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arXiv · 2604.01505

Phase-space integrals through Mellin-Barnes representation

Taushif Ahmed·Syed Mehedi Hasan·Andreas Rapakoulias
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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.

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Taushif Ahmed, Syed Mehedi Hasan, Andreas Rapakoulias. 2026-04-02. Phase-space integrals through Mellin-Barnes representation. https://arxiv.org/abs/2604.01505

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