The integrand form of infrared singularities of two-loop QCD scattering amplitudes

TL;DR

This paper develops a method to express the singular parts of two-loop QCD scattering amplitudes using a basis of finite master integrals, simplifying the analysis of infrared singularities.

Contribution

It introduces a systematic approach to represent amplitude singularities with locally finite integrals in two-loop massless QCD, enhancing computational efficiency.

Findings

Representation of amplitude singularities using finite master integrals

Explicit example for digluon production amplitude

Manifestly locally finite finite part of the amplitude

Abstract

In this work, we express the singular part of a scattering amplitude in terms of Feynman integrals compatible with topologies appearing in the bare amplitude, and we choose a basis of locally finite Master Integrals. In two-loop massless QCD, we find such a representation of the amplitude singularities using a systematic ansatz reconstruction of the integrand from a predicted integrated form. As an example application, we write the finite part of an amplitude for the digluon production in quark annihilation for some helicity configurations as manifestly locally finite.