Three-loop evolution kernel for transversity operator

TL;DR

This paper computes the three-loop evolution kernel for transversity operators in QCD, providing explicit anomalous dimensions and advancing the understanding of their quantum corrections.

Contribution

It presents the first calculation of the three-loop evolution kernel for transversity operators, including explicit anomalous dimensions in the Gegenbauer basis.

Findings

Explicit three-loop evolution kernel derived.

Anomalous dimension matrix provided for initial operators.

Advances precision in QCD transversity operator analysis.

Abstract

We calculate quantum corrections to the symmetry generators for the transversity operators in quantum chromodynamics (QCD) in the two-loop approximation. Using this result, we obtain the evolution kernel for the corresponding operators at three loops. The explicit expression for the anomalous dimension matrix in the Gegenbauer basis is given for the first few operators.