====== TTP99-25 Second Order QCD Corrections to $\Gamma(t \to Wb)$ ====== Corrections of $O(\alpha_s^2)$ 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 Pad\'e approximations. The described method allows to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important cross-checks against recent results for the decay rate $b \to u l \bar\nu$ and the two-loop QED corrections to $\mu$-decay are performed. |**K.G. Chetyrkin, R. Harlander, T. Seidensticker, and M. Steinhauser** | |** Phys. Rev. D 60 114015 1999 ** | | {{preprints:1999:ttp99-25.pdf|PDF}} {{preprints:1999:ttp99-25.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9906273|arXiv]] | | |