Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions

TL;DR

This work delivers the complete four-loop renormalization structure of QCD by analytically computing the gluon and ghost field anomalous dimensions and the ghost-ghost-gluon and quark-quark-gluon vertices. Combined with known four-loop results for the coupling, quark field, and mass anomalous dimensions, it yields the full set of renormalization constants for the QCD Lagrangian at four loops. The authors derive scheme- and scale-invariant gluon and ghost propagators at NNNLO and establish the four-loop anomalous dimension of the composite operator $A^2$ in the Landau gauge, supported by extensive cross-checks and a public data resource for general SU($N$). These results complete the four-loop renormalization program in perturbative QCD and enable precise comparisons with nonperturbative insights and lattice data.

Abstract

The anomalous dimensions of the gluon and ghost fields as well as the ghost-ghost-gluon and quark-quark-gluon vertexes are analytically computed in pQCD. Taken together with already available anomalous dimensions of the coupling constant, the quark field and the mass the results lead to complete knowledge of all renormalization constant entering into the renormalization of the QCD Lagrangian at the four-loop level. As a by-product we get scale and scheme invariant gluon and ghost propagators at NNNLO. Using a theorem due to Dudal, Verschelde and Sorella, we also construct the four-loop anomalous dimension of the ``gluon mass operator'', A^2, in the Landau gauge.