The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Bernd A. Kniehl - One of the best experts on this subject based on the ideXlab platform.

  • mellin barnes representations of Feynman Diagrams linear systems of differential equations and polynomial solutions
    Physics Letters B, 2012
    Co-Authors: Mikhail Yu Kalmykov, Bernd A. Kniehl
    Abstract:

    We argue that the Mellin-Barnes representations of Feynman Diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman Diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals.

  • the epsilon expansion of Feynman Diagrams via hypergeometric functions and differential reduction
    arXiv: Mathematical Physics, 2011
    Co-Authors: Scott A. Yost, Bernd A. Kniehl, Yu M Kalmykov, V V Bytev, B.f.l. Ward
    Abstract:

    Higher-order Diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman Diagrams. The hypergeometric representation supplies an analytic framework that is useful for deriving such stable representations. We discuss the reduction of Feynman Diagrams to master integrals, and compare integration-by-parts methods to differential reduction of hypergeometric functions. We describe the problem of constructing higher-order terms in the epsilon expansion, and characterize the functions generated in such expansions.

  • differential reduction of generalized hypergeometric functions from Feynman Diagrams one variable case
    Nuclear Physics, 2010
    Co-Authors: V V Bytev, Mikhail Yu Kalmykov, Bernd A. Kniehl
    Abstract:

    Abstract The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of the same functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman Diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed.

  • Feynman Diagrams, Differential Reduction, and Hypergeometric Functions
    Proceedings of XII Advanced Computing and Analysis Techniques in Physics Research — PoS(ACAT08), 2009
    Co-Authors: Mikhail Yu Kalmykov, Bernd A. Kniehl, V V Bytev, Bennie F.l. Ward, Scott A. Yost
    Abstract:

    Department of Physics, The Citadel, 171 Moultrie St., Charleston, SC 29409, USAE-mail: scott.yost@citadel.eduWe will present some (formal) arguments that any Feynman diagram can be understood as aparticular case of a sum of Horn-type multivariable hypergeometric functions. The advantagesand disadvantages of this type of approach to the evaluation of Feynman Diagrams is discussed.XII Advanced Computing and Analysis Techniques in Physics ResearchNovember 3-7, 2008Erice, Italy

  • Feynman Diagrams differential reduction and hypergeometric functions
    arXiv: High Energy Physics - Theory, 2009
    Co-Authors: Yu M Kalmykov, Bernd A. Kniehl, B.f.l. Ward, V V Bytev, Scott A. Yost
    Abstract:

    We will present some (formal) arguments that any Feynman diagram can be understood as a particular case of a Horn-type multivariable hypergeometric function. The advantages and disadvantages of this type of approach to the evaluation of Feynman Diagrams is discussed.

Sandro Uccirati - One of the best experts on this subject based on the ideXlab platform.

  • The frontier of multi-loop Feynman Diagrams: (Semi-) numerical techniques
    Nuclear Physics B - Proceedings Supplements, 2003
    Co-Authors: Andrea Ferroglia, Giampiero Passarino, Massimo Passera, Sandro Uccirati
    Abstract:

    Abstract Fast and efficient ways to compute multi-loop and multi-leg Feynman Diagrams are discussed.

  • all purpose numerical evaluation of one loop multi leg Feynman Diagrams
    Nuclear Physics, 2003
    Co-Authors: A Ferroglia, Giampiero Passarino, Massimo Passera, Sandro Uccirati
    Abstract:

    Abstract A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman Diagrams, with special attention to the behavior around (possibly) singular points in phase space. No particular restriction is imposed on kinematics, and complex masses (poles) are allowed.

  • algebraic numerical evaluation of Feynman Diagrams two loop self energies
    Nuclear Physics, 2002
    Co-Authors: Giampiero Passarino, Sandro Uccirati
    Abstract:

    Abstract A recently proposed scheme for numerical evaluation of Feynman Diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F.V. Tkachov and it is based on the so-called generalized Bernstein functional relation. On-shell derivatives of self-energies are also considered and their infrared properties analyzed to prove that the method which is aimed to a numerical evaluation of massive Diagrams can handle the infrared problem within the scheme of dimensional regularization. Particular care is devoted to study the general massive Diagrams around their leading and non-leading Landau singularities.

Eduardo De Rafael - One of the best experts on this subject based on the ideXlab platform.

