The Massive Soft Anomalous Dimension Matrix at Two Loops

TL;DR

This paper analyzes two-loop anomalous dimension matrices in QCD, revealing conditions under which they are diagonal in the same basis as one-loop matrices, aiding threshold resummation in heavy quark production.

Contribution

It demonstrates that for two-to-two processes, the two-loop anomalous dimension matrix is diagonal in the same basis as the one-loop matrix under specific conditions.

Findings

Diagrams linking three massive Wilson lines do not vanish in general.

Two-loop anomalous dimension matrix is diagonal at threshold and ninety degrees scattering.

Results facilitate threshold resummation in heavy quark production.

Abstract

We study two-loop anomalous dimension matrices in QCD and related gauge theories for products of Wilson lines coupled at a point. We verify by an analysis in Euclidean space that the contributions to these matrices from diagrams that link three massive Wilson lines do not vanish in general. We show, however, that for two-to-two processes the two-loop anomalous dimension matrix is diagonal in the same color-exchange basis as the one-loop matrix for arbitrary masses at absolute threshold and for scattering at ninety degrees in the center of mass. This result is important for applications of threshold resummation in heavy quark production.