Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix

TL;DR

This paper investigates the matter dependence of the three-loop soft anomalous dimension matrix in QCD, confirming that the proportionality observed at two loops extends to three loops for massless processes, aiding precision calculations.

Contribution

It demonstrates that the matter-dependent part of the three-loop soft anomalous dimension matrix maintains proportionality, extending previous two-loop results to three loops in generic gauge theories.

Findings

Proportionality extends to three loops for matter-dependent parts.

Supports the extension of two-loop proportionality to higher loops.

Enhances understanding of soft gluon exchange in QCD.

Abstract

The resummation of soft gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions, which has been computed through two loops. The two-loop matrix is proportional to the one-loop matrix. Recently there have been proposals that this proportionality extends to higher loops. One can test such proposals by computing the dependence of this matrix on the matter content in a generic gauge theory. It is shown that for the matter-dependent part the proportionality extends to three loops for arbitrary massless processes.