  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-bar 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.
