We present the analytical calculation of the four-loop QCD β-function within the minimal subtraction scheme.

The prescription for the $\gamma_5$-matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.Comment: 11 pages, 1 figure available on request from the author, NIKHEF-H/92-1

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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.Comment: 11 pages, Late