficiency of green construction development.

  2. The determination of light elements in heavy matrix using proton induced X-ray emission

    International Nuclear Information System (INIS)

    Levenets, V.V.; Omel'nik, A.P.; Shchur, A.A.; Chernov, A.E.; Usikov, N.P.; Zats, A.V.

    2007-01-01

    In this report the possibility of determination of light impurities in heavy matrixes is studied using proton induced X-Ray emission. The wide-band X-ray emission filter made from pyrolytic graphite was used in spectrometric scheme of experiment. The results of studying of filter features in energy range of X-ray emission from 4 to 12 keV were presented. The possibilities were examined of application of pyrolytic graphite filter to modify the X-rays spectrum for determination of iron, using characteristic emission of K-series, and hafnium, using L-series, in substances on base of zirconium (glasses, alloys etc.). It was shown, that the using of similar filter allows to reach the significant improving of metrological characteristics of analysis of mentioned impurities: the limits of detection of iron and hafnium were lowered single-order of magnitude. (authors)

  3. Milling Behavior of Matrix Graphite Powders with Different Binder Materials in HTGR Fuel Element Fabrication: I. Variation in Particle Size Distribution

    International Nuclear Information System (INIS)

    Lee, Young Woo; Cho, Moon Sung

    2011-01-01

    The fuel element for HTGR is manufactured by mixing coated fuel particles with matrix graphite powder and forming into either pebble type or cylindrical type compacts depending on their use in different HTGR cores. The coated fuel particle, the so-called TRISO particle, consists of 500-μm spherical UO 2 particles coated with the low density buffer Pyrolytic Carbon (PyC) layer, the inner and outer high density PyC layer and SiC layer sandwiched between the two inner and outer PyC layers. The coated TRISO particles are mixed with a matrix graphite powder properly prepared and pressed into a spherical shape or a cylindrical compact finally heat-treated at about 1900 .deg. C. These fuel elements can have different sizes and forms of compact. The basic steps for manufacturing a fuel element include preparation of graphite matrix powder, overcoating the fuel particles, mixing the fuel particles with a matrix powder, carbonizing green compact, and the final high-temperature heat treatment of the carbonized fuel compact. In order to develop a fuel compact fabrication technology, it is important to develop a technology to prepare the matrix graphite powder (MGP) with proper characteristics, which has a strong influence on further steps and the material properties of fuel element. In this work, the milling behavior of matrix graphite powder mixture with different binder materials and their contents was investigated by analyzing the change in particle size distribution with different milling time

  4. The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de; Schoenwald, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Goedicke, A. [Karlsruher Institut fuer Technologie (KIT), Karlsruhe (Germany). Inst. fuer Theoretische Teilchenphysik; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC)

    2017-12-15

    We report on our latest results in the calculation of the two-mass contributions to 3-loop operator matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inelastic scattering structure functions and to generalize the variable flavor number scheme by including both charm and bottom quarks. We present the results for the non-singlet and A{sub gq,Q} OMEs, and compare the size of their contribution relative to the single mass case. Results for the gluonic OME A{sub gg,Q} are given in the physical case, going beyond those presented in a previous publication where scalar diagrams were computed. We also discuss our recently published two-mass contribution to the pure singlet OME, and present an alternative method of calculating the corresponding diagrams.

  5. Constraints on parity-mixing matrix elements from hard-pion exchange corrections to first-forbidden beta decays

    International Nuclear Information System (INIS)

    Kirchbach, M.

    1986-01-01

    In this paper the experience in extracting the value of the weak pion-nucleon coupling constant f/sub π//sup l/ from the parity-mixing matrix element + , T = 1; 1.042 MeV | V/sub PNC/ | O - , T = 0; 1.081 MeV> in 18 F is summarized with the aim to reveal some sources of uncertainties of the models exploited. We show that beyond of the long wavelenth approximation and in treating non-soft pion corrections to the two-body nuclear chiral charge density an upper bound for f/sub π//sup l/ is obtained which is about two times smaller as compared to results of previous analyses of similar character. Finally, we accentuate on the importance of the heavy-meson exchanges in the weak NN-potential for understanding recent measurement results of f/sub π//sup l/ which strongly deviate from earlier data. (author)

  6. Finite element evaluation of elasto-plastic accommodation energies during solid state transformations: Coherent, spherical precipitate in finite matrix

    International Nuclear Information System (INIS)

    Sen, S.; Balasubramaniam, R.; Sethuraman, R.

    1996-01-01

    The molar volume difference between the matrix and the precipitate phases in the case of solid state phase transformations results in the creation of stain energy in the system due to the misfit strains. A finite element model based on the initial strain approach is proposed to evaluate elasto-plastic accommodation energies during solid state transformation. The three-dimensional axisymmetric model has been used to evaluate energies as a function of transformation for α-β hydrogen transformations in the Nb-H system. The transformation has been analyzed for the cases of transformation progressing both from the center to surface and from the surface to center of the system. The effect of plastic deformation has been introduced to make the model realistic, specifically to the Nb-NbH phase transformation which involves a 4% linear misfit strain. It has been observed that plastic deformation reduces the strain energies compared to the linear elastic analysis

  7. The summation of the matrix elements of Hamiltonian and transition operators. The variance of the emission spectrum

    International Nuclear Information System (INIS)

    Karaziya, R.I.; Rudzikajte, L.S.

    1988-01-01

    The general method to obtain the explicit expressions for sums of the matrix elements of Hamiltonian and transition operators has been extended. It can be used for determining the main characteristics of atomic spectra, such as the mean energy, the variance, the asymmetry coefficient, etc., as well as for the average quantities which describe the configuration mixing. By mean of this method the formula for the variance of the emission spectrum has been derived. It has been shown that this quantity of the emission spectrum can be expressed by the variances of the energy spectra of the initial and final configurations and by additional terms, caused by the distribution of the intensity in spectrum

  8. Bivariate- distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems.

    Science.gov (United States)

    Kota, V K B; Chavda, N D; Sahu, R

    2006-04-01

    Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F > lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.

  9. Chirality dependence of dipole matrix element of carbon nanotubes in axial magnetic field: A third neighbor tight binding approach

    Science.gov (United States)

    Chegel, Raad; Behzad, Somayeh

    2014-02-01

    We have studied the electronic structure and dipole matrix element, D, of carbon nanotubes (CNTs) under magnetic field, using the third nearest neighbor tight binding model. It is shown that the 1NN and 3NN-TB band structures show differences such as the spacing and mixing of neighbor subbands. Applying the magnetic field leads to breaking the degeneracy behavior in the D transitions and creates new allowed transitions corresponding to the band modifications. It is found that |D| is proportional to the inverse tube radius and chiral angle. Our numerical results show that amount of filed induced splitting for the first optical peak is proportional to the magnetic field by the splitting rate ν11. It is shown that ν11 changes linearly and parabolicly with the chiral angle and radius, respectively.

  10. The role of the tunneling matrix element and nuclear reorganization in the design of quantum-dot cellular automata molecules

    Science.gov (United States)

    Henry, Jackson; Blair, Enrique P.

    2018-02-01

    Mixed-valence molecules provide an implementation for a high-speed, energy-efficient paradigm for classical computing known as quantum-dot cellular automata (QCA). The primitive device in QCA is a cell, a structure with multiple quantum dots and a few mobile charges. A single mixed-valence molecule can function as a cell, with redox centers providing quantum dots. The charge configuration of a molecule encodes binary information, and device switching occurs via intramolecular electron transfer between dots. Arrays of molecular cells adsorbed onto a substrate form QCA logic. Individual cells in the array are coupled locally via the electrostatic electric field. This device networking enables general-purpose computing. Here, a quantum model of a two-dot molecule is built in which the two-state electronic system is coupled to the dominant nuclear vibrational mode via a reorganization energy. This model is used to explore the effects of the electronic inter-dot tunneling (coupling) matrix element and the reorganization energy on device switching. A semi-classical reduction of the model also is made to investigate the competition between field-driven device switching and the electron-vibrational self-trapping. A strong electron-vibrational coupling (high reorganization energy) gives rise to self-trapping, which inhibits the molecule's ability to switch. Nonetheless, there remains an expansive area in the tunneling-reorganization phase space where molecules can support adequate tunneling. Thus, the relationship between the tunneling matrix element and the reorganization energy affords significant leeway in the design of molecules viable for QCA applications.

  11. Order α'(two-loop) equivalence of the string equations of motion and the σ-model Weyl invariance conditions

    International Nuclear Information System (INIS)

    Metsaev, R.R.; Tseytlin, A.A.

    1987-01-01

    We prove the on-shell equivalence of the order α' terms in the string effective equations (for the graviton, dilaton and the antisymmetric tensor) to the vanishing of the corresponding (two-loop) terms in the Weyl anomaly coefficients for the general bosonic σ-model. We first determine the α' term in the string effective action starting with the known expression for the 3- and 4-point string amplitudes. Then we compute the two-loop β-function in the general σ-model with the antisymmetric tensor coupling. Special emphasis is made on the renormalization scheme dependence of the β-function. Our result disagrees with the previously known one and cannot be manifestly expressed in terms of the generalized curvature for the connection with torsion. We also prove (to the order α' 2 ) that the parallelizable spaces are solutions of the string equations of motion and establish the complete 3-loop expression for the 'central charge' coefficient. (orig.)

  12. Comment on the prediction of two-loop standard chiral perturbation theory for low-energy ππ scattering

    International Nuclear Information System (INIS)

    Girlanda, L.; Moussallam, B.; Stern, J.; Knecht, M.

    1997-03-01

    Four of the six parameters defining the two-loop ππ scattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard χ PT expressions, the threshold parameters, low-energy phases and the O(p 4 ) constants l 1 r , l 2 r are obtained. The result reproduces the correct D-waves but it is incompatible with existing Standard χ PT analyses of K 14 form factors beyond one loop. (author)

  13. Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems

    Science.gov (United States)

    Rück, Marlon; Reuther, Johannes

    2018-04-01

    We implement an extension of the pseudofermion functional renormalization group method for quantum spin systems that takes into account two-loop diagrammatic contributions. An efficient numerical treatment of the additional terms is achieved within a nested graph construction which recombines different one-loop interaction channels. In order to be fully self-consistent with respect to self-energy corrections, we also include certain three-loop terms of Katanin type. We first apply this formalism to the antiferromagnetic J1-J2 Heisenberg model on the square lattice and benchmark our results against the previous one-loop plus Katanin approach. Even though the renormalization group (RG) equations undergo significant modifications when including the two-loop terms, the magnetic phase diagram, comprising Néel ordered and collinear ordered phases separated by a magnetically disordered regime, remains remarkably unchanged. Only the boundary position between the disordered and the collinear phases is found to be moderately affected by two-loop terms. On the other hand, critical RG scales, which we associate with critical temperatures Tc, are reduced by a factor of ˜2 indicating that the two-loop diagrams play a significant role in enforcing the Mermin-Wagner theorem. Improved estimates for critical temperatures are also obtained for the Heisenberg ferromagnet on the three-dimensional simple cubic lattice where errors in Tc are reduced by ˜34 % . These findings have important implications for the quantum phase diagrams calculated within the previous one-loop plus Katanin approach which turn out to be already well converged.

  14. Two-loop O(ααs) corrections to the on-shell fermion propagator in the standard model

    International Nuclear Information System (INIS)

    Eiras, Dolors; Steinhauser, Matthias

    2006-01-01

    In this paper we consider mixed two-loop electroweak corrections to the top quark propagator in the Standard Model. In particular, we compute the on-shell renormalization constant for the mass and wave function, which constitute building blocks for many physical processes. The results are expressed in terms of master integrals. For the latter practical approximations are derived. In the case of the mass renormalization constant we find agreement with the results in the literature

  15. High-resolution magnetic resonance angiography of the lower extremities with a dedicated 36-element matrix coil at 3 Tesla.

    Science.gov (United States)

    Kramer, Harald; Michaely, Henrik J; Matschl, Volker; Schmitt, Peter; Reiser, Maximilian F; Schoenberg, Stefan O

    2007-06-01

    Recent developments in hard- and software help to significantly increase image quality of magnetic resonance angiography (MRA). Parallel acquisition techniques (PAT) help to increase spatial resolution and to decrease acquisition time but also suffer from a decrease in signal-to-noise ratio (SNR). The movement to higher field strength and the use of dedicated angiography coils can further increase spatial resolution while decreasing acquisition times at the same SNR as it is known from contemporary exams. The goal of our study was to compare the image quality of MRA datasets acquired with a standard matrix coil in comparison to MRA datasets acquired with a dedicated peripheral angio matrix coil and higher factors of parallel imaging. Before the first volunteer examination, unaccelerated phantom measurements were performed with the different coils. After institutional review board approval, 15 healthy volunteers underwent MRA of the lower extremity on a 32 channel 3.0 Tesla MR System. In 5 of them MRA of the calves was performed with a PAT acceleration factor of 2 and a standard body-matrix surface coil placed at the legs. Ten volunteers underwent MRA of the calves with a dedicated 36-element angiography matrix coil: 5 with a PAT acceleration of 3 and 5 with a PAT acceleration factor of 4, respectively. The acquired volume and acquisition time was approximately the same in all examinations, only the spatial resolution was increased with the acceleration factor. The acquisition time per voxel was calculated. Image quality was rated independently by 2 readers in terms of vessel conspicuity, venous overlay, and occurrence of artifacts. The inter-reader agreement was calculated by the kappa-statistics. SNR and contrast-to-noise ratios from the different examinations were evaluated. All 15 volunteers completed the examination, no adverse events occurred. None of the examinations showed venous overlay; 70% of the examinations showed an excellent vessel conspicuity

  16. Perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: Two-loop corrections

    Science.gov (United States)

    Maelger, J.; Reinosa, U.; Serreau, J.

