Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case

TL;DR

This paper discusses a differential-reduction algorithm for hypergeometric functions in Feynman diagram evaluations, showing how it can simplify complex integrals and relate to existing reduction techniques.

Contribution

It introduces a differential-reduction approach for hypergeometric functions in Feynman diagrams and links this to the reducibility criteria of multiloop integrals.

Findings

The differential-reduction algorithm expresses hypergeometric functions with arbitrary parameters in terms of shifted parameters.

The reducibility of Feynman integrals can be reformulated using hypergeometric function criteria.

Comparison with standard techniques shows the effectiveness of the differential-reduction method.

Abstract

The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such 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.