Phase-space integrals through Mellin-Barnes representation

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 $\mathcal{O}(\hat{I}{\mu }^2)$ and the single-massive case to $\mathcal{O}(\hat{I}\mu )$; for four denominators, both the massless and single-massive cases are solved to $\mathcal{O}(\hat{I}{\mu }^0)$. 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.

8 pages, 17th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology (RADCOR2025)