    2018-04-01

    We extend a previous investigation [U. Reinosa et al., Phys. Rev. D 92, 025021 (2015), 10.1103/PhysRevD.92.025021] of the QCD phase diagram with heavy quarks in the context of background field methods by including the two-loop corrections to the background field effective potential. The nonperturbative dynamics in the pure-gauge sector is modeled by a phenomenological gluon mass term in the Landau-DeWitt gauge-fixed action, which results in an improved perturbative expansion. We investigate the phase diagram at nonzero temperature and (real or imaginary) chemical potential. Two-loop corrections yield an improved agreement with lattice data as compared to the leading-order results. We also compare with the results of nonperturbative continuum approaches. We further study the equation of state as well as the thermodynamic stability of the system at two-loop order. Finally, using simple thermodynamic arguments, we show that the behavior of the Polyakov loops as functions of the chemical potential complies with their interpretation in terms of quark and antiquark free energies.

  17. Multi-scale damage modelling in a ceramic matrix composite using a finite-element microstructure meshfree methodology

    Science.gov (United States)

    2016-01-01

    The problem of multi-scale modelling of damage development in a SiC ceramic fibre-reinforced SiC matrix ceramic composite tube is addressed, with the objective of demonstrating the ability of the finite-element microstructure meshfree (FEMME) model to introduce important aspects of the microstructure into a larger scale model of the component. These are particularly the location, orientation and geometry of significant porosity and the load-carrying capability and quasi-brittle failure behaviour of the fibre tows. The FEMME model uses finite-element and cellular automata layers, connected by a meshfree layer, to efficiently couple the damage in the microstructure with the strain field at the component level. Comparison is made with experimental observations of damage development in an axially loaded composite tube, studied by X-ray computed tomography and digital volume correlation. Recommendations are made for further development of the model to achieve greater fidelity to the microstructure. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’. PMID:27242308

  18. Exact and approximate exchange potentials investigated in terms of their matrix elements with the Kohn-Sham orbitals

    International Nuclear Information System (INIS)

    Holas, A.; Cinal, M.

    2005-01-01

    Three approximate exchange potentials of high accuracy v x Y (r), Y=A,B,C, for the density-functional theory applications are obtained by replacing the matrix elements of the exact potential between the Kohn-Sham (KS) orbitals with such elements of the Fock exchange operator (within the virtual-occupied subset only) in three representations found for any local potential. A common identity is the base of these representations. The potential v x C happens to be the same as that derived by Harbola and Sahni, and v x A as that derived by Gritsenko and Baerends, and Della Sala and Goerling. The potentials obtained can be expressed in terms of occupied KS orbitals only. At large r, their asymptotic form -1/r is the same as that of the exact potential. The high quality of these three approximations is demonstrated by direct comparison with the exact potential and using various consistency tests. A common root established for the three approximations could be helpful in finding new and better approximations via modification of identities employed in the present investigation

  19. Matrix elements of intraband transitions in quantum dot intermediate band solar cells: the influence of quantum dot presence on the extended-state electron wave-functions

    International Nuclear Information System (INIS)

    Nozawa, Tomohiro; Arakawa, Yasuhiko

    2014-01-01

    The intraband transitions which are essential for quantum dot intermediate band solar cells (QD IBSCs) are theoretically investigated by estimating the matrix elements from a ground bound state, which is often regarded as an intermediate band (IB), to conduction band (CB) states for a structure with a quantum dot (QD) embedded in a matrix (a QD/matrix structure). We have found that the QD pushes away the electron envelope functions (probability densities) from the QD region in almost all quantum states above the matrix CB minimum. As a result, the matrix elements of the intraband transitions in the QD/matrix structure are largely reduced, compared to those calculated assuming the envelope functions of free electrons (i.e., plane-wave envelope functions) in a matrix structure as the final states of the intraband transitions. The result indicates the strong influence of the QD itself on the intraband transitions from the IB to the CB states in QD IBSC devices. This work will help in better understanding the problem of the intraband transitions and give new insight, that is, engineering of quantum states is indispensable for the realization of QD IBSCs with high solar energy conversion efficiencies. (paper)

  20. An experimental determination of the parameters describing the K/sup + / to pi /sup +/ pi /sup 0/ pi /sup 0/ decay matrix element

    CERN Document Server

    Braun, H; Erriquez, O; Martyn, H U; Renton, P B; Romano, F; Vilain, P; Waldren, D

    1976-01-01

    The matrix element of the three pion decay mode of the kaon is expressed in terms of Mandelstam variables. An analysis of the Dalitz plot density distribution gives information on the parameters of the expression. From an analysis of the decays of stopping K/sup +/ mesons involving neutral pions in the CERN heavy-liquid bubble chamber filled with a propane ethane mixture, it is concluded that the energy dependence of the decay matrix element is compatible with a linear behaviour. (3 refs).

  1. System-Level Heat Transfer Analysis, Thermal- Mechanical Cyclic Stress Analysis, and Environmental Fatigue Modeling of a Two-Loop Pressurized Water Reactor. A Preliminary Study

    Energy Technology Data Exchange (ETDEWEB)

    Mohanty, Subhasish [Argonne National Lab. (ANL), Argonne, IL (United States); Soppet, William [Argonne National Lab. (ANL), Argonne, IL (United States); Majumdar, Saurin [Argonne National Lab. (ANL), Argonne, IL (United States); Natesan, Ken [Argonne National Lab. (ANL), Argonne, IL (United States)

    2015-01-03

    This report provides an update on an assessment of environmentally assisted fatigue for light water reactor components under extended service conditions. This report is a deliverable in April 2015 under the work package for environmentally assisted fatigue under DOE's Light Water Reactor Sustainability program. In this report, updates are discussed related to a system level preliminary finite element model of a two-loop pressurized water reactor (PWR). Based on this model, system-level heat transfer analysis and subsequent thermal-mechanical stress analysis were performed for typical design-basis thermal-mechanical fatigue cycles. The in-air fatigue lives of components, such as the hot and cold legs, were estimated on the basis of stress analysis results, ASME in-air fatigue life estimation criteria, and fatigue design curves. Furthermore, environmental correction factors and associated PWR environment fatigue lives for the hot and cold legs were estimated by using estimated stress and strain histories and the approach described in NUREG-6909. The discussed models and results are very preliminary. Further advancement of the discussed model is required for more accurate life prediction of reactor components. This report only presents the work related to finite element modelling activities. However, in between multiple tensile and fatigue tests were conducted. The related experimental results will be presented in the year-end report.

  2. NNLO QCD corrections to the $B\\to X_s \\gamma$ matrix elements using interpolation in $m_c$

    CERN Document Server

    Misiak, M; Misiak, Mikolaj; Steinhauser, Matthias

    2007-01-01

    One of the most troublesome contributions to the NNLO QCD corrections to B -> X_s gamma originates from three-loop matrix elements of four-quark operators. A part of this contribution that is proportional to the QCD beta-function coefficient beta_0 was found in 2003 as an expansion in m_c/m_b. In the present paper, we evaluate the asymptotic behaviour of the complete contribution for m_c >> m_b/2. The asymptotic form of the beta_0-part matches the small-m_c expansion very well at the threshold m_c = m_b/2. For the remaining part, we perform an interpolation down to the measured value of m_c, assuming that the beta_0-part is a good approximation at m_c=0. Combining our results with other contributions to the NNLO QCD corrections, we find BR(B -> X_s gamma) = (3.15 +_ 0.23) x 10^-4 for E_gamma > 1.6 GeV in the B-meson rest frame. The indicated error has been obtained by adding in quadrature the following uncertainties: non-perturbative (5%), parametric (3%), higher-order perturbative (3%), and the interpolation...

  3. Search for rare processes with a Z+bb signature at the LHC, with the matrix element method

    CERN Document Server

    Beluffi, Camille; Lemaitre, Vincent

    This thesis presents a detailed study of the final state with the Z boson decaying into two leptons, produced in the CMS detector at the LHC. In order to tag this topology, sophisticated b jet tagging algorithms have been used, and the calibration of one of them, the Jet Probability (JP) tagger is exposed. A study of the tagger degradation at high energy has been done and led to a small gain of performance. This investigation is followed by the search for the associated production of the standard model (SM) Higgs boson with a Z boson and decaying into two b quarks (ZH channel), using the Matrix Element Method (MEM) and two b-taggers: JP and Combined Secondary Vertex (CSV). The MEM is an advanced tool that produces an event-by-event discriminating variable, called weight. To apply it, several sets of transfer function have been produced. The final results give an observed limit on the ZH production cross section with the H → bb branching ratio of 5.46xσSM when using the CSV tagger and 4.89xσSM when using t...

  4. Measurement of the CKM Matrix Element |V sub u sub b | with B -> rho e nu Decays

    CERN Document Server

    Wilden, L

    2003-01-01

    We present a measurement of the branching fraction for the rare decays B -> rho e nu and extract a value for the magnitude of V sub u sub b , one of the smallest elements of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix. The results are given for five different calculations of form factors used to parametrize the hadronic current in semileptonic decays. Using a sample of 55 million B(bar B) meson pairs recorded with the BABAR detector at the PEP-II e sup + e sup - storage ring, we obtain BETA(B sup 0 -> rho sup - sup 1 e sup + nu) = (3.29 +- 0.42 +- 0.47 +- 0.60) x 10 sup - sup 4 and |V sub u sub b | = (3.64 +- 0.22 +- 0.25 sub - sub 0 sub . sub 5 sub 6 sup + sup 0 sup . sup 3 sup 9) x 10 sup - sup 3 , where the uncertainties are statistical, systematic, and theoretical, respectively.

  5. A Measurement of the Top Quark Mass in 1.96 TeV Proton-Antiproton Collisions Using a Novel Matrix Element Method

    International Nuclear Information System (INIS)

    CDF Collaboration; Freeman, John; Freeman, John

    2007-01-01

    A measurement of the top quark mass in t(bar t) → l + jets candidate events, obtained from p(bar p) collisions at √s = 1.96 TeV at the Fermilab Tevatron using the CDF II detector, is presented. The measurement approach is that of a matrix element method. For each candidate event, a two dimensional likelihood is calculated in the top pole mass and a constant scale factor, 'JES', where JES multiplies the input particle jet momenta and is designed to account for the systematic uncertainty of the jet momentum reconstruction. As with all matrix element techniques, the method involves an integration using the Standard Model matrix element for t(bar t) production and decay. However, the technique presented is unique in that the matrix element is modified to compensate for kinematic assumptions which are made to reduce computation time. Background events are dealt with through use of an event observable which distinguishes signal from background, as well as through a cut on the value of an event's maximum likelihood. Results are based on a 955 pb -1 data sample, using events with a high-p T lepton and exactly four high-energy jets, at least one of which is tagged as coming from a b quark; 149 events pass all the selection requirements. They find M meas = 169.8 ± 2.3(stat.) ± 1.4(syst.) GeV/c 2

  6. The matrix-elements of two-particle residual interaction in the shell-model formalism with the M.S.D.I. approximation. Part 2

    International Nuclear Information System (INIS)

    Jasielska, A.; Wiktor, S.

    1977-01-01

    The table of two-particle matrix elements calculated according to the formalism of MSDI approximation for the orbits 1fsub(7/2), 2psub(3/2), 2psub(1/2) and 1fsub(5/2) and published previously is now supplemented by inclusion of the 1gsub(9/2) orbit. (author)

  7. Multiphonon K/sup π/+ states in even-even deformed nuclei. II. Calculation of matrix elements of a general Hamiltonian

    International Nuclear Information System (INIS)

    Silvestre-Brac, B.; Piepenbring, R.

    1978-01-01

    Matrix elements of a general Hamiltonian H in a subspace spanned by collective K/sup π/+ deformed phonons are derived with the help of recursion formulas. Various approximations are discussed both in the fermion space and in the boson space. Careful comparisons are made in the framework of a simple solvable model

  8. Electric dipole moment function of the X1 Sigma/+/ state of CO - Vibration-rotation matrix elements for transitions of gas laser and astrophysical interest

    Science.gov (United States)

    Chackerian, C., Jr.

    1976-01-01

    The electric dipole moment function of the ground electronic state of carbon monoxide has been determined by combining numerical solutions of the radial Schrodinger equation with absolute intensity data of vibration-rotation bands. The derived dipole moment function is used to calculate matrix elements of interest to stellar astronomy and of importance in the carbon monoxide laser.

  9. Multi-Target Angle Tracking Algorithm for Bistatic Multiple-Input Multiple-Output (MIMO Radar Based on the Elements of the Covariance Matrix

    Directory of Open Access Journals (Sweden)

    Zhengyan Zhang

    2018-03-01

    Full Text Available In this paper, we consider the problem of tracking the direction of arrivals (DOA and the direction of departure (DOD of multiple targets for bistatic multiple-input multiple-output (MIMO radar. A high-precision tracking algorithm for target angle is proposed. First, the linear relationship between the covariance matrix difference and the angle difference of the adjacent moment was obtained through three approximate relations. Then, the proposed algorithm obtained the relationship between the elements in the covariance matrix difference. On this basis, the performance of the algorithm was improved by averaging the covariance matrix element. Finally, the least square method was used to estimate the DOD and DOA. The algorithm realized the automatic correlation of the angle and provided better performance when compared with the adaptive asymmetric joint diagonalization (AAJD algorithm. The simulation results demonstrated the effectiveness of the proposed algorithm. The algorithm provides the technical support for the practical application of MIMO radar.

  10. Multi-Target Angle Tracking Algorithm for Bistatic Multiple-Input Multiple-Output (MIMO) Radar Based on the Elements of the Covariance Matrix.

