Feynman Integral Reduction without Integration-By-Parts

TL;DR

This paper introduces a novel method for Feynman integral reduction that bypasses traditional integration-by-parts identities by analyzing integral contour equivalences in Feynman parameter space.

Contribution

It proposes a new contour-based approach for integral reduction, extending beyond the Cheng-Wu theorem, applicable to one-loop and potentially multi-loop integrals.

Findings

Derived universal reduction formulas for one-loop integrals

Demonstrated the generalization of integration contours beyond Cheng-Wu theorem

Potential applicability to multi-loop integral reduction

Abstract

We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parameterization. We find that the integration contour can take a more general form than that given by the Cheng-Wu theorem. We apply this idea to one-loop integrals, and derive universal reduction formulas that can be used to efficiently reduce any one-loop integral. We expect that this approach can be useful in the reduction of multi-loop integrals as well.