Complete 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 $\mathrm{\Gamma }(Z\to b\bar{b})$ involving the top quark only the leading terms of order $\alpha {\alpha }_s$ in the $1\mathrm{/}{M}_t$ expansion are known. In this work we compute the missing next-to-leading corrections. Thus at $O(\alpha {\alpha }_s)$ the complete corrections to the decay of the Z boson into bottom quarks are at hand.