A new treatment of mixed virtual and real IR-singularities

TL;DR

This paper presents a Mellin-Barnes based method for analyzing infrared singularities in massive one-loop 5-point functions, addressing both internal line and phase space endpoint singularities.

Contribution

It introduces a novel approach using Mellin-Barnes representations to systematically handle mixed virtual and real IR singularities in complex Feynman diagrams.

Findings

Mellin-Barnes integrals effectively treat IR singularities.

Residue evaluation yields inverse binomial sums.

The method clarifies the structure of singularities in 5-point functions.

Abstract

We discuss the determination of the infrared singularities of massive one-loop 5-point functions with Mellin-Barnes (MB) representations. Massless internal lines may lead to poles in the $\eps$ expansion of the Feynman diagram, while unresolved massless final state particles give endpoint singularities of the phase space integrals. MB integrals are an elegant tool for their common treatment. An evaluation by taking residues leads to inverse binomial sums.