    Science.gov (United States)

    Zhang, Zhengyan; Zhang, Jianyun; Zhou, Qingsong; Li, Xiaobo

    2018-03-07

    In this paper, we consider the problem of tracking the direction of arrivals (DOA) and the direction of departure (DOD) of multiple targets for bistatic multiple-input multiple-output (MIMO) radar. A high-precision tracking algorithm for target angle is proposed. First, the linear relationship between the covariance matrix difference and the angle difference of the adjacent moment was obtained through three approximate relations. Then, the proposed algorithm obtained the relationship between the elements in the covariance matrix difference. On this basis, the performance of the algorithm was improved by averaging the covariance matrix element. Finally, the least square method was used to estimate the DOD and DOA. The algorithm realized the automatic correlation of the angle and provided better performance when compared with the adaptive asymmetric joint diagonalization (AAJD) algorithm. The simulation results demonstrated the effectiveness of the proposed algorithm. The algorithm provides the technical support for the practical application of MIMO radar.

  11. Two-Loop Effective Theory Analysis of π (K)→eνe[γ] Branching Ratios

    International Nuclear Information System (INIS)

    Cirigliano, Vincenzo; Rosell, Ignasi

    2007-01-01

    We study the ratios R e/μ (P) ≡Γ(P→eν e [γ])/Γ(P→μν μ [γ]) (P=π, K) in Chiral Perturbation Theory to order e 2 p 4 . We complement the two-loop effective theory results with a matching calculation of the counterterm, finding R e/μ (π) =(1.2352±0.0001)x10 -4 and R e/μ (K) =(2.477±0.001)x10 -5

  12. Soft radiation in heavy-particle pair production: All-order colour structure and two-loop anomalous dimension

    International Nuclear Information System (INIS)

    Beneke, M.; Falgari, P.; Schwinn, C.

    2010-01-01

    We consider the total production cross section of heavy coloured particle pairs in hadronic collisions at the production threshold. We construct a basis in colour space that diagonalizes to all orders in perturbation theory the soft function, which appears in a new factorization formula for the combined resummation of soft gluon and Coulomb gluon effects. This extends recent results on the structure of soft anomalous dimensions and allows us to determine an analytic expression for the two-loop soft anomalous dimension at threshold for all production processes of interest.

  13. Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogenlike ions

    Science.gov (United States)

    Yerokhin, V. A.

    2018-05-01

    The two-loop self-energy correction to the Lamb shift of hydrogenlike ions is calculated for the 1 s , 2 s , and 2 p1 /2 states and nuclear charge numbers Z =30 -100 . The calculation is performed to all orders in the nuclear binding strength parameter Z α . As compared to previous calculations of this correction, numerical accuracy is improved by an order of magnitude and the region of the nuclear charges is extended. An analysis of the Z dependence of the obtained results demonstrates their consistency with the known Z α -expansion coefficients.

  14. Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph

    International Nuclear Information System (INIS)

    Remiddi, Ettore; Tancredi, Lorenzo

    2014-01-01

    A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities are then used in the case of the two-loop sunrise graph with arbitrary masses for recovering the second-order differential equation for the scalar amplitude in d=2 dimensions, as well as a chained set of equations for all the coefficients of the expansions in (d−2). The shift from d≈2 to d≈4 dimensions is then discussed

  15. Two-loop top and bottom Yukawa corrections to the Higgs-boson masses in the complex MSSM

    Science.gov (United States)

    Paßehr, Sebastian; Weiglein, Georg

    2018-03-01

    Results for the two-loop corrections to the Higgs-boson masses of the MSSM with complex parameters of O{( α _t^2+α _tα _b+α _b^2) } from the Yukawa sector in the gauge-less limit are presented. The corresponding self-energies and their renormalization have been obtained in the Feynman-diagrammatic approach. The impact of the new contributions on the Higgs spectrum is investigated. Furthermore, a comparison with an existing result in the limit of the MSSM with real parameters is carried out. The new results will be included in the public code FeynHiggs.

  16. A new deformation of W-infinity and applications to the two-loop WZNW and conformal affine Toda models

    International Nuclear Information System (INIS)

    Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Zimerman, A.H.

    1992-01-01

    We constructed a center less W-infinity type of algebra in terms of a generator of a center less Virasoro algebra and an Abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra w ∞ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth W ∞ invariance of these models. (author)

  17. Two-loop top and bottom Yukawa corrections to the Higgs-boson masses in the complex MSSM

    International Nuclear Information System (INIS)

    Passehr, Sebastian; Weiglein, Georg

    2017-05-01

    Results for the two-loop corrections to the Higgs-boson masses of the MSSM with complex parameters of O(α 2 t +α t α b +α 2 b ) from the Yukawa sector in the gauge-less limit are presented. The corresponding self-energies and their renormalization have been obtained in the Feynman-diagrammatic approach. The impact of the new contributions on the Higgs spectrum is investigated. Furthermore, a comparison with an existing result in the limit of the MSSM with real parameters is carried out. The new results will be included in the public code FeynHiggs.

  18. 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.)

  19. Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

    CERN Document Server

    Dixon, Lance J.; Henn, Johannes M.

    2012-01-01

    We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two function...

  20. Two-loop controller for maximizing performance of a grid-connected photovoltaic - fuel cell hybrid power plant

    Science.gov (United States)

    Ro, Kyoungsoo

    The study started with the requirement that a photovoltaic (PV) power source should be integrated with other supplementary power sources whether it operates in a stand-alone or grid-connected mode. First, fuel cells for a backup of varying PV power were compared in detail with batteries and were found to have more operational benefits. Next, maximizing performance of a grid-connected PV-fuel cell hybrid system by use of a two-loop controller was discussed. One loop is a neural network controller for maximum power point tracking, which extracts maximum available solar power from PV arrays under varying conditions of insolation, temperature, and system load. A real/reactive power controller (RRPC) is the other loop. The RRPC meets the system's requirement for real and reactive powers by controlling incoming fuel to fuel cell stacks as well as switching control signals to a power conditioning subsystem. The RRPC is able to achieve more versatile control of real/reactive powers than the conventional power sources since the hybrid power plant does not contain any rotating mass. Results of time-domain simulations prove not only effectiveness of the proposed computer models of the two-loop controller, but also their applicability for use in transient stability analysis of the hybrid power plant. Finally, environmental evaluation of the proposed hybrid plant was made in terms of plant's land requirement and lifetime COsb2 emissions, and then compared with that of the conventional fossil-fuel power generating forms.

  1. Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions

    Science.gov (United States)

    Chen, Zhenhua; Chen, Xun; Wu, Wei

    2013-04-01

    In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.

  2. Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

    CERN Document Server

    Anastasiou, C; Bucherer, S; Daleo, A; Kunszt, Zoltán; Anastasiou, Charalampos; Beerli, Stefan; Bucherer, Stefan; Daleo, Alejandro; Kunszt, Zoltan

    2007-01-01

    We compute all two-loop master integrals which are required for the evaluation of next-to-leading order QCD corrections in Higgs boson production via gluon fusion. Many two-loop amplitudes for 2 -> 1 processes in the Standard Model and beyond can be expressed in terms of these integrals using automated reduction techniques. These integrals also form a subset of the master integrals for more complicated 2 -> 2 amplitudes with massive propagators in the loops. As a first application, we evaluate the two-loop amplitude for Higgs boson production in gluon fusion via a massive quark. Our result is the first independent check of the calculation of Spira, Djouadi, Graudenz and Zerwas. We also present for the first time the two-loop amplitude for gg -> h via a massive squark.

  3. Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

    International Nuclear Information System (INIS)

    Henn, Johannes M.; Melnikov, Kirill; Smirnov, Vladimir A.

    2014-01-01

    We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals in this class are the two-loop four-point functions where two external lines are on the light-cone and two other external lines have different invariant masses. We compute these and other relevant integrals analytically using differential equations in external kinematic variables and express our results in terms of Goncharov polylogarithms. The case of two equal off-shellnesses, recently considered in ref. http://dx.doi.org/10.1007/JHEP08(2013)070, appears as a particular case of our general solution

  4. Dominant two-loop electroweak corrections to the hadroproduction of a pseudoscalar Higgs boson and its photonic decay

    International Nuclear Information System (INIS)

    Brod, J.; Kniehl, B.A.

    2008-01-01

    We present the dominant two-loop electroweak corrections to the partial decay widths to gluon jets and prompt photons of the neutral CP-odd Higgs boson A 0 , with mass M A 0 W , in the two-Higgs-doublet model for low to intermediate values of the ratio tan β=v 2 /v 1 of the vacuum expectation values. They apply as they stand to the production cross sections in hadronic and two-photon collisions, at the Tevatron, the LHC, and a future photon collider. The appearance of three γ 5 matrices in closed fermion loops requires special care in the dimensional regularization of ultraviolet divergences. The corrections are negative and amount to several percent, so that they fully compensate or partly screen the enhancement due to QCD corrections. (orig.)

  5. On the Kählerian symmetries of the two-loop action of the effective string theory

    CERN Document Server

    Ozkurt, S S

    2003-01-01

    Sometimes ago, it has been proposed in a paper by N.Kaloper and K.A.Meissner (\\PR {\\bf D56} (1997) 7940) that if one makes local redefinitions of fields, it does not change the equations of motion (in the redefined fields); however, this comment has not generally been accepted, namely, the redefined fields satisfy different equations of motion. For this reason, in this paper, it is proved that the whole action can be written as a square of the zeroth-order field equations. In this way, we show that any solution of the zeroth-order field equations, which has some K\\"{a}hler symmetry, at the same time, is also a solution of the two-loop equations.

  6. Two-loop top and bottom Yukawa corrections to the Higgs-boson masses in the complex MSSM

    Energy Technology Data Exchange (ETDEWEB)

    Passehr, Sebastian; Weiglein, Georg

    2017-05-15

    Results for the two-loop corrections to the Higgs-boson masses of the MSSM with complex parameters of O(α{sup 2}{sub t}+α{sub t}α{sub b}+α{sup 2}{sub b}) from the Yukawa sector in the gauge-less limit are presented. The corresponding self-energies and their renormalization have been obtained in the Feynman-diagrammatic approach. The impact of the new contributions on the Higgs spectrum is investigated. Furthermore, a comparison with an existing result in the limit of the MSSM with real parameters is carried out. The new results will be included in the public code FeynHiggs.

  7. Application of code scaling, applicability and uncertainty methodology to large break LOCA analysis of two loop PWR

    International Nuclear Information System (INIS)

    Mavko, B.; Stritar, A.; Prosek, A.

    1993-01-01

    In NED 119, No. 1 (May 1990) a series of six papers published by a Technical Program Group presented a new methodology for the safety evaluation of emergency core cooling systems in nuclear power plants. This paper describes the application of that new methodology to the LB LOCA analysis of the two loop Westinghouse power plant. Results of the original work were used wherever possible, so that the analysis was finished in less than one man year of work. Steam generator plugging level and safety injection flow rate were used as additional uncertainty parameters, which had not been used in the original work. The computer code RELAP5/MOD2 was used. Response surface was generated by the regression analysis and by the artificial neural network like Optimal Statistical Estimator method. Results were compared also to the analytical calculation. (orig.)

  8. Neutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions. Part 1: bare matrix elements and physical results

    International Nuclear Information System (INIS)

    Garron, Nicolas; Hudspith, Renwick J.; Lytle, Andrew T.

    2016-01-01

    We compute the hadronic matrix elements of the four-quark operators relevant for K 0 −K̄ 0 mixing beyond the Standard Model. Our results are from lattice QCD simulations with n f =2+1 flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing (a∼0.08 and a∼0.11 fm) and with lightest unitary pion mass ∼300 MeV. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description of the renormalisation procedure is presented in a companion paper. We argue that the intermediate renormalisation scheme is responsible for the discrepancies found by different collaborations. We also study different normalisations and determine the matrix elements of the relevant four-quark operators with a precision of ∼5% or better.

