The $n_{f}$ terms of the three-loop cusp anomalous dimension in QCD

TL;DR

This paper presents the calculation of the $n_f$ dependent part of the three-loop cusp anomalous dimension in QCD, revealing a surprising similarity to analogous functions in ${ m extbf{N=4}}$ SYM, and employs advanced integral computation techniques.

Contribution

It provides the first explicit analytic expression for the $n_f$ dependent three-loop cusp anomalous dimension in QCD using harmonic polylogarithms.

Findings

The $n_f$ dependent three-loop cusp anomalous dimension is expressed in terms of harmonic polylogarithms.

The result shares functional forms with anomalous dimensions in ${ m extbf{N=4}}$ SYM.

All master integrals are computed using a refined differential equation method.

Abstract

In this talk we present the result for the $n_f$ dependent piece of the three-loop cusp anomalous dimension in QCD. Remarkably, it is parametrized by the same simple functions appearing in analogous anomalous dimensions in ${\mathcal N}=4$ SYM at one and two loops. We also compute all required master integrals using a recently proposed refinement of the differential equation method. The analytic results are expressed in terms of harmonic polylogarithms of uniform weight.