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${\cal O}(α\as \ln m_t^2)$ Non-Universal Corrections to the Decay Rate $Γ(Z\rightarrow b\bar{b})$

The partial decay rate $Γ(Z\to b\bar{b})$ is significantly influenced by the mass of the top quark due to electroweak radiative corrections. The leading $\sim m_t^2$ and the next-to-leading contribution $\sim \ln m_t^2$ are known to be numerically of similar size. In this work we calculate the QCD corrections to the logarithmic correction using the heavy top mass expansion. The ${\cal O} (α\as \ln m_t^2)$ corrections are of the same order as the QCD corrections to the quadratic top mass term, but of different sign.