Five-loop renormalisation of QCD in covariant gauges

TL;DR

This work delivers the full five-loop renormalisation constant set for QCD in general covariant gauges, including complete gauge-parameter dependence, by merging the global $R^*$ method with Forcer. It extends known results beyond Feynman gauge to arbitrary simple gauge groups and gauges, enabling precise Landau-gauge extractions such as the scheme-independent propagators and the $A^2$ anomalous dimension. The authors provide explicit five-loop anomalous dimensions $\gamma_2$, $\gamma_3$, and $\gamma_3^{c}$, validate them against established results, and apply the findings to scheme-independent propagators and the $A^2$ operator, with results available in ancillary files. These advances enhance high-precision QCD predictions and support robust comparisons with lattice data and non-perturbative approaches. The work also demonstrates methodological innovations in extending the $R^*$ framework to general gauge groups and gauges, with cross-checks confirming consistency with independent computations.

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 $ξ$ 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.