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

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 fourth-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. (C) 1997 Elsevier Science B.V.