TTP93-12 Leading Top Mass Corrections of Order ${\cal O}(\alpha\as m_t^2/M_W^2)$ to the Partial Decay Rate $\Gamma(Z\rightarrow b\bar{b})$

The order ${\cal O} (\alpha\as m_t^2/M_W^2)$ corrections to the partial decay rate of $\Gamma(Z\rightarrow b\bar{b})$ are computed using the heavy top mass expansion. They are given by the absorptive part of the corresponding three loop $Z$-self energy diagrams. Our method provides an independent way to calculate the QCD corrections to the electroweak one loop result for $\Gamma(Z\rightarrow b\bar{b})$ and our result represents another confirmation of the one recently published by Fleischer et al.