Multidimensional Residues for Feynman Integrals with Generic Power of Propagators

TL;DR

This paper introduces a novel method using multidimensional residues to directly extract scalar master integral coefficients from one-loop Feynman integrals with arbitrary propagator powers, simplifying the reduction process.

Contribution

It presents a new residue-based approach that bypasses traditional IBP techniques for coefficient extraction in Feynman integrals.

Findings

Successfully extracted scalar box integral coefficients.

Demonstrated the method's potential to simplify integral reduction.

Provided a proof-of-concept for direct coefficient extraction.

Abstract

We propose that the concept of multidimensional residues can be used to directly extracting the coefficients of scalar master integrals (with single propagators only) from one-loop Feynman integrals with generic power of propagators. Unlike the usual integration-by-parts (IBP) technique, where one has to solve iteratively a complicated set of equations to carry out the reduction and determine the coefficients of scalar master integrals, using multidimensional residues provides the possibility of directly extracting the coefficients of the master integrals. As the first application of this idea, we show how to directly extract the scalar box integral coefficients.