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
We present algorithms for the group independent reduction of group theory factors of Feynman diagrams. We also give formulas and values for a large number of group invariants in which the group theory factors are expressed. This includes formulas for various contractions of symmetric invariant tensors, formulas and algorithms for the computation of characters and generalized Dynkin indices and trace identities. Tables of all Dynkin indices for all exceptional algebras are presented, as well as all trace identities to order equal to the dual Coxeter number. Further results are available through efficient computer algorithms.
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