Renormalization of twist-two operators in covariant gauge to three loops in QCD

TL;DR

This paper presents a new systematic method to extract counterterm Feynman rules for gauge-variant operators in covariant gauge, enabling the calculation of three-loop anomalous dimensions of twist-two operators in QCD, confirming previous results.

Contribution

The authors develop a novel approach to derive counterterm Feynman rules for gauge-variant operators, facilitating higher-loop calculations in covariant gauges in QCD.

Findings

Rederived three-loop singlet anomalous dimensions independently.

Confirmed gauge parameter independence of results.

Validated the new method by matching previous calculations.

Abstract

The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark and gluon operators. The anomalous dimensions of these operators determine the splitting functions that govern the scale evolution of parton distribution functions. In massless QCD, these anomalous dimensions can be determined through the calculation of off-shell operator matrix elements, typically performed in a covariant gauge, where the physical operators mix with gauge-variant operators of the same quantum numbers. We derive a new method to systematically extract the counterterm Feynman rules resulting from these gauge-variant operators. As a first application of the new method, we rederive the unpolarized three-loop singlet anomalous dimensions, independently confirming previous results obtained with other methods. Employing a general covariant gauge, we observe the explicit cancellation of the gauge parameter dependence in these results.