Four-loop massive cusp anomalous dimension in QCD: a calculation from asymptotics

TL;DR

This paper introduces a high-precision method based on asymptotic analysis to compute the four-loop massive cusp anomalous dimension in QCD, validated at lower loops and applicable to complex color structures.

Contribution

It develops a novel asymptotic approach for calculating the four-loop massive cusp anomalous dimension in QCD, extending the method's applicability beyond previous loop orders.

Findings

Method accurately reproduces known two and three-loop results.

Provides new four-loop cusp anomalous dimension calculations.

Analyzes effects of different flavor numbers and color structures.

Abstract

I present a general method for determining the massive cusp anomalous dimension in QCD to a very high degree of accuracy using its asymptotic behavior at small and large quark velocities. I show that the method works exceedingly well at two and three loops where exact results are already known. I then present a calculation of the massive cusp anomalous dimension using its asymptotics at four loops, and I provide a detailed study of the results for different values of the number of flavors and for separate color structures. The method can be further extended and applied to higher numbers of loops.