Three-loop cusp anomalous dimension and a conjecture for n loops

Abstract

I present analytical expressions for the massive cusp anomalous dimension in QCD through three loops, first calculated in 2014, in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a conjecture for the n-loop cusp anomalous dimension in terms of the lower-loop results. I also present numerical results and simple approximate formulas for the cusp anomalous dimension relevant to top-quark production.