  9. Measurement of the matrix elements for the decays η'→η π+π- and η'→η π0π0

    Science.gov (United States)

    Ablikim, M.; Achasov, M. N.; Ahmed, S.; Albrecht, M.; Amoroso, A.; An, F. F.; An, Q.; Bai, J. Z.; Bai, Y.; Bakina, O.; Baldini Ferroli, R.; Ban, Y.; Bennett, D. W.; Bennett, J. V.; Berger, N.; Bertani, M.; Bettoni, D.; Bian, J. M.; Bianchi, F.; Boger, E.; Boyko, I.; Briere, R. A.; Cai, H.; Cai, X.; Cakir, O.; Calcaterra, A.; Cao, G. F.; Cetin, S. A.; Chai, J.; Chang, J. F.; Chelkov, G.; Chen, G.; Chen, H. S.; Chen, J. C.; Chen, M. L.; Chen, S. J.; Chen, X. R.; Chen, Y. B.; Chu, X. K.; Cibinetto, G.; Dai, H. L.; Dai, J. P.; Dbeyssi, A.; Dedovich, D.; Deng, Z. Y.; Denig, A.; Denysenko, I.; Destefanis, M.; de Mori, F.; Ding, Y.; Dong, C.; Dong, J.; Dong, L. Y.; Dong, M. Y.; Dorjkhaidav, O.; Dou, Z. L.; Du, S. X.; Duan, P. F.; Fang, J.; Fang, S. S.; Fang, X.; Fang, Y.; Farinelli, R.; Fava, L.; Fegan, S.; Feldbauer, F.; Felici, G.; Feng, C. Q.; Fioravanti, E.; Fritsch, M.; Fu, C. D.; Gao, Q.; Gao, X. L.; Gao, Y.; Gao, Y. G.; Gao, Z.; Garzia, I.; Goetzen, K.; Gong, L.; Gong, W. X.; Gradl, W.; Greco, M.; Gu, M. H.; Gu, S.; Gu, Y. T.; Guo, A. Q.; Guo, L. B.; Guo, R. P.; Guo, Y. P.; Haddadi, Z.; Han, S.; Hao, X. Q.; Harris, F. A.; He, K. L.; He, X. Q.; Heinsius, F. H.; Held, T.; Heng, Y. K.; Holtmann, T.; Hou, Z. L.; Hu, C.; Hu, H. M.; Hu, T.; Hu, Y.; Huang, G. S.; Huang, J. S.; Huang, X. T.; Huang, X. Z.; Huang, Z. L.; Hussain, T.; Ikegami Andersson, W.; Ji, Q.; Ji, Q. P.; Ji, X. B.; Ji, X. L.; Jiang, X. S.; Jiang, X. Y.; Jiao, J. B.; Jiao, Z.; Jin, D. P.; Jin, S.; Jin, Y.; Johansson, T.; Julin, A.; Kalantar-Nayestanaki, N.; Kang, X. L.; Kang, X. S.; Kavatsyuk, M.; Ke, B. C.; Khan, T.; Khoukaz, A.; Kiese, P.; Kliemt, R.; Koch, L.; Kolcu, O. B.; Kopf, B.; Kornicer, M.; Kuemmel, M.; Kuhlmann, M.; Kupsc, A.; Kühn, W.; Lange, J. S.; Lara, M.; Larin, P.; Lavezzi, L.; Leithoff, H.; Leng, C.; Li, C.; Li, Cheng; Li, D. M.; Li, F.; Li, F. Y.; Li, G.; Li, H. B.; Li, H. J.; Li, J. C.; Li, Jin; Li, K.; Li, K.; Li, K. J.; Li, Lei; Li, P. L.; Li, P. R.; Li, Q. Y.; Li, T.; Li, W. D.; Li, W. G.; Li, X. L.; Li, X. N.; Li, X. Q.; Li, Z. B.; Liang, H.; Liang, Y. F.; Liang, Y. T.; Liao, G. R.; Lin, D. X.; Liu, B.; Liu, B. J.; Liu, C. X.; Liu, D.; Liu, F. H.; Liu, Fang; Liu, Feng; Liu, H. B.; Liu, H. H.; Liu, H. H.; Liu, H. M.; Liu, J. B.; Liu, J. P.; Liu, J. Y.; Liu, K.; Liu, K. Y.; Liu, Ke; Liu, L. D.; Liu, P. L.; Liu, Q.; Liu, S. B.; Liu, X.; Liu, Y. B.; Liu, Z. A.; Liu, Zhiqing; Long, Y. F.; Lou, X. C.; Lu, H. J.; Lu, J. G.; Lu, Y.; Lu, Y. P.; Luo, C. L.; Luo, M. X.; Luo, X. L.; Lyu, X. R.; Ma, F. C.; Ma, H. L.; Ma, L. L.; Ma, M. M.; Ma, Q. M.; Ma, T.; Ma, X. N.; Ma, X. Y.; Ma, Y. M.; Maas, F. E.; Maggiora, M.; Magnoni, A. S.; Malik, Q. A.; Mao, Y. J.; Mao, Z. P.; Marcello, S.; Meng, Z. X.; Messchendorp, J. G.; Mezzadri, G.; Min, J.; Min, T. J.; Mitchell, R. E.; Mo, X. H.; Mo, Y. J.; Morales Morales, C.; Morello, G.; Muchnoi, N. Yu.; Muramatsu, H.; Mustafa, A.; Nefedov, Y.; Nerling, F.; Nikolaev, I. B.; Ning, Z.; Nisar, S.; Niu, S. L.; Niu, X. Y.; Olsen, S. L.; Ouyang, Q.; Pacetti, S.; Pan, Y.; Papenbrock, M.; Patteri, P.; Pelizaeus, M.; Pellegrino, J.; Peng, H. P.; Peters, K.; Pettersson, J.; Ping, J. L.; Ping, R. G.; Poling, R.; Prasad, V.; Qi, H. R.; Qi, M.; Qian, S.; Qiao, C. F.; Qin, N.; Qin, X.; Qin, X. S.; Qin, Z. H.; Qiu, J. F.; Rashid, K. H.; Redmer, C. F.; Richter, M.; Ripka, M.; Rolo, M.; Rong, G.; Rosner, Ch.; Ruan, X. D.; Sarantsev, A.; Savrié, M.; Schnier, C.; Schoenning, K.; Shan, W.; Shao, M.; Shen, C. P.; Shen, P. X.; Shen, X. Y.; Sheng, H. Y.; Song, J. J.; Song, W. M.; Song, X. Y.; Sosio, S.; Sowa, C.; Spataro, S.; Sun, G. X.; Sun, J. F.; Sun, L.; Sun, S. S.; Sun, X. H.; Sun, Y. J.; Sun, Y. K.; Sun, Y. Z.; Sun, Z. J.; Sun, Z. T.; Tang, C. J.; Tang, G. Y.; Tang, X.; Tapan, I.; Tiemens, M.; Tsednee, B. T.; Uman, I.; Varner, G. S.; Wang, B.; Wang, B. L.; Wang, D.; Wang, D. Y.; Wang, Dan; Wang, K.; Wang, L. L.; Wang, L. S.; Wang, M.; Wang, P.; Wang, P. L.; Wang, W. P.; Wang, X. F.; Wang, Y.; Wang, Y. D.; Wang, Y. F.; Wang, Y. Q.; Wang, Z.; Wang, Z. G.; Wang, Z. H.; Wang, Z. Y.; Wang, Z. Y.; Weber, T.; Wei, D. H.; Wei, J. H.; Weidenkaff, P.; Wen, S. P.; Wiedner, U.; Wolke, M.; Wu, L. H.; Wu, L. J.; Wu, Z.; Xia, L.; Xia, Y.; Xiao, D.; Xiao, H.; Xiao, Y. J.; Xiao, Z. J.; Xie, Y. G.; Xie, Y. H.; Xiong, X. A.; Xiu, Q. L.; Xu, G. F.; Xu, J. J.; Xu, L.; Xu, Q. J.; Xu, Q. N.; Xu, X. P.; Yan, L.; Yan, W. B.; Yan, W. C.; Yan, Y. H.; Yang, H. J.; Yang, H. X.; Yang, L.; Yang, Y. H.; Yang, Y. X.; Ye, M.; Ye, M. H.; Yin, J. H.; You, Z. Y.; Yu, B. X.; Yu, C. X.; Yu, J. S.; Yuan, C. Z.; Yuan, Y.; Yuncu, A.; Zafar, A. A.; Zeng, Y.; Zeng, Z.; Zhang, B. X.; Zhang, B. Y.; Zhang, C. C.; Zhang, D. H.; Zhang, H. H.; Zhang, H. Y.; Zhang, J.; Zhang, J. L.; Zhang, J. Q.; Zhang, J. W.; Zhang, J. Y.; Zhang, J. Z.; Zhang, K.; Zhang, L.; Zhang, S. Q.; Zhang, X. Y.; Zhang, Y.; Zhang, Y.; Zhang, Y. H.; Zhang, Y. T.; Zhang, Yu; Zhang, Z. H.; Zhang, Z. P.; Zhang, Z. Y.; Zhao, G.; Zhao, J. W.; Zhao, J. Y.; Zhao, J. Z.; Zhao, Lei; Zhao, Ling; Zhao, M. G.; Zhao, Q.; Zhao, S. J.; Zhao, T. C.; Zhao, Y. B.; Zhao, Z. G.; Zhemchugov, A.; Zheng, B.; Zheng, J. P.; Zheng, W. J.; Zheng, Y. H.; Zhong, B.; Zhou, L.; Zhou, X.; Zhou, X. K.; Zhou, X. R.; Zhou, X. Y.; Zhou, Y. X.; Zhu, J.; Zhu, K.; Zhu, K. J.; Zhu, S.; Zhu, S. H.; Zhu, X. L.; Zhu, Y. C.; Zhu, Y. S.; Zhu, Z. A.; Zhuang, J.; Zou, B. S.; Zou, J. H.; Besiii Collaboration

    2018-01-01

    Based on a sample of 1.31 ×109 J /ψ events collected with the BESIII detector, the matrix elements for the decays η'→η π+π- and η'→η π0π0 are determined using 351,016 η'→(η →γ γ )π+π- and 56,249 η'→(η →γ γ )π0π0 events with background levels less than 1%. Two commonly used representations are used to describe the Dalitz plot density. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between η'→η π+π- and η'→η π0π0 is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in η'→η π0π0 is observed.

  10. The O(αs3) massive operator matrix elements of O(nf) for the structure function F2(x,Q2) and transversity

    International Nuclear Information System (INIS)

    Ablinger, J.; Bluemlein, J.; Klein, S.; Schneider, C.; Wissbrock, F.

    2011-01-01

    The contributions ∝n f to the O(α s 3 ) massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit Q 2 >>m 2 are computed for the structure function F 2 (x,Q 2 ) and transversity for general values of the Mellin variable N. Here, for two matrix elements, A qq,Q PS (N) and A qg,Q (N), the complete result is obtained. A first independent computation of the contributions to the 3-loop anomalous dimensions γ qg (N), γ qq PS (N), and γ qq NS,(TR) (N) is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only.

  11. Study on the fabrication of Al matrix composites strengthened by combined in-situ alumina particle and in-situ alloying elements

    International Nuclear Information System (INIS)

    Huang Zanjun; Yang Bin; Cui Hua; Zhang Jishan

    2003-01-01

    A new idea to fabricate aluminum matrix composites strengthened by combined in-situ particle strengthening and in-situ alloying has been proposed. Following the concept of in-situ alloying and in-situ particle strengthening, aluminum matrix composites reinforced by Cu and α-Al 2 O 3 particulate (material I) and the same matrix reinforced by Cu, Si alloying elements and α-Al 2 O 3 particulate (material II) have been obtained. SEM observation, EDS and XRD analysis show that the alloy elements Cu and Si exist in the two materials, respectively. In-situ Al 2 O 3 particulates are generally spherical and their mean size is less than 0.5 μm. TEM observation shows that the in-situ α-Al 2 O 3 particulates have a good cohesion with the matrix. The reaction mechanism of the Al 2 O 3 particulate obtained by this method was studied. Thermodynamic considerations are given to the in-situ reactions and the distribution characteristic of in-situ the α-Al 2 O 3 particulate in the process of solidification is also discussed

  12. Simplified boson realization of the SOq(3) subalgebra of Uq(3) and matrix elements of SO(3) quadrupole operators

    International Nuclear Information System (INIS)

    Bonatsos, D.; Lo Liduce, N.; Raychev, P.; Roussev, R.; Terziev, P.

    1996-01-01

    Quantum algebras (also called quantum groups) are nonlinear generalization of the usual Lie algebras, to which the reduce in the limiting case when the deformed parameters are set equal to unity. From mathematical point of view they have the structure of Holf algebras. The interest for applications of quantum algebras in physics was triggered in 1989 by the introduction of the q-deformed harmonic oscillator. In this connection the quantum algebra su q (2) has been used for description of superdeformed bands of even-even nuclei and rotational nuclear and molecular spectra. The construction of chains of subalgebras of a given q-algebra is a non trivial problem, since the existence of a chain of subalgebras of the corresponding Lie algebra does not guarantee the existence of the q-analogue of this chain. In particular, the so q (3) subalgebra of u q (3) has attracted much attention, since its classical analogue is a basic ingredient of several nuclear models, as the Elliot model and the su(3) limit of the Interacting Boson Model (IBM), the Fermion Dynamical Symmetry Model (FDSM), the Interacting Vector Boson Model (IVBM), the nuclear vibron model for clustering, as well as of the su(3) limit of the vibron model for molecules. In the present report we compute the reduced matrix elements of a special second-rank tensor operator (quadrupole operator) in the so q (3) subgroup of u q (3) basis (for the most symmetric u q (3)-representations) and investigate some of their properties. Also we construct a simplified boson realization of the so q (3) subalgebra of u q (3) and the corresponding so q (3) basis states. It should be noted that the obtained results are valid only for real values of the deformation parameter q. On the other hand the comparison of the experimental data with the predictions of a number of physical models, based on the q deformed su q (2) algebra, shows that one can achieve a good agreement between theory and experiment only if q is a pure phase (q

  13. Measurement of the top quark mass with the matrix element method in the semileptonic decay channel at D0

    International Nuclear Information System (INIS)

    Haefner, Petra

    2008-01-01

    The top quark plays a special role in the Standard Model of Particle Physics. With its enormous mass of about 170 GeV it is as heavy as a gold atom and is the only quark with a mass near the electroweak scale. Together with the W boson mass, the top quark mass allows indirect constraints on the mass of the hypothetical Higgs boson, which might hold the clue to the origin of mass. Top pair production with a semileptonic decay t anti t→W ± W -+ b anti b→q anti qlνb anti b is the ''golden channel'' for mass measurements, due to a large branching fraction and a relatively low background contamination compared to other decay channels. Top mass measurements based on this decay, performed with the matrix element method, have always been among the single best measurements in the world. In 2007, the top mass world average broke the 1% level of precision. Its measurement is no longer dominated by statistical but instead by systematic uncertainties. The reduction of systematic uncertainties has therefore become a key issue for further progress. This thesis introduces two new developments in the treatment of b jets. The first improvement is an optimization in the way b identification information is used. It leads to an enhanced separation between signal and background processes and reduces the statistical uncertainty by about 16%. The second improvement determines differences in the detector response and thus the energy scales of light jets and b jets. Thereby, it addresses the major source of systematic uncertainty in the latest top mass measurements. The method was validated on Monte Carlo events at the generator level, calibrated with fully simulated events, including detector simulation, and applied to D0 Run II data corresponding to 1 fb -1 of integrated luminosity. Possible sources of systematic uncertainties were studied. The top mass is measured to be: m t =(169.2±3.5(stat.)±1.0(syst.)) GeV. The simultaneous measurement of a scaling factor for the jet energy

