The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge

TL;DR

The paper verifies the five-loop Beta function $\beta$ for a non-Abelian gauge theory with a general gauge group and $N_f$ fermions in a single representation, using an independent UV-divergence approach in the ${\overline{MS}}$ scheme and confirming all-$N_f$ results. It advances the five-loop renormalization program by deriving the linear terms in the covariant gauge parameter $\xi$ for three anomalous dimensions (ghost, ghost-gluon vertex, and quark) around the Feynman gauge, enabling partial gauge-parameter dependence studies. A minimal set of renormalization constants $(\gamma_m,\beta,\gamma_3^{c},\gamma_1^{ccg},\gamma_2)$ is used to reconstruct the rest, with a simplified UV-divergence extraction based on an auxiliary mass $M$ and Taylor expansion, followed by master-integral reduction. The results include explicit five-loop $\beta$-function coefficients and linear-$\xi$ terms, and are cross-validated against independent computations and large-$N_f$ limits; ancillary data files provide complete renormalization constants for further use.

Abstract

We focus on a non-abelian gauge field coupled to a single (but general) representation of a family of Nf fermions. By using the same machinery that had allowed us to evaluate the sub-leading large-Nf term of the five-loop Beta function earlier, we here report on a confirmation of the all-Nf result that has in the meantime been published by another group. Furthermore, in order to push forward the 5-loop renormalization program regarding gauge parameter dependence, we present the linear terms of the complete set of anomalous dimensions, in an expansion in the covariant gauge parameter around the Feynman gauge.