Second order QCD corrections toΓ(t→Wb)

Corrections of $O\left({\alpha }_s^2\right)$ to the decay of the top quark into a W boson and a bottom quark are calculated. The method is based on an expansion of the top quark propagator for small external momentum q as compared to the top quark mass $M_t.$ The physical point $q^2{=M}_t^2$ is reached through Padé approximations. The described method allows us to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important crosschecks against recent results for the decay rate $\overrightarrow{b}\mathrm{ul}\overline{\nu }$ and the two-loop QED corrections to $\mu$ decay are performed.