  14. Measurement of the top quark mass with the matrix element method in the semileptonic decay channel at D0

    Energy Technology Data Exchange (ETDEWEB)

    Haefner, Petra

    2008-07-31

    The top quark plays a special role in the Standard Model of Particle Physics. With its enormous mass of about 170 GeV it is as heavy as a gold atom and is the only quark with a mass near the electroweak scale. Together with the W boson mass, the top quark mass allows indirect constraints on the mass of the hypothetical Higgs boson, which might hold the clue to the origin of mass. Top pair production with a semileptonic decay t anti t{yields}W{sup {+-}}W{sup -+}b anti b{yields}q anti ql{nu}b anti b is the ''golden channel'' for mass measurements, due to a large branching fraction and a relatively low background contamination compared to other decay channels. Top mass measurements based on this decay, performed with the matrix element method, have always been among the single best measurements in the world. In 2007, the top mass world average broke the 1% level of precision. Its measurement is no longer dominated by statistical but instead by systematic uncertainties. The reduction of systematic uncertainties has therefore become a key issue for further progress. This thesis introduces two new developments in the treatment of b jets. The first improvement is an optimization in the way b identification information is used. It leads to an enhanced separation between signal and background processes and reduces the statistical uncertainty by about 16%. The second improvement determines differences in the detector response and thus the energy scales of light jets and b jets. Thereby, it addresses the major source of systematic uncertainty in the latest top mass measurements. The method was validated on Monte Carlo events at the generator level, calibrated with fully simulated events, including detector simulation, and applied to D0 Run II data corresponding to 1 fb{sup -1} of integrated luminosity. Possible sources of systematic uncertainties were studied. The top mass is measured to be: m{sub t}=(169.2{+-}3.5(stat.){+-}1.0(syst.)) GeV. The

  15. Application of dot matrix LCD in multi-element portable X-ray fluorescence spectrometry The LCD is stated for Liquid Crystal Display

    CERN Document Server

    Lin Yan Chang; Lai Wan Chang; Zhou Si Chun

    2002-01-01

    Dot matrix LCD based on T6963C is a low power supply module. It needs no complex interface circuits connecting with MCU. Application in text and graphics is easy. Application of this LCD in multi-element portable XRF spectrometry is show. How to use it in Chinese, pull-down menu, spectrum and how to design the interface circuits with embedded computer are shown as well

  16. Algebraic manipulation of the states associated with the U(5)containsO(5)containsO(3) chain of groups: Orthonormalization and matrix elements

    International Nuclear Information System (INIS)

    Yannouleas, C.; Pacheco, J.M.

    1989-01-01

    A collection of procedures able to perform algebraic manipulations for the orthonormalization and for the calculation of matrix elements between the states associated with the U(5)containsO(5)containsO(3) chain of groups is presented. These procedures combine both the exact- and the bigfloat-arithmetic modes and thus return arbitrarily accurate results; this is particulary relevant to the Gram-Schmidt orthonormalization, where strong cancellations usually pose serious problems in all floating-point implementations. (orig.)

  17. A Measurement of the Top Quark Mass in 1.96 TeV Proton-Antiproton Collisions Using a Novel Matrix Element Method

    Energy Technology Data Exchange (ETDEWEB)

    Freeman, John [Univ. of California, Berkeley, CA (United States)

    2007-01-01

    A measurement of the top quark mass in t$\\bar{t}$ → l + jets candidate events, obtained from p$\\bar{p}$ collisions at √s = 1.96 TeV at the Fermilab Tevatron using the CDF II detector, is presented. The measurement approach is that of a matrix element method. For each candidate event, a two dimensional likelihood is calculated in the top pole mass and a constant scale factor, 'JES', where JES multiplies the input particle jet momenta and is designed to account for the systematic uncertainty of the jet momentum reconstruction. As with all matrix element techniques, the method involves an integration using the Standard Model matrix element for t$\\bar{t}$ production and decay. However, the technique presented is unique in that the matrix element is modified to compensate for kinematic assumptions which are made to reduce computation time. Background events are dealt with through use of an event observable which distinguishes signal from background, as well as through a cut on the value of an event's maximum likelihood. Results are based on a 955 pb-1 data sample, using events with a high-pT lepton and exactly four high-energy jets, at least one of which is tagged as coming from a b quark; 149 events pass all the selection requirements. They find Mmeas = 169.8 ± 2.3(stat.) ± 1.4(syst.) GeV/c2.

  18. Computationally efficient analytic representations of relativistic bound-bound, bound-unbound and unbound-unbound transition matrix elements of hydrogenic atoms

    International Nuclear Information System (INIS)

    Soldatov, A.; Seke, J.; Adam, G.; Polak, M.

    2008-01-01

    Full text: A closed analytic form for relativistic transition matrix elements between bound-bound, bound-unbound and unbound-unbound relativistic eigenstates of hydrogenic atoms by using the plane-wave expansion for the electromagnetic-field vector potential was derived in a form convenient for large-scale numerical calculations in QED. By applying the obtained formulae, these transition matrix elements can be evaluated analytically and numerically. These exact matrix elements, which to our knowledge have not been calculated as yet, are of great importance in the analysis of various atom-field interaction processes where retardation effects cannot be ignored. The ultimate goal of the ongoing research is to develop a general universal calculation technique for Seke's approximation and renormalization method in QED, for which the usage of the plane vector expansion for the vector potential is a preferable choice. However, our primary interest lies in the Lamb-shift calculation. Our nearest objective is to carry out the plain-style relativistic calculations of the Lamb shift of the energy levels of hydrogen-like atoms and ions from first principles in the second and higher perturbative orders, using the corresponding convenient as well as novel expressions for the magnitude in question as they stand, i.e. without any additional approximations. Due to that there is no way to achieve all the above-declared goals without recourse to large-scale laborious and time-consuming high-precision numerical calculations, having the transition matrix elements of all possible types in an analytic, convenient for their efficient numerical evaluation form, would be highly advantageous and even unavoidable, especially for calculations of various QED effects in higher perturbative orders be it, equally, in traditional or novel approach. (author)

  19. A Measurement of the Top Quark Mass with the D0 Detector at s**(1/2) = 1.96-TeV using the Matrix Element Method

    Energy Technology Data Exchange (ETDEWEB)

    Kroeninger, Kevin Alexander; /Bonn U.

    2004-04-01

    Using a data set of 158 and 169 pb{sup -1} of D0 Run-II data in the electron and muon plus jets channel, respectively, the top quark mass has been measured using the Matrix Element Method. The method and its implementation are described. Its performance is studied in Monte Carlo using ensemble tests and the method is applied to the Moriond 2004 data set.

  20. The transition matrix element A{sub gq}(N) of the variable flavor number scheme at O(α{sub s}{sup 3})

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Blümlein, J.; De Freitas, A. [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Hasselhuhn, A. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Manteuffel, A. von [PRISMA Cluster of Excellence and Institute of Physics, J. Gutenberg University, D-55099 Mainz (Germany); Round, M. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Schneider, C. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Wißbrock, F. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)

    2014-05-15

    We calculate the massive unpolarized operator matrix element A{sub gq}{sup (3)}(N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at O(α{sub s}{sup 3}). A first independent recalculation is performed for the contributions ∝N{sub F} of the 3-loop anomalous dimension γ{sub gq}{sup (2)}(N)

  1. The logarithmic contributions to the O(α{sub s}{sup 3}) asymptotic massive Wilson coefficients and operator matrix elements in deeply inelastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Bierenbaum, I. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Klein, S. [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie, Aachen (Germany); Wissbrock, F. [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Linz (Austria); IHES, Bures-sur-Yvette (France)

    2014-09-15

    We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given in Mellin N-space. (orig.)

  2. High-Energy Anomaly in the Angle-Resolved Photoemission Spectra of Nd2-xCexCuO4: Evidence for a Matrix Element Effect

    Science.gov (United States)

    Rienks, E. D. L.; ńrrälä, M.; Lindroos, M.; Roth, F.; Tabis, W.; Yu, G.; Greven, M.; Fink, J.

    2014-09-01

    We use polarization-dependent angle-resolved photoemission spectroscopy (ARPES) to study the high-energy anomaly (HEA) in the dispersion of Nd2-xCexCuO4, x =0.123. We find that at particular photon energies the anomalous, waterfall-like dispersion gives way to a broad, continuous band. This suggests that the HEA is a matrix element effect: it arises due to a suppression of the intensity of the broadened quasiparticle band in a narrow momentum range. We confirm this interpretation experimentally, by showing that the HEA appears when the matrix element is suppressed deliberately by changing the light polarization. Calculations of the matrix element using atomic wave functions and simulation of the ARPES intensity with one-step model calculations provide further evidence for this scenario. The possibility to detect the full quasiparticle dispersion further allows us to extract the high-energy self-energy function near the center and at the edge of the Brillouin zone.

  3. High-energy anomaly in the angle-resolved photoemission spectra of Nd(2-x)Ce(x)CuO₄: evidence for a matrix element effect.

    Science.gov (United States)

    Rienks, E D L; Ärrälä, M; Lindroos, M; Roth, F; Tabis, W; Yu, G; Greven, M; Fink, J

    2014-09-26

    We use polarization-dependent angle-resolved photoemission spectroscopy (ARPES) to study the high-energy anomaly (HEA) in the dispersion of Nd(2-x)Ce(x)CuO₄, x=0.123. We find that at particular photon energies the anomalous, waterfall-like dispersion gives way to a broad, continuous band. This suggests that the HEA is a matrix element effect: it arises due to a suppression of the intensity of the broadened quasiparticle band in a narrow momentum range. We confirm this interpretation experimentally, by showing that the HEA appears when the matrix element is suppressed deliberately by changing the light polarization. Calculations of the matrix element using atomic wave functions and simulation of the ARPES intensity with one-step model calculations provide further evidence for this scenario. The possibility to detect the full quasiparticle dispersion further allows us to extract the high-energy self-energy function near the center and at the edge of the Brillouin zone.

  4. Impact of band structure and transition matrix elements on polarization properties of the photoluminescence of semipolar and nonpolar InGaN quantum wells

    Energy Technology Data Exchange (ETDEWEB)

    Schade, L.; Schwarz, U.T. [Department of Microsystems Engineering, University of Freiburg, Georges-Koehler-Allee 103, 79108 Freiburg (Germany); Fraunhofer Institute for Applied Solid State Physics (IAF), Tullastrasse 72, 79108 Freiburg (Germany); Wernicke, T. [Institute of Solid State Physics, Technical University, Hardenbergstrasse 36, 10623 Berlin (Germany); Weyers, M. [Ferdinand-Braun-Institut fuer Hoechstfrequenztechnik, Gustav-Kirchhoff-Strasse 4, 12489 Berlin (Germany); Kneissl, M. [Institute of Solid State Physics, Technical University, Hardenbergstrasse 36, 10623 Berlin (Germany); Ferdinand-Braun-Institut fuer Hoechstfrequenztechnik, Gustav-Kirchhoff-Strasse 4, 12489 Berlin (Germany)

    2011-03-15

    Partial or full linear polarization is characteristic for the spontaneous emission of light from semipolar and nonpolar InGaN quantum wells. This property is an implication of the crystalline anisotropy as a basic property of the wurtzite structure. The influence of this anisotropy on the band structure and the transition matrix elements was calculated by a k.p-method for arbitrary quantum well orientations with respect to the c-axis; results are shown here in detail. Optical polarization is a direct consequence of a broken symmetry, mainly affecting the transition matrix elements from the conduction to the valence bands. Furthermore, the strain of the InGaN quantum well strongly depends on the crystal orientation of the substrate, resulting in a valence band mixing. The composition of the eigenfunctions has emerged to be most important for the polarization dependence of strained semipolar and nonpolar InGaN QW. The matrix elements, in combination with the thermal occupation of the bands, determine the polarization of the spontaneously emitted light. Our photoluminescence measurements of nonpolar QW match well with this model. However, in contrast to calculations with standard band parameters, the two topmost subbands show a larger separation in the emitted energy. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  5. New approach to nonleptonic weak interactions. I. Derivation of asymptotic selection rules for the two-particle weak ground-state-hadron matrix elements

    International Nuclear Information System (INIS)

    Tanuma, T.; Oneda, S.; Terasaki, K.

