Four-dimensional differential equations for the leading divergences of dimensionally-regulated loop integrals

TL;DR

This paper introduces an automated approach utilizing four-dimensional integration-by-parts identities to efficiently compute the divergent parts of Feynman integrals in dimensional regularization, demonstrated through a three-loop heavy quark effective theory example.

Contribution

The paper presents a novel automated method that simplifies the calculation of divergences in Feynman integrals using four-dimensional identities and differential equations.

Findings

Successfully applied to three-loop heavy quark effective theory

Automates divergence computation in dimensional regularization

Utilizes simplified four-dimensional IBP identities

Abstract

We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the literature, we show how to find simple differential equations for the divergent part of Feynman integrals. We illustrate the method by an application to heavy quark effective theory at three loops.