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

The anomalous dimensions of the gluon and ghost fields as well as those of the ghost–ghost–gluon and quark–quark–gluon vertexes are analytically computed at four loops 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”, image, in the Landau gauge.