Angular phase-space integrals with four denominators through Mellin--Barnes

TL;DR

This paper develops a method using Mellin--Barnes integrals to compute complex angular phase-space integrals with four denominators, applicable to various scattering scenarios involving massless and massive particles.

Contribution

It introduces a systematic approach to evaluate four-denominator angular integrals with Mellin--Barnes technique, including a partial fraction decomposition for massive momenta.

Findings

Expressed integrals in terms of Goncharov polylogarithms.

Unified treatment for massless and massive momenta scenarios.

Derived results up to finite order in dimensional regularisation.

Abstract

We compute four-denominator angular phase-space integrals using the Mellin--Barnes (MB) technique in dimensional regularisation. Independent of the scattering process, an angular integral can be categorised based on the nature of the momenta appearing in the denominators. We address all scenarios involving fully massless and massive momenta. We present a partial fraction decomposition that relates angular integrals with multiple massive momenta to those with a single massive momentum. By solving six- and seven-fold MB integrals, we express the final results up to the finite order in the dimensional regulator in terms of Goncharov polylogarithms.