Corrections of O(ααs) to the decay of the Z boson into bottom quarks

For the vertex corrections to the partial decay rate Γ(Z→bb̄) involving the top quark only the leading terms of order ααs in the 1/Mt 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 O(ααs) analysis to arrive at reliable predictions.