Second Order QCD Corrections to $Γ(t \to Wb)$

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.