Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering

Abstract

The method for obtaining functional equations, recently proposed by one of the authors, is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric functions admitting one-fold integral representation is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation.

14 pages, 3 figures

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Cited by in corpus (13)

• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
• 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
• Analytic result for the one-loop scalar pentagon integral with massless propagators
• HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables
• Soft-parton contributions to heavy-quark production at low transverse momentum
• Four-point function in general kinematics through geometrical splitting and reduction
• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• Geometrical splitting and reduction of Feynman diagrams
• Methods for deriving functional equations for Feynman integrals
• Derivation of Functional Equations for Feynman Integrals from Algebraic Relations