Phase-space integrals through Mellin-Barnes representation

TL;DR

This paper analytically computes complex angular phase-space integrals with multiple denominators using Mellin-Barnes representation, expressing results in Goncharov polylogarithms and deriving recursion relations.

Contribution

It introduces a Mellin-Barnes based method to evaluate multi-denominator phase-space integrals analytically, including recursion relations for higher powers.

Findings

Results obtained to specific epsilon orders for massless and massive cases.

All-massless and single-massive integrals explicitly computed.

Recursion relations established for integrals with higher denominator powers.

Abstract

We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric integrals and expresses all results in terms of Goncharov polylogarithms (GPLs). For three denominators, all-massless results are obtained to $\mathcal{O}(\epsilon^2)$ and the single-massive case to $\mathcal{O}(\epsilon)$; for four denominators, both the massless and single-massive cases are solved to $\mathcal{O}(\epsilon^0)$. Integrals with multiple massive momenta follow from a partial fraction decomposition reducing them to the single-massive case. Recursion relations relating integrals with higher denominator powers to master integrals are derived. These are essential ingredients to solving full phase-space integrals.