Complete renormalization of QCD at five loops

TL;DR

This work completes the five-loop renormalization program for non-Abelian gauge theories in the Feynman gauge by deriving analytic five-loop anomalous dimensions for the ghost field and the ghost-gluon vertex for general gauge groups. The authors employ a rigorous multiloop pipeline—diagram generation, color algebra, infrared mass-regulation, IBP/Laporta reduction to 110 master integrals, and high-precision $ varepsilon$-expansions with PSLQ to obtain analytic combinations—and validate the results against known SU($N$) cases and large-$N_f$ limits. They also provide the complete set of renormalization constants by exploiting gauge-invariance relations, with electronic ancillary files containing the full expressions. The findings solidify the five-loop framework for gauge theories, enabling precise RG studies in QCD-like theories and offering a blueprint for extending the analysis to the gluon sector and gauge-parameter dependence.

Abstract

We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.