Mass Corrections to the Tau Decay Rate

In this note radiative corrections to the total hadronic decay rate of the $\tau$-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate ration $R_{\tau }$ to the order $\mathcal{O}({\alpha }_s^2{m}^2)$ and find that they contribute appreciably to the Cabbibo supressed decay modes of the $\tau$-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.