The cusp anomalous dimension at three loops and beyond

We derive an analytic formula at three loops for the cusp anomalous dimension Γcusp(ϕ) in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = {4} $\end{document} 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.