    1984-01-01

    A new approach to nonleptonic weak interactions is presented. It is argued that the presence and violation of the Vertical BarΔIVertical Bar = 1/2 rule as well as those of the quark-line selection rules can be explained in a unified way, along with other fundamental physical quantities [such as the value of g/sub A/(0) and the smallness of the isoscalar nucleon magnetic moments], in terms of a single dynamical asymptotic ansatz imposed at the level of observable hadrons. The ansatz prescribes a way in which asymptotic flavor SU(N) symmetry is secured levelwise for a certain class of chiral algebras in the standard QCD model. It yields severe asymptotic constraints upon the two-particle hadronic matrix elements of nonleptonic weak Hamiltonians as well as QCD currents and their charges. It produces for weak matrix elements the asymptotic Vertical BarΔIVertical Bar = 1/2 rule and its charm counterpart for the ground-state hadrons, while for strong matrix elements quark-line-like approximate selection rules. However, for the less important weak two-particle vertices involving higher excited states, the Vertical BarΔIVertical Bar = 1/2 rule and its charm counterpart are in general violated, providing us with an explicit source of the violation of these selection rules in physical processes

  6. Measurement of the electroweak top quark production cross section and the CKM matrix element Vtb with the D0 experiment

    International Nuclear Information System (INIS)

    Kirsch, Matthias

    2009-01-01

    At particle accelerators the Standard Model has been tested and will be tested further to a great precision. The data analyzed in this thesis have been collected at the world's highest energetic-collider, the Tevatron, located at the Fermi National Accelerator Laboratory (FNAL) in the vicinity of Chicago, IL, USA. There, protons and antiprotons are collided at a center-of-mass energy of √s = 1.96 TeV. The discovery of the top quark was one of the remarkable results not only for the CDF and D0 experiments at the Tevatron collider, but also for the Standard Model, which had predicted the existence of the top quark because of symmetry arguments long before already. Still, the Tevatron is the only facility able to produce top quarks. The predominant production mechanism of top quarks is the production of a top-antitop quark pair via the strong force. However, the Standard Model also allows the production of single top quarks via the electroweak interaction. This process features the unique opportunity to measure the |V tb | matrix element of the Cabbibo-Kobayashi-Maskawa (CKM) matrix directly, without assuming unitarity of the matrix or assuming that the number of quark generations is three. Hence, the measurement of the cross section of electroweak top quark production is more than the technical challenge to extract a physics process that only occurs one out of ten billion collisions. It is also an important test of the V-A structure of the electroweak interaction and a potential window to physics beyond the Standard Model in the case where the measurement of |V tb | would result in a value significantly different from 1, the value predicted by the Standard Model. At the Tevatron two production processes contribute significantly to the production of single top quarks: the production via the t-channel, also called W-gluon fusion, and the production via the s-channel, known as well as W* process. This analysis searches for the combined s+t channel production cross

  7. Measurement of the electroweak top quark production cross section and the CKM matrix element Vtb with the D0 experiment

    Energy Technology Data Exchange (ETDEWEB)

    Kirsch, Matthias [RWTH Aachen Univ. (Germany)

    2009-06-29

    At particle accelerators the Standard Model has been tested and will be tested further to a great precision. The data analyzed in this thesis have been collected at the world's highest energetic-collider, the Tevatron, located at the Fermi National Accelerator Laboratory (FNAL) in the vicinity of Chicago, IL, USA. There, protons and antiprotons are collided at a center-of-mass energy of {radical}s = 1.96 TeV. The discovery of the top quark was one of the remarkable results not only for the CDF and D0 experiments at the Tevatron collider, but also for the Standard Model, which had predicted the existence of the top quark because of symmetry arguments long before already. Still, the Tevatron is the only facility able to produce top quarks. The predominant production mechanism of top quarks is the production of a top-antitop quark pair via the strong force. However, the Standard Model also allows the production of single top quarks via the electroweak interaction. This process features the unique opportunity to measure the |Vtb| matrix element of the Cabbibo-Kobayashi-Maskawa (CKM) matrix directly, without assuming unitarity of the matrix or assuming that the number of quark generations is three. Hence, the measurement of the cross section of electroweak top quark production is more than the technical challenge to extract a physics process that only occurs one out of ten billion collisions. It is also an important test of the V-A structure of the electroweak interaction and a potential window to physics beyond the Standard Model in the case where the measurement of |V{sub tb}| would result in a value significantly different from 1, the value predicted by the Standard Model. At the Tevatron two production processes contribute significantly to the production of single top quarks: the production via the t-channel, also called W-gluon fusion, and the production via the s-channel, known as well as W* process. This analysis searches for the combined s

  8. Use of stirred tanks for studying matrix effects caused by inorganic acids, easily ionized elements and organic solvents in inductively coupled plasma atomic emission spectrometry

    Energy Technology Data Exchange (ETDEWEB)

    Paredes, Eduardo [Departamento de Quimica Analitica, Nutricion y Bromatologia, University of Alicante, 03080 Alicante (Spain); Maestre, Salvador E. [Departamento de Quimica Analitica, Nutricion y Bromatologia, University of Alicante, 03080 Alicante (Spain); Todoli, Jose L. [Departamento de Quimica Analitica, Nutricion y Bromatologia, University of Alicante, 03080 Alicante (Spain)]. E-mail: jose.todoli@ua.es

    2006-03-15

    A stirred tank was used for the first time to elucidate the mechanism responsible for inductively coupled plasma atomic emission spectroscopy (ICP-AES) matrix effects caused by inorganic, acids and easily ionized elements (EIEs), as well as organic, ethanol and acetic acid, compounds. In order to gradually increase the matrix concentration, a matrix solution was introduced inside a stirred container (tank) initially filled with an aqueous multielement standard. PolyTetraFluoroEthylene (PTFE) tubing was used to deliver the resulting solution to the liquid sample introduction system. Matrix concentration ranged from 0 to 2 mol l{sup -1} in the case of inorganic acids (i.e., nitric, sulfuric, hydrochloric and a mixture of them), from 0 to about 2500 mg l{sup -1} for EIEs (i.e., sodium, calcium and mixtures of both) and from 0% to 15%, w/w for organic compounds. Up to 40-50 different solutions were prepared and measured in a period of time shorter than 6-7 min. This investigation was carried out in terms of emission intensity and tertiary aerosols characteristics. The experimental setup used in the present work allowed to thoroughly study the effect of matrix concentration on analytical signal. Generally speaking, the experiments concerning tertiary aerosol characterization revealed that, in the case of inorganic acids and EIEs, the mechanism responsible for changes in aerosol characteristics was the droplet fission. In contrast, for organic matrices it was found that the interference was caused by a change in both aerosol transport and plasma thermal characteristics. The extent of the interferences caused by organic as well as inorganic compounds was compared for a set of 14 emission lines through a wide range of matrix concentrations. With a stirred tank, it is possible to choose an efficient internal standard for any given matrix composition. The time required to complete this procedure was shorter than 7 min.

  9. Use of stirred tanks for studying matrix effects caused by inorganic acids, easily ionized elements and organic solvents in inductively coupled plasma atomic emission spectrometry

    International Nuclear Information System (INIS)

    Paredes, Eduardo; Maestre, Salvador E.; Todoli, Jose L.

    2006-01-01

    A stirred tank was used for the first time to elucidate the mechanism responsible for inductively coupled plasma atomic emission spectroscopy (ICP-AES) matrix effects caused by inorganic, acids and easily ionized elements (EIEs), as well as organic, ethanol and acetic acid, compounds. In order to gradually increase the matrix concentration, a matrix solution was introduced inside a stirred container (tank) initially filled with an aqueous multielement standard. PolyTetraFluoroEthylene (PTFE) tubing was used to deliver the resulting solution to the liquid sample introduction system. Matrix concentration ranged from 0 to 2 mol l -1 in the case of inorganic acids (i.e., nitric, sulfuric, hydrochloric and a mixture of them), from 0 to about 2500 mg l -1 for EIEs (i.e., sodium, calcium and mixtures of both) and from 0% to 15%, w/w for organic compounds. Up to 40-50 different solutions were prepared and measured in a period of time shorter than 6-7 min. This investigation was carried out in terms of emission intensity and tertiary aerosols characteristics. The experimental setup used in the present work allowed to thoroughly study the effect of matrix concentration on analytical signal. Generally speaking, the experiments concerning tertiary aerosol characterization revealed that, in the case of inorganic acids and EIEs, the mechanism responsible for changes in aerosol characteristics was the droplet fission. In contrast, for organic matrices it was found that the interference was caused by a change in both aerosol transport and plasma thermal characteristics. The extent of the interferences caused by organic as well as inorganic compounds was compared for a set of 14 emission lines through a wide range of matrix concentrations. With a stirred tank, it is possible to choose an efficient internal standard for any given matrix composition. The time required to complete this procedure was shorter than 7 min

  10. Measurement of the top quark mass with the matrix element method in the semileptonic decay channel at D0

    Energy Technology Data Exchange (ETDEWEB)

    Haefner, Petra [Ludwig Maximilian Univ., Munich (Germany)

    2008-07-31

    The top quark plays a special role in the Standard Model of Particle Physics. With its enormous mass of about 170 GeV it is as heavy as a gold atom and is the only quark with a mass near the electroweak scale. Together with theW boson mass, the top quark mass allows indirect constraints on the mass of the hypothetical Higgs boson, which might hold the clue to the origin of mass. Top pair production with a semileptonic decay t $\\bar{t}$ →W±W b$\\bar{b}$ →q $\\bar{t}$lnb$\\bar{b}$ is the ”golden channel” for mass measurements, due to a large branching fraction and a relatively low background contamination compared to other decay channels. Top mass measurements based on this decay, performed with the matrix element method, have always been among the single best measurements in the world. In 2007, the top mass world average broke the 1% level of precision. Its measurement is no longer dominated by statistical but instead by systematic uncertainties. The reduction of systematic uncertainties has therefore become a key issue for further progress. This thesis introduces two new developments in the treatment of b jets. The first improvement is an optimization in the way b identification information is used. It leads to an enhanced separation between signal and background processes and reduces the statistical uncertainty by about 16%. The second improvement determines differences in the detector response and thus the energy scales of light jets and b jets. Thereby, it addresses the major source of systematic uncertainty in the latest top mass measurements. The method was validated on Monte Carlo events at the generator level, calibrated with fully simulated events, including detector simulation, and applied to D0 Run II data corresponding to 1 fb-1 of integrated luminosity. Possible sources of systematic uncertainties were studied. The top mass is measured to be: mt = (169.2±3.5(stat.)±1.0(syst.)) GeV . The

  11. Measurement of the electroweak top quark production cross section and the CKM matrix element Vtb with the DOe experiment

    International Nuclear Information System (INIS)

    Kirsch, Matthias

    2009-01-01

    exceeds the Standard Model expectation by 2 standard deviations. The result of the analysis presented here is in good agreement with the result of σ(p anti p→tb+X,tqb+X)=4.8± 1.3 pb, obtained from the combination of three other analyses performed on the same data set. From the cross section measurement a measurement of the strength vertical stroke V tb x f 1 L vertical stroke of the V-A coupling at the Wtb-vertex has been extracted. The result is vertical stroke V tb x f 1 L vertical stroke =1.42 -0.20 +0.21 . This value is above the Standard Model expectation by about 2∝standard deviations. The measurement agrees within uncertainties with the measurement of vertical stroke V tb x f 1 L vertical stroke =1.31 -0.21 +0.25 obtained by another analysis performed on the same data set. Constraining the prior of this measurement to the interval [0,1], i.e. setting the strength of the left-handed coupling f 1 L =1, a result for the CKM matrix element vertical stroke V tb vertical stroke has been determined to vertical stroke V tb vertical stroke =1.00 -0.08 +0.00 . From the posterior probability density of this measurement a lower limit for V tb has been set at 95% confidence level: vertical stroke V tb vertical stroke >0.79 rate at 95% C.L. (orig.)

  12. BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

    Science.gov (United States)

    Caffo, Michele; Czyż, Henryk; Gunia, Michał; Remiddi, Ettore

    2009-03-01

    We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations. Program summaryProgram title: BOKASUN Catalogue identifier: AECG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9404 No. of bytes in distributed program, including test data, etc.: 104 123 Distribution format: tar.gz Programming language: FORTRAN77 Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUX Operating system: LINUX RAM: 120 kbytes Classification: 4.4 Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum. Solution method: The integrals depend on three internal masses and the external momentum squared p. The method is a combination of an accelerated expansion in 1/p in its (pretty large!) region of fast convergence and of a Runge-Kutta numerical solution of a system of linear differential equations. Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge-Kutta method (depending

  13. The use of cation exchange matrix separation coupled with ICP-MS to directly determine platinum group element (PGE) and other trace element emissions from passenger cars equipped with diesel particulate filters (DPF)

    Energy Technology Data Exchange (ETDEWEB)

    Cairns, Warren R.L.; Cozzi, Giulio [Institute for the Dynamics of Environmental Processes-CNR, Venice (Italy); De Boni, Antonella; Gabrieli, Jacopo [University of Venice, Department of Environmental Science, Venice (Italy); Asti, Massimo; Merlone Borla, Edoardo; Parussa, Flavio [Centro Ricerche Fiat, Orbassano (Italy); Moretto, Ezio [FIAT Powertrain Technologies S.p.A, Turin (Italy); Cescon, Paolo; Barbante, Carlo [University of Venice, Department of Environmental Science, Venice (Italy); Institute for the Dynamics of Environmental Processes-CNR, Venice (Italy); Boutron, Claude [Laboratoire de Glaciologie et Geophysique de l' Environnement, UMR CNRS 5183, B.P. 96, Saint Martin d' Heres Cedex (France)

    2011-03-15

    Inductively coupled plasma-mass spectrometry coupled with cation exchange matrix separation has been optimised for the direct determination of platinum group element (PGE) and trace element emissions from a diesel engine car. After matrix separation method detection limits of 1.6 ng g{sup -1} for Pd, 0.4 ng g{sup -1} for Rh and 4.3 ng g{sup -1} for Pt were achieved, the method was validated against the certified reference material BCR 723, urban road dust. The test vehicle was fitted with new and aged catalytic converters with and without diesel particulate filters (DPF). Samples were collected after three consecutive New European Driving Cycle (NEDC) of the particulate and ''soluble'' phases using a home-made sampler optimised for trace element analysis. Emission factors for the PGEs ranged from 0.021 ng km{sup -1} for Rh to 70.5 ng km{sup -1} for Pt; when a DPF was fitted, the emission factors for the PGEs actually used in the catalysts dropped by up to 97% (for Pt). Trace element emission factors were found to drop by a maximum of 92% for Ni to a minimum of 18% for Y when a DPF was fitted; a new DPF was also found to cause a reduction of up to 86% in the emission of particulate matter. (orig.)

