Off-forward anomalous dimensions of non-singlet transversity operators

TL;DR

This paper calculates the anomalous dimension matrix for non-singlet transversity operators mixing with total derivatives at four-loop order in QCD, using a large flavor number approximation and a consistency relation.

Contribution

It provides the first four-loop order calculation of the anomalous dimensions for these operators in the large $n_f$ limit, advancing theoretical understanding of operator mixing in QCD.

Findings

Anomalous dimension matrix determined at four-loop order.

Utilizes a novel consistency relation from renormalization structure.

Results applicable in the large $n_f$ limit in the $ar{MS}$ scheme.

Abstract

We determine the anomalous dimension matrix for the transversity operator mixing into total derivative operators in the limit of a large number of quark flavors $n_f$ to fourth order in the strong coupling $\alpha_s$ in the $\overline{\text{MS}}$-scheme. This is achieved by using a consistency relation between the operator anomalous dimensions, which follows from the renormalization structure of the operators in the chiral limit.