Four-loop QCD cusp anomalous dimension at small angle

TL;DR

This paper computes the four-loop small angle expansion of the QCD cusp anomalous dimension, providing new insights into heavy-quark field anomalous dimensions and their relation to supersymmetric theories.

Contribution

It presents the first four-loop calculation of the small angle expansion of the QCD cusp anomalous dimension and explores its connection to N=4 supersymmetric Yang-Mills theory.

Findings

Calculated four-loop QCD cusp anomalous dimension at small angles.

Derived four-loop anomalous dimension of heavy-quark field in HQET.

Found a proportionality between QCD Bremsstrahlung function and N=4 SYM counterpart.

Abstract

We calculate the small angle expansion of the four-loop QCD cusp anomalous dimension. As a byproduct of our calculation, we also obtain the four-loop anomalous dimension of the heavy-quark field in HQET. The validity of the calculational setup is cross-checked by the independent calculation of the four-loop QCD beta-function from heavy-quark-gluon vertex renormalization in HQET. We check the obtained results for the cusp anomalous dimension and heavy-quark field anomalous dimension against available analytical and numerical results. Finally, we find that the maximal transcendentality contribution to the QCD Bremsstrahlung function coincides, up to a factor 3/2, with the Bremsstrahlung function in N = 4 supersymmetric Yang-Mills theory, at least, through 4 loops.