  14. Development of a diffuse element matrix in 'planar' technology. A particular application: logical gate with coupled emitter; Etude et realisation d'une matrice d'elements diffuses selon la technologie 'planar'. Application particuliere: porte logique a emetteurs couples

    Energy Technology Data Exchange (ETDEWEB)

    Rousseau, P [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1967-06-01

    In a first part, after a brief recall concerning 'planar' technology we discuss the various parasitic elements associated with integrated circuits components. Mathematical formulae of these elements are derived. In a second part, we present a matrix of 22 transistors and 12 resistors which has been realized. This matrix enables the integration of the major part of nuclear circuits. Some of the obtained circuits are shown, particularly an emitter coupled logic gate which presents good electrical behaviour. (author) [French] Dans uns premiere partie, apres un bref rappel de la technologie 'planar' nous etudions les divers elements parasites associes a tout composant d'un circuit integre. Un developpement sommaire des expressions mathematiques de ces elements est propose. Dans une seconde partie nous presentons la matrice de 22 transistors et 12 resistances que nous avons realisee. Cette matrice repond aux principaux besoins de l'electronique nucleaire. Nous proposons ensuite quelques exemples de circuits realises a partir de cette matrice dont notamment une porte logique a emetteurs couples de performances tres interessantes. (auteur)

  15. Basic Finite Element Method

    International Nuclear Information System (INIS)

    Lee, Byeong Hae

    1992-02-01

    This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.

  16. Matrix effect on the detection limit and accuracy in total reflection X-ray fluorescence analysis of trace elements in environmental and biological samples

    International Nuclear Information System (INIS)

    Karjou, J.

    2007-01-01

    The effect of matrix contents on the detection limit of total reflection X-ray fluorescence analysis was experimentally investigated using a set of multielement standard solutions (500 ng/mL of each element) in variable concentrations of NH 4 NO 3 . It was found that high matrix concentration, i.e. 0.1-10% NH 4 NO 3 , had a strong effect on the detection limits for all investigated elements, whereas no effect was observed at lower matrix concentration, i.e. 0-0.1% NH 4 NO 3 . The effect of soil and blood sample masses on the detection limit was also studied. The results showed decreasing the detection limit (in concentration unit, μg/g) with increasing the sample mass. However, the detection limit increased (in mass unit, ng) with increasing sample mass. The optimal blood sample mass of ca. 200 μg was sufficient to improve the detection limit of Se determination by total reflection X-ray fluorescence. The capability of total reflection X-ray fluorescence to analyze different kinds of samples was discussed with respect to the accuracy and detection limits based on certified and reference materials. Direct analysis of unknown water samples from several sources was also presented in this work

  17. Matrix calculus

    CERN Document Server

    Bodewig, E

    1959-01-01

    Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well

  18. Two-loop planar master integrals for Higgs →3 partons with full heavy-quark mass dependence

    International Nuclear Information System (INIS)

    Bonciani, Roberto; Duca, Vittorio Del; Frellesvig, Hjalte; Henn, Johannes M.; Moriello, Francesco; Smirnov, Vladimir A.

    2016-01-01

    We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.

  19. Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

    Energy Technology Data Exchange (ETDEWEB)

    Bonciani, Roberto [' ' La Sapienza' ' Univ., Rome (Italy). Dipt. di Fisica; INFN Sezione Roma (Italy); Di Vita, Stefano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Mastrolia, Pierpaolo [Max-Planck-Institut fuer Physik, Muenchen (Germany); Padova Univ. (Italy). Dipt. di Fisica e Astronomia; INFN Sezione di Padova (Italy); Schubert, Ulrich [Max-Planck-Institut fuer Physik, Muenchen (Germany)

    2016-04-15

    We present the calculation of the master integrals needed for the two-loop QCD x EW corrections to q+ anti q → l{sup -}+l{sup +} and q+ anti q{sup '} → l{sup -}+ anti ν, for massless external particles. We treat W and Z bosons as degenerate in mass. We identify three types of diagrams, according to the presence of massive internal lines: the no-mass type, the one-mass type, and the two-mass type, where all massive propagators, when occurring, contain the same mass value. We find a basis of 49 master integrals and evaluate them with the method of the differential equations. The Magnus exponential is employed to choose a set of master integrals that obeys a canonical system of differential equations. Boundary conditions are found either by matching the solutions onto simpler integrals in special kinematic configurations, or by requiring the regularity of the solution at pseudo-thresholds. The canonical master integrals are finally given as Taylor series around d=4 space-time dimensions, up to order four, with coefficients given in terms of iterated integrals, respectively up to weight four.

  20. Two-loop planar master integrals for Higgs →3 partons with full heavy-quark mass dependence

    Energy Technology Data Exchange (ETDEWEB)

    Bonciani, Roberto [Dipartimento di Fisica, Sapienza - Università di Roma,Piazzale Aldo Moro 5, 00185, Rome (Italy); INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185, Rome (Italy); Duca, Vittorio Del [ETH Zurich, Institut fur theoretische Physik, Wolfgang-Paulistr. 27, 8093, Zurich (Switzerland); INFN Laboratori Nazionali di Frascati, 00044 Frascati, Roma (Italy); Frellesvig, Hjalte [Institute of Nuclear and Particle Physics, NCSR Demokritos, Agia Paraskevi, 15310 (Greece); Henn, Johannes M. [PRISMA Cluster of Excellence, Johannes Gutenberg University, 55099 Mainz (Germany); Moriello, Francesco [Dipartimento di Fisica, Sapienza - Università di Roma,Piazzale Aldo Moro 5, 00185, Rome (Italy); INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185, Rome (Italy); ETH Zurich, Institut fur theoretische Physik, Wolfgang-Paulistr. 27, 8093, Zurich (Switzerland); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics of Moscow State University, 119991 Moscow (Russian Federation)

    2016-12-19

    We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.

  1. On the possibility of reprocessing of fuel elements of dispersion type with copper matrix by pyrochemical methods

    International Nuclear Information System (INIS)

    Vasin, B.D.; Ivanov, V.A.; Shchetinskij, A.V.; Vavilov, S.K.; Savochkin, Yu.P.; Bychkov, A.V.; Kormilitsyn, M.V.

    2005-01-01

    A consideration is given to pyrochemical processes suitable for separation of uranium dioxide from structural materials when reprocessing cermet type fuel elements. The estimation of the possibility to apply liquid antimony and bismuth, potassium and copper chlorides melts is made. The specimens compacted of copper and uranium dioxide powders in a stainless steel can are used as simulators of fuel element sections. It is concluded that the dissolution of structural materials in molten salts at the stage of uranium dioxide concentration is the process of choice for reprocessing of dispersion type fuel elements [ru

  2. Intercomparison and certification of some Chinese and international food and biological matrix CRMs for several uncertified ultratrace elements by NAA

    International Nuclear Information System (INIS)

    Weizhi, T.; Bangfa, N.; Pingsheng, W.; Huiling, N.; Lei, C.; Yangmei, Z.

    2001-01-01

    Radiochemical neutron activation analysis was used for determinations of 8 rare elements (La, Ce, Nd, Sm, Eu, Tb, Yb and Lu) in two Chinese CRMs, GBW 08503 (wheat) and GBW 09101 (hair), and Cs, Sr, Th and U in five NIST SRMs, 1548 (Total Diet), 1486 (Bone Meal), 8414 (Bovine Muscle), 1566a (Oyster Powder ) and 1575 (Pine Needles). These determinations are for eventual certification of above ultratrace elements so far not certified. The radiochemical separation scheme used in RNAA of NIST SRMs is an anion exchange followed by the coprecipitation by (REE)F 3 for U and Th, and SrSo 4 precipitation for Sr and Cs. For RNAA of the two Chinese CRMs, a one step (REE)F 3 precipitation was used. Chemical yields were determined for all relevant elements by tracer experiments. All these materials were also analyzed by ICPMS, that offered an opportunity to compare the two major trace analytical techniques on their merits and drawbacks for these particular cases. RNAA is proven to be one of the important techniques in ultratrace analysis, especially in certification of some ultratrace elements. Determination of elements in sub-ng/g level is still an area to be further investigated because: (1) some such elements are important in food and health related environmental studies, (2) many of these elements have no (or very few) certified values in existing biological CRMs, (3) reliable techniques qualified for ultratrace analysis are needed to be established, and (4) sampling behavior of elements at these levels is still not very well known (recommended minimum sample size may not be adequate). (author)

  3. Multiphonon states in even-even spherical nuclei. Pt. 2. Calculation of the matrix elements of one and two body operators

    International Nuclear Information System (INIS)

    Piepenbring, R.; Protasov, K.V.; Silvestre-Brac, B.

    1995-01-01

    Matrix elements of one and two body operators, which appear in a general hamiltonian and in electromagnetic transitions are derived in a subspace spanned by multiphonon states. The method is illustrated for a single j-shell, where phonons built with one type of particles are introduced. The eigenvalues obtained within the space spanned by the phonons of lowest angular momentum are compared to those of the full space. In such a method, the Pauli principle is fully and properly taken into account. ((orig.))

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

    Science.gov (United States)

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

    2018-03-01

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

  5. Formulae for the determination of the elements of the E\\"otvos matrix of the Earth's normal gravity field and a relation between normal and actual Gaussian curvature

    OpenAIRE

    Manoussakis, G.; Delikaraoglou, D.

    2011-01-01

    In this paper we form relations for the determination of the elements of the E\\"otv\\"os matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the normal equipotential surface and the Gauss curvature of the actual equipotential surface both passing through the point P is presented. For this purpose we use a global Cartesian system (X, Y, Z) and use the variables X, and Y to form a local parameterization a normal equipotential surface to describe its ...

  6. Two-loop N=4 super-Yang-Mills effective action and interaction between D3-branes

    International Nuclear Information System (INIS)

    Buchbinder, I.L.; Petrov, A.Yu.; Tseytlin, A.A.

    2002-01-01

    We compute the leading low-energy term in the planar part of the 2-loop contribution to the effective action of N=4 SYM theory in 4 dimensions, assuming that the gauge group SU(N+1) is broken to SU(N)xU(1) by a constant scalar background X. While the leading 1-loop correction is the familiar c 1 F 4 /vertical bar X vertical bar 4 term, the 2-loop expression starts with c 2 F 6 /vertical bar X vertical bar 8 . The 1-loop constant c 1 is known to be equal to the coefficient of the F 4 term in the Born-Infeld action for a probe D3-brane separated by distance vertical bar X vertical bar from a large number N of coincident D3-branes. We show that the same is true also for the 2-loop constant c 2 : it matches the coefficient of the F 6 term in the D3-brane probe action. In the context of the AdS/CFT correspondence, this agreement suggests a non-renormalization of the coefficient of the F 6 term beyond two loops. Thus the result of hep-th/9706072 about the agreement between the v 6 term in the D0-brane supergravity interaction potential and the corresponding 2-loop term in the (1+0)-dimensional reduction of N=4 SYM theory has indeed a direct generalization to 1+3 dimensions, as conjectured earlier in hep-th/9709087. We also discuss the issue of gauge theory-supergravity correspondence for higher order (F 8 , etc.) terms

  7. On the two-loop corrections to the pole mass of the B quark in the gaugeless limit of the MSSM

    International Nuclear Information System (INIS)

    Bednyakov, A.V.; Kazakov, D.I.; )

    2007-01-01

    The result for the two-loop corrections to the pole mass of the b quark in the gaugeless limit of the MSSM is presented. In this limit it is assumed that the contribution from the electroweak gauge interactions is small. The result presented here differs from one obtained earlier, especially in some particular regions of the MSSM parameter space [ru

  8. Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

    Energy Technology Data Exchange (ETDEWEB)

    Chankowski, Piotr H. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Lewandowski, Adrian [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Meissner, Krzysztof A. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland)

    2016-11-18

    We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional (MS)-bar scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the (MS)-bar scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

  9. Apparatus and method for identification of matrix materials in which transuranic elements are embedded using thermal neutron capture gamma-ray emission

    Science.gov (United States)

    Close, D.A.; Franks, L.A.; Kocimski, S.M.

    1984-08-16

    An invention is described that enables the quantitative simultaneous identification of the matrix materials in which fertile and fissile nuclides are embedded to be made along with the quantitative assay of the fertile and fissile materials. The invention also enables corrections for any absorption of neutrons by the matrix materials and by the measurement apparatus by the measurement of the prompt and delayed neutron flux emerging from a sample after the sample is interrogated by simultaneously applied neutrons and gamma radiation. High energy electrons are directed at a first target to produce gamma radiation. A second target receives the resulting pulsed gamma radiation and produces neutrons from the interaction with the gamma radiation. These neutrons are slowed by a moderator surrounding the sample and bathe the sample uniformly, generating second gamma radiation in the interaction. The gamma radiation is then resolved and quantitatively detected, providing a spectroscopic signature of the constituent elements contained in the matrix and in the materials within the vicinity of the sample. (LEW)

  10. Neutral kaon mixing beyond the Standard Model with n{sub f}=2+1 chiral fermions. Part 1: bare matrix elements and physical results

    Energy Technology Data Exchange (ETDEWEB)

    Garron, Nicolas [Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool,Brownlow Hill, Liverpool, L69 3BX (United Kingdom); Hudspith, Renwick J. [Department of Physics and Astronomy, York University,4700 Keele Street, Toronto, Ontario, M3J 1P3 (Canada); Lytle, Andrew T. [SUPA, School of Physics and Astronomy, University of Glasgow,University Avenue, Glasgow, G12 8QQ (United Kingdom); Collaboration: The RBC/UKQCD collaboration

    2016-11-02

    We compute the hadronic matrix elements of the four-quark operators relevant for K{sup 0}−K̄{sup 0} mixing beyond the Standard Model. Our results are from lattice QCD simulations with n{sub f}=2+1 flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing (a∼0.08 and a∼0.11 fm) and with lightest unitary pion mass ∼300 MeV. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description of the renormalisation procedure is presented in a companion paper. We argue that the intermediate renormalisation scheme is responsible for the discrepancies found by different collaborations. We also study different normalisations and determine the matrix elements of the relevant four-quark operators with a precision of ∼5% or better.

