The cusp anomalous dimension at three loops and beyond

TL;DR

This paper derives an analytic three-loop formula for the cusp anomalous dimension in N=4 super Yang-Mills, connecting it to Regge limits, QCD, and strong coupling behaviors, advancing understanding of gauge theory amplitudes.

Contribution

It provides the first analytic three-loop expression for the cusp anomalous dimension in N=4 SYM, linking it to Regge limits and partial QCD results, and explores ladder diagram limits.

Findings

Analytic three-loop cusp anomalous dimension formula derived.

Agreement with strong coupling in ladder diagram limit.

Partial three-loop results applicable to QCD.

Abstract

We derive an analytic formula at three loops for the cusp anomalous dimension Gamma_cusp(phi) in N=4 super Yang-Mills. This is done by exploiting the relation of the latter to the Regge limit of massive amplitudes. We comment on the corresponding three loops quark anti-quark potential. Our result also determines a considerable part of the three-loop cusp anomalous dimension in QCD. Finally, we consider a limit in which only ladder diagrams contribute to physical observables. In that limit, a precise agreement with strong coupling is observed.