O(\alpha^n\alpha_s^m) Corrections in e^+e^- Annihilation and \tau Decay

Abstract

The results of evaluation of mixed QED X QCD corrections to R(s) in e^+e^- annihilation and R_{\tau} in hadronic decay of the \tau lepton to O(\alpha^n\alpha_s^m), m+n \leq 3, are presented. The net effect on \alpha_s(M_Z) from the Z decay is only about 0.1% and in the \tau decay case the net effect is negligible, as expected.