An algorithm towards $\varepsilon$-factorising Feynman Integrals

TL;DR

This paper discusses an algorithm that simplifies complex Feynman integrals into an epsilon-factorized form, demonstrated through examples including three-loop banana integrals with unequal masses.

Contribution

It introduces a novel algorithm capable of epsilon-factorizing Feynman integrals regardless of their geometric complexity, with detailed examples.

Findings

Successful epsilon-factorization of various Feynman integrals

Application to three-loop banana integrals with unequal masses

Algorithm works beyond geometric intuition

Abstract

In this talk, we use several examples to elaborate on how a recently proposed algorithm can turn non-trivial Feynman integrals into an $\varepsilon $-factorised manner, regardless of their hidden geometric essence. In particular, some extra details about three-loop banana integrals with unequal-mass configuration are provided.