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Mass Corrections to the Tau Decay Rate

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 ${\cal O}(α_s^2 m^2)$ 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.