Five-loop renormalisation of QCD in covariant gauges

TL;DR

This paper computes five-loop renormalisation constants in QCD for a general gauge, providing comprehensive results that include gauge dependence and enabling precise calculations of anomalous dimensions and propagators.

Contribution

It presents the first complete five-loop renormalisation constants in QCD for a general covariant gauge, extending previous results limited to Feynman gauge.

Findings

Confirmed known results in Feynman gauge

Derived five-loop anomalous dimensions of $A^2$ operator in Landau gauge

Calculated scheme-independent gluon, ghost, and fermion propagators at five loops

Abstract

We present the complete set of vertex, wave function and charge renormalisation constants in QCD in a general simple gauge group and with the complete dependence on the covariant gauge parameter $\xi$ in the minimal subtraction scheme of conventional dimensional regularisation. Our results confirm all already known results, which were obtained in the Feynman gauge, and allow the extraction of other useful gauges such as the Landau gauge. We use these results to extract the Landau gauge five-loop anomalous dimensions of the composite operator $A^2$ as well as the Landau gauge scheme independent gluon, ghost and fermion propagators at five loops.