The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements

TL;DR

This paper computes three-loop unpolarized and polarized non-singlet anomalous dimensions and splitting functions in QCD using off-shell operator matrix elements, including the first direct calculation for transversity.

Contribution

It provides the first direct calculation of three-loop transversity anomalous dimensions and compares these results with existing literature.

Findings

Calculated three-loop anomalous dimensions and splitting functions in QCD.

First direct computation of transversity anomalous dimensions at three loops.

Results are consistent with previous literature.

Abstract

We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{\rm NS}^+, P_{\rm NS}^-$ and $P_{\rm NS}^{\rm s}$ in QCD in the $\overline{\sf MS}$ scheme by using the traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For the first time we also calculate the three--loop anomalous dimensions $P_{\rm NS}^{\rm \pm tr}$ for transversity directly. We compare our results to the literature.