Computation of the Soft Anomalous Dimension Matrix in Coordinate Space

TL;DR

This paper completes the coordinate space calculation of the three-parton correlation in the two-loop massive soft anomalous dimension matrix, confirming previous results and highlighting the symmetry properties of the diagrams.

Contribution

It provides a full coordinate space derivation of the two-loop soft anomalous dimension matrix, demonstrating its color symmetries and comparing massive and massless cases.

Findings

Coordinate space calculation matches previous results.

Color symmetries are transparent in this approach.

Examines behavior at absolute threshold.

Abstract

We complete the coordinate space calculation of the three-parton correlation in the two-loop massive soft anomalous dimension matrix. The full answer agrees with the result found previously by a different approach. The coordinate space treatment of renormalized two-loop gluon exchange diagrams exhibits their color symmetries in a transparent fashion. We compare coordinate space calculations of the soft anomalous dimension matrix with massive and massless eikonal lines and examine its nonuniform limit at absolute threshold.