The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction

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.

12 pages, Proceedings of DPF2011, Brown University, Providence, R.I., Aug. 9-13, 2011. Version 2 adds references, corrects the author list, and fixes several misprints. Version 3 has some relatively minor corrections

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Cited by in corpus (12)

• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
• Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions
• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: $F_D$ and $F_S$ Horn-type hypergeometric functions of three variables
• Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation
• HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables
• Generalized Log-sine integrals and Bell polynomials
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• When epsilon-expansion of hypergeometric functions is expressible in terms of multiple polylogarithms: the two-variables examples
• Expansion of hypergeometric functions in terms of polylogarithms with nontrivial variable change
• Epsilon expansion of Appell and Kampé de Fériet functions
• Counting master integrals: Integration by parts vs. functional equations