One-loop Feynman integrals for $2\to3$ scattering involving many scales including internal masses

TL;DR

This paper applies the Simplified Differential Equations method to compute complex one-loop five-point Feynman integrals with multiple scales and masses, providing new results in terms of Goncharov polylogarithms.

Contribution

It is the first application of the Simplified Differential Equations approach to multiscale Feynman integrals involving internal masses, extending computational techniques in quantum field theory.

Findings

Derived explicit expressions for integrals with up to weight four polylogarithms.

Analyzed cases with various combinations of massive and massless external legs.

Demonstrated the method's effectiveness for complex multiscale integrals.

Abstract

We study several multiscale one-loop five-point families of Feynman integrals. More specifically, we employ the Simplified Differential Equations approach to obtain results in terms of Goncharov polylogarithms of up to transcendental weight four for families with two and three massive external legs and massless propagators, as well as with one massive internal line and up to two massive external legs. This is the first time this computational approach is applied to cases involving internal masses.