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In this note radiative corrections to the total hadronic decay rate of the τ -lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate ration R τ to the order O(α 2 s m 2 ) and find that they contribute appreciably to the Cabbibo supressed decay modes of the τ -lepton. We also discuss corrections of mass dimension D = 4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.

Quark mass effects in O(α 2 s ) QCD corrections to the decay rates of intermediate Higgs bosons are studied. The total hadronic rate and the partial decay rate into bottom quarks are analyzed for the Standard (scalar) Higgs boson as well as for pseudoscalar Higgs bosons. The calculations of three different contributions are presented. First, the flavour singlet diagrams containing two closed fermion loops are calculated for a nonvanishing bottom mass in the heavy top limit. Their leading contribution, which is of the same order as the quasi-massless nonsinglet corrections, and the subleading terms are found. Large logarithms arise due to the separation of the pure gluon final state from the bottom final states. Second, quadratic bottom mass corrections originating from nonsinglet diagrams are presented. Third, nonsinglet corrections induced by virtual heavy top quarks are calculated in leading and subleading orders. It is demonstrated that, in order α 2 s , the first contribution numerically dominates over the second and the third ones.