  • asymptotics of Feynman Diagrams and the mellin barnes representation
    Physics Letters B, 2005
    Co-Authors: Samuel Friot, David Greynat, Eduardo De Rafael
    Abstract:

    Abstract It is shown that the integral representation of Feynman Diagrams in terms of the traditional Feynman parameters, when combined with properties of the Mellin–Barnes representation and the so-called converse mapping theorem, provide a very simple and efficient way to obtain the analytic asymptotic behaviours in both the large and small ratios of mass scales.

Mikhail Yu Kalmykov - One of the best experts on this subject based on the ideXlab platform.

  • mellin barnes representations of Feynman Diagrams linear systems of differential equations and polynomial solutions
    Physics Letters B, 2012
    Co-Authors: Mikhail Yu Kalmykov, Bernd A. Kniehl
    Abstract:

    We argue that the Mellin-Barnes representations of Feynman Diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman Diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals.

  • differential reduction of generalized hypergeometric functions from Feynman Diagrams one variable case
    Nuclear Physics, 2010
    Co-Authors: V V Bytev, Mikhail Yu Kalmykov, Bernd A. Kniehl
    Abstract:

    Abstract The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of the same functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman Diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed.

  • Feynman Diagrams, Differential Reduction, and Hypergeometric Functions
    Proceedings of XII Advanced Computing and Analysis Techniques in Physics Research — PoS(ACAT08), 2009
    Co-Authors: Mikhail Yu Kalmykov, Bernd A. Kniehl, V V Bytev, Bennie F.l. Ward, Scott A. Yost
    Abstract:

    Department of Physics, The Citadel, 171 Moultrie St., Charleston, SC 29409, USAE-mail: scott.yost@citadel.eduWe will present some (formal) arguments that any Feynman diagram can be understood as aparticular case of a sum of Horn-type multivariable hypergeometric functions. The advantagesand disadvantages of this type of approach to the evaluation of Feynman Diagrams is discussed.XII Advanced Computing and Analysis Techniques in Physics ResearchNovember 3-7, 2008Erice, Italy

Yu M Kalmykov - One of the best experts on this subject based on the ideXlab platform.

  • the epsilon expansion of Feynman Diagrams via hypergeometric functions and differential reduction
    arXiv: Mathematical Physics, 2011
    Co-Authors: Scott A. Yost, Bernd A. Kniehl, Yu M Kalmykov, V V Bytev, B.f.l. Ward
    Abstract:

    Higher-order Diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman Diagrams. The hypergeometric representation supplies an analytic framework that is useful for deriving such stable representations. We discuss the reduction of Feynman Diagrams to master integrals, and compare integration-by-parts methods to differential reduction of hypergeometric functions. We describe the problem of constructing higher-order terms in the epsilon expansion, and characterize the functions generated in such expansions.

  • Feynman Diagrams differential reduction and hypergeometric functions
    arXiv: High Energy Physics - Theory, 2009
    Co-Authors: Yu M Kalmykov, Bernd A. Kniehl, B.f.l. Ward, V V Bytev, Scott A. Yost
    Abstract:

    We will present some (formal) arguments that any Feynman diagram can be understood as a particular case of a Horn-type multivariable hypergeometric function. The advantages and disadvantages of this type of approach to the evaluation of Feynman Diagrams is discussed.

  • hypergeometric functions their epsilon expansions and Feynman Diagrams
    arXiv: High Energy Physics - Theory, 2008
    Co-Authors: Yu M Kalmykov, Bernd A. Kniehl, B.f.l. Ward, Scott A. Yost
    Abstract:

    We review the hypergeometric function approach to Feynman Diagrams. Special consideration is given to the construction of the Laurent expansion. As an illustration, we describe a collection of physically important one-loop vertex Diagrams for which this approach is useful.

  • massive Feynman Diagrams and inverse binomial sums
    Nuclear Physics, 2004
    Co-Authors: Andrei I Davydychev, Yu M Kalmykov
    Abstract:

    Abstract When calculating higher terms of the ɛ -expansion of massive Feynman Diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with respect to their parameters. Exploring this connection and using it together with an approach based on generating functions, we analytically calculate a number of such infinite sums, for an arbitrary value of the argument which corresponds to an arbitrary value of the off-shell external momentum. In such a way, we find a number of new results for physically important Feynman Diagrams. Considered examples include two-loop two- and three-point Diagrams, as well as three-loop vacuum Diagrams with two different masses. The results are presented in terms of generalized polylogarithmic functions. As a physical example, higher-order terms of the ɛ -expansion of the polarization function of the neutral gauge bosons are constructed.