TTP97-52 Corrections of O(\alpha\alpha_s) to the Decay of the Z Boson into Bottom Quarks

For the vertex corrections to the partial decay rate $\Gamma(Z\to b\bar{b})$ involving the top quark only the leading terms of order $\alpha\alpha_s$ in the $1/M_t$ expansion are known. In this work we compute the missing next-to-leading corrections. They turn out to be equally important as the leading term and therefore have to be included into an ${\cal O}(\alpha\alpha_s)$ analysis to arrive at reliable predictions.