The three-loop cusp anomalous dimension in QCD

TL;DR

This paper provides the complete three-loop analytic expression for the cusp anomalous dimension in QCD, enabling precise predictions of infrared divergences in scattering processes involving massive particles.

Contribution

It delivers the first full analytic three-loop result for the angle-dependent cusp anomalous dimension in QCD and proposes a universal effective coupling related to gauge theories.

Findings

Analytic three-loop cusp anomalous dimension in QCD obtained.

Predictions for non-planar four-loop cusp anomalous dimension terms.

Evidence for universality of a related effective coupling across gauge theories.

Abstract

We present the full analytic result for the three-loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a closely related quantity in terms of an effective coupling defined by the light-like cusp anomalous dimension. We find evidence that this quantity is universal for any gauge theory, and use this observation to predict the non-planar $n_{f}$-dependent terms of the four-loop cusp anomalous dimension.