The 4-loop quark mass anomalous dimension and the invariant quark mass.

Abstract

We present the analytical calculation of the four-loop quark mass anomalous dimension in Quantum Chromodynamics within the minimal subtraction scheme. On the basis of this result we find that the so-called invariant quark mass is a very good reference mass for the accurate evolution of the running MS quark mass in phenomenological applications. We also obtain for the first time a complete 4-th order perturbative QCD expression for a physical quantity, the total Higgs boson decay rate into hadrons, and analyze the infrared fixed point for this case. PACS numbers: 13.85.Hd, 12.38.-t, 12.38.Bx 1 The renormalization group equations play an important role in our understanding of Quantum Chromodynamics and the strong interactions. The beta function and the quarks mass anomalous dimension are among the most prominent objects that appear in these renormalization group equations. The quark mass anomalous dimension in QCD was calculated at the 3-loop level in [1]. In a previous paper [2] we calculated analytically the 4-loop QCD β-function. Here we complete