  11. A search for the ttH (H → bb) channel at the Large Hadron Collider with the ATLAS detector using a matrix element method

    CERN Document Server

    Basye, Austin Thomas

    A matrix element method analysis of the Standard Model Higgs boson, produced in association with two top quarks decaying to the lepton-plus-jets channel is presented. Based on 20.3 fb−1 of √s=8 TeV data, produced at the Large Hadron Collider and collected by the ATLAS detector, this analysis utilizes multiple advanced techniques to search for tt ̄H signatures with a 125 GeV Higgs boson decaying to two b-quarks. After categorizing selected events based on their jet and b-tag multiplicities, signal rich regions are analyzed using the matrix element method. Resulting variables are then propagated to two parallel multivariate analyses utilizing Neural Networks and Boosted Decision Trees respectively. As no significant excess is found, an observed (expected) limit of 3.4 (2.2) times the Standard Model cross-section is determined at 95% confidence, using the CLs method, for the Neural Network analysis. For the Boosted Decision Tree analysis, an observed (expected) limit of 5.2 (2.7) times the Standard Model cr...

  12. Theory and computation of the matrix elements of the full interaction of the electromagnetic field with an atomic state: Application to the Rydberg and the continuous spectrum

    International Nuclear Information System (INIS)

    Komninos, Yannis; Mercouris, Theodoros; Nicolaides, Cleanthes A.

    2002-01-01

    We develop practical formulas for the calculation of the matrix elements of the interaction of the electromagnetic field with an atomic state, beyond the long-wavelength approximation. The atom-plus-field Hamiltonian is chosen to have the multipolar form, containing the electric, paramagnetic, and diamagnetic operators. The final workable expressions include the interactions to all orders and are derived by first expanding the fields in partial waves. The electric-field operator reaches a constant value as the radial variable becomes large, contrary to the result of the electric-dipole approximation (EDA) where the value of the corresponding operator increases indefinitely. Applications are given for Rydberg states of hydrogen up to n=50 and for free-free transitions in a Coulomb potential. Such matrix elements are relevant to a number of real and virtual processes occurring during laser-atom interactions. The computation is done numerically, using a combination of analytic with numerical techniques. By comparing the results of the EDA with those of the exact treatment, it is shown that the former is inadequate in such cases. This finding has repercussions on the theory and understanding of the physics of quantum systems in high-lying Rydberg levels and wave packets or in scattering states

  13. Matrix elements of the electric multiple transition and relativistic correction operators in the case of complex configurations

    International Nuclear Information System (INIS)

    Kanyauskas, Yu.M.; Rudzikas, Z.B.

    1976-01-01

    Operators and their submatrix elements are studied in the framework of the electric multipole transitions of complex atoms with account of relativistic corrections of the order of the square of the fine structure constant. The analysis is performed by means of irreducible tensor operators and genealogical coefficients. It has been assumed that angular momenta of individual shells are coupled with each other according to ls, lk, jk and jj coupling. Formulas are given for the operator which causes the relativistic corrections for the single-electron multipole transition and for its submatrix element in the case of configurations with two unfilled shells. A possibility is discussed of using the formulas suggested for calculation. As follows from analysis, the relativistic correction operators even with the pure ls coupling allow intercombination transitions with ΔS equals +-1. The expressions obtained may turn out to be useful for performing calculations in the case of the intermediate type of coupling

  14. Top Quark Produced Through the Electroweak Force: Discovery Using the Matrix Element Analysis and Search for Heavy Gauge Bosons Using Boosted Decision Trees

    Energy Technology Data Exchange (ETDEWEB)

    Pangilinan, Monica [Brown Univ., Providence, RI (United States)

    2010-05-01

    The top quark produced through the electroweak channel provides a direct measurement of the Vtb element in the CKM matrix which can be viewed as a transition rate of a top quark to a bottom quark. This production channel of top quark is also sensitive to different theories beyond the Standard Model such as heavy charged gauged bosons termed W'. This thesis measures the cross section of the electroweak produced top quark using a technique based on using the matrix elements of the processes under consideration. The technique is applied to 2.3 fb-1 of data from the D0 detector. From a comparison of the matrix element discriminants between data and the signal and background model using Bayesian statistics, we measure the cross section of the top quark produced through the electroweak mechanism σ(p$\\bar{p}$ → tb + X, tqb + X) = 4.30-1.20+0.98 pb. The measured result corresponds to a 4.9σ Gaussian-equivalent significance. By combining this analysis with other analyses based on the Bayesian Neural Network (BNN) and Boosted Decision Tree (BDT) method, the measured cross section is 3.94 ± 0.88 pb with a significance of 5.0σ, resulting in the discovery of electroweak produced top quarks. Using this measured cross section and constraining |Vtb| < 1, the 95% confidence level (C.L.) lower limit is |Vtb| > 0.78. Additionally, a search is made for the production of W' using the same samples from the electroweak produced top quark. An analysis based on the BDT method is used to separate the signal from expected backgrounds. No significant excess is found and 95% C.L. upper limits on the production cross section are set for W' with masses within 600-950 GeV. For four general models of W{prime} boson production using decay channel W' → t$\\bar{p}$, the lower mass limits are the following: M(W'L with SM couplings) > 840 GeV; M(W'R) > 880 GeV or 890 GeV if the

  15. Measurement of the Top Quark Mass at D0 Run II with the Matrix Element Method in the Lepton+Jets Final State

    Energy Technology Data Exchange (ETDEWEB)

    Schieferdecker, Philipp [Ludwig Maximilian Univ. of Munich (Germany)

    2005-08-05

    The mass of the top quark is a fundamental parameter of the Standard Model. Its precise knowledge yields valuable insights into unresolved phenomena in and beyond the Standard Model. A measurement of the top quark mass with the matrix element method in the lepton+jets final state in D0 Run II is presented. Events are selected requiring an isolated energetic charged lepton (electron or muon), significant missing transverse energy, and exactly four calorimeter jets. For each event, the probabilities to originate from the signal and background processes are calculated based on the measured kinematics, the object resolutions and the respective matrix elements. The jet energy scale is known to be the dominant source of systematic uncertainty. The reference scale for the mass measurement is derived from Monte Carlo events. The matrix element likelihood is defined as a function of both, m{sub top} and jet energy scale JES, where the latter represents a scale factor with respect to the reference scale. The top mass is obtained from a two-dimensional correlated fit, and the likelihood yields both the statistical and jet energy scale uncertainty. Using a dataset of 320 pb-1 of D0 Run II data, the mass of the top quark is measured to be: m$ℓ+jets\\atop{top}$ = 169.5 ± 4.4(stat. + JES)$+1.7\\atop{-1.6}$(syst.) GeV; m$e+jets\\atop{top}$ = 168.8 ± 6.0(stat. + JES)$+1.9\\atop{-1.9}$(syst.) GeV; m$μ+jets\\atop{top}$ = 172.3 ± 9.6(stat.+JES)$+3.4\\atop{-3.3}$(syst.) GeV. The jet energy scale measurement in the ℓ+jets sample yields JES = 1.034 ± 0.034, suggesting good consistency of the data with the simulation. The measurement forecasts significant improvements to the total top mass uncertainty during Run II before the startup of the LHC, as the data sample will grow by a factor of ten and D0's tracking capabilities will be employed in jet energy reconstruction and flavor identification.

  16. Measurement of the t-channel single-top-quark-production cross section and the CKM-matrix element Vtb with the CMS experiment

    International Nuclear Information System (INIS)

    Klingebiel, Dennis

    2014-01-01

    The electroweak production of single top quarks offers a unique access to the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V tb , which is a fundamental parameter of the Standard Model of particle physics (SM). In this thesis, measurements of the inclusive t-channel single-top-quark-production cross section, the CKM-matrix element V tb , and the ratio of t-channel top-quark-production and top-antiquark-production cross sections are presented. Proton-proton collisions with a center-of-mass energy of 7 TeV are analyzed. These collisions were recorded with the Compact Muon Solenoid (CMS) experiment at the particle-accelerator complex Large Hadron Collider (LHC), which is operated by the European Organization for Nuclear Research (CERN) near Geneva, Switzerland. The analyzed data correspond to an integrated luminosity of 1.6/fb. This analysis uses events with at least two jets and either an electron or muon. Each event is classified according to the flavor and charge of the electron or muon, the number of jets, and the number of b-tagged jets. Signal and background processes are discriminated using Boosted Decision Trees (BDTs). The signal cross section is simultaneously measured in twelve orthogonal categories. A Bayesian approach is used to infer the signal cross section from data. Particular emphasis is placed on the modeling of systematic uncertainties and the evaluation of their impact on the measurement. Systematic uncertainties are incorporated as additional nuisance parameters into the likelihood function. Marginalization is used to eliminate the nuisance parameters. The single-top-quark t-channel production cross section is measured to be (66.6 +6.7 -6.2 ) pb. The measured value is in agreement with the next-to-next-to-leading order SM prediction. With a relative uncertainty of -9.3% +10.1%, this measurement is significantly more precise than previous measurements in proton-proton und proton-antiproton collisions. The absolute value of the CKM-matrix element

  17. Evaluation of matrix effect on the determination of rare earth elements and As, Bi, Cd, Pb, Se and In in honey and pollen of native Brazilian bees (Tetragonisca angustula - Jataí) by Q-ICP-MS.

    Science.gov (United States)

    de Oliveira, Fernanda Ataide; de Abreu, Adriana Trópia; de Oliveira Nascimento, Nathália; Froes-Silva, Roberta Eliane Santos; Antonini, Yasmine; Nalini, Hermínio Arias; de Lena, Jorge Carvalho

    2017-01-01

    Bees are considered the main pollinators in natural and agricultural environments. Chemical elements from honey and pollen have been used for monitoring the environment, the health of bees and the quality of their products. Nevertheless, there are not many studies on honey and pollen of native Brazilian bees. The goal of this work was to determine important chemical elements (Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Lu and Yb) along with As, Bi, Cd, Pb, Se and In, in honey and pollen of native Brazilian bees, assessing analytical interferences from the matrix. A proposed analytical method was developed for these elements by quadrupole ICP-MS. Matrix effect was verified in honey matrix in the quantification of As, Bi and Dy; and in pollen matrix for Bi, Cd, Ce, Gd, La, Pb and Sc. The quality of the method was considered satisfactory taking into consideration the recovery rate of each element in the spiked solutions: honey matrix (91.6-103.9%) and pollen matrix (94.1-115.6%). The quantification limits of the method ranged between 0.00041 and 10.3μgL -1 for honey and 0.00041-0.095μgL -1 for pollen. The results demonstrate that the method is accurate, precise and suitable. Copyright © 2016 Elsevier B.V. All rights reserved.

  18. Study of K/sup -/p. -->. anti K*(890)n at 13GeV. [Differential cross sections, density matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Brandenburg, G W; Dunwoodie, W M; Lasinski, T A; Leith, D W.G.S.; Williams, S H [Stanford Linear Accelerator Center, Calif. (USA); Carnegie, R K [Carleton Univ., Ottawa, Ontario (Canada). Dept. of Physics; Cashmore, R J [Oxford Univ. (UK). Dept. of Physics; Davier, M [Lab. de l' Accelerateur Lineaire, Orsay, France; Matthews, J A.J. [Michigan State Univ., East Lansing (USA). Dept. of Physics; Walden, P [British Columbia Univ., Vancouver (Canada). TRIUMF Facility

    1975-11-24

    The results of a wire chamber spectrometer experiment studying anti K*(890) production in the reaction K/sup -/p..-->..K/sup -/..pi../sup +/n at 13 GeV are presented. Strong forward structure is observed for mod(t)matrix elements and differential cross section. These features are similar to those observed in ..pi../sup -/p..-->..rho/sup 0/n data and are characteristic of ..pi.. exchange. In contrast in the intermediate, mod(t)approximately 0.2 GeV/sup 2/, and large momentum transfer regions anti K*(890) production is dominated by the natural parity rho-A/sub 2/ exchange contribution.

  19. Automatic generation of 2D micromechanical finite element model of silicon–carbide/aluminum metal matrix composites: Effects of the boundary conditions

    DEFF Research Database (Denmark)

    Qing, Hai

    2013-01-01

    Two-dimensional finite element (FE) simulations of the deformation and damage evolution of Silicon–Carbide (SiC) particle reinforced aluminum alloy composite including interphase are carried out for different microstructures and particle volume fractions of the composites. A program is developed...... for the automatic generation of 2D micromechanical FE-models with randomly distributed SiC particles. In order to simulate the damage process in aluminum alloy matrix and SiC particles, a damage parameter based on the stress triaxial indicator and the maximum principal stress criterion based elastic brittle damage...... model are developed within Abaqus/Standard Subroutine USDFLD, respectively. An Abaqus/Standard Subroutine MPC, which allows defining multi-point constraints, is developed to realize the symmetric boundary condition (SBC) and periodic boundary condition (PBC). A series of computational experiments...

  20. Determination of the CKM-matrix element |Vub| from the electron energy spectrum measured in inclusive B→Xueν decay with the BABAR detector

    International Nuclear Information System (INIS)

    Lueck, Thomas

    2013-01-01

    This document presents a measurement of the CKM matrix-element vertical stroke V ub vertical stroke in inclusive semileptonic B→X u eν events on a dataset of 471 million B anti B events recorded by the BABAR detector. Inclusive B→X u eν decays are selected by reconstructing a high energetic electron (positron). Background suppression is achieved by selecting events with electron (positron) energies near the kinematical allowed endpoint of B→X u eν decays. A B→D * eν veto is applied to further suppress background. This veto uses D * mesons which have been reconstructed with a partial reconstruction technique.