Top Quark Contribution to Hadronic Decays of the Z-Boson at Alpha_s^2 in QCD

Abstract

We evaluate the effect of a virtual top quark on the coefficient of ${\alpha }_s^2$ in the decay rates $\Gamma (Z\to \mathrm{hadrons})$ and $\Gamma (Z\to b\overline{b})$. We treat the dependence on the top quark mass exactly instead of using a large mass expansion. The present work completes the evaluation of the ${\alpha }_s^2$ contributions to these quantities. The calculation uses both the $\overline{\mathrm{MS}}$ and Collins-Wilczek-Zee renormalization prescriptions. The results can be applied to the hadronic decays of the $\tau$-lepton.

Comments: 10 pages, REVTeX 3.0 with 4 postscript figures compressed with uufiles, University of Oregon preprint OITS 545