The 3-loop anomalous dimensions from off-shell operator matrix elements

TL;DR

This paper calculates three-loop anomalous dimensions for polarized and unpolarized operators using off-shell matrix elements, correcting previous two-loop results and extending the theoretical understanding of quantum chromodynamics.

Contribution

It introduces a novel calculation of three-loop anomalous dimensions using off-shell operator matrix elements and corrects earlier two-loop results in the literature.

Findings

Computed three-loop polarized and unpolarized anomalous dimensions.

Corrected errors in previous two-loop unpolarized singlet anomalous dimensions.

Extended theoretical framework for off-shell operator matrix elements.

Abstract

We report on the calculation of the three-loop polarized and unpolarized flavor non-singlet and the polarized singlet anomalous dimensions using massless off-shell operator matrix elements in a gauge-variant framework. We also reconsider the unpolarized two-loop singlet anomalous dimensions and correct errors in the foregoing literature.