Infrared singularities of QCD amplitudes with massive partons

TL;DR

This paper derives a formula for two-loop infrared singularities in QCD amplitudes involving massive and massless partons, revealing complex structures and correlations that extend previous understanding.

Contribution

It introduces a new formula for two-loop infrared singularities in QCD with massive partons, highlighting complex color and momentum structures beyond the dipole approximation.

Findings

Two-loop singularities involve new color and momentum structures.

Three-parton correlations can be expressed with two functions.

The structure differs significantly from the massless case.

Abstract

A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a renormalization-group equation, and factorization constraints on the relevant anomalous-dimension matrix are analyzed. The simplicity of the structure of the matrix relevant for massless partons does not carry over to the case with massive legs, where starting at two-loop order new color and momentum structures arise, which are not of the color-dipole form. The resulting two-loop three-parton correlations can be expressed in terms of two functions, for which some general properties are derived. This explains observations recently made by Mitov et al. in terms of symmetry arguments.