Phase-space integrals through Mellin-Barnes representation

TL;DR

This paper presents a new analytical method using Mellin-Barnes integrals to compute phase-space integrals in particle physics, providing explicit results and recursion relations for simplifying complex integrals.

Contribution

It introduces a novel Mellin-Barnes based approach for phase-space integrals, including explicit expressions and recursion relations, enhancing precision in particle physics calculations.

Findings

Expressions in terms of Goncharov polylogarithms for three-denominator integrals

Results up to (^2) for massless momenta

Recursion relations for higher powers of denominators

Abstract

This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta up to $\cal{O}(\epsilon^2)$ and for one massive momentum up to $\cal{O}(\epsilon)$. Additionally, we derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine the angular part with the radial one which requires a careful handling of singularities.