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 $α_{s}^{2}$ in the decay rates $Γ(Z \rightarrow {\rm hadrons})$ and $Γ(Z \rightarrow b\overline{b} )$. 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 $α_{s}^{2}$ contributions to these quantities. The calculation uses both the $\overline{\rm MS}$ and Collins-Wilczek-Zee renormalization prescriptions. The results can be applied to the hadronic decays of the $τ$-lepton.