The cusp anomalous dimension at three loops and beyond

Abstract

We derive an analytic formula at three loops for the cusp anomalous dimension Γ cusp(φ) 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. © 2012 SISSA.