General massive one-loop off-shell three-point functions

Abstract

In this work we compute the most general massive one-loop off-shell three-point vertex in D-dimensions, where the masses, external momenta, and exponents of propagators are arbitrary. This follows our previous paper in which we have calculated several new hypergeometric series representations for massless and massive (with equal masses) scalar one-loop three-point functions, in the negative dimensional approach.

16 pages, 2 figures, 4 tables

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• Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
• Optimized Negative Dimensional Integration Method (NDIM) and multiloop Feynman diagram calculation
• A massive Feynman integral and some reduction relations for Appell functions
• Method of Brackets and Feynman diagrams evaluation
• Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams
• Analytic continuations of the Horn $H_1$ and $H_5$ functions
• GKZ-system of the 2-loop self energy with 4 propagators
• Feynman Diagrams and a Combination of the Integration by Parts (IBP) and the Integration by Fractional Expansion (IBFE) Techniques