====== TTP99-38 Second Order Corrections to the Muon Lifetime and the Semileptonic $B$ Decay ====== In this article two-loop QED corrections to the muon decay and corrections of order $\alpha_s^2$ to the semileptonic decay of the bottom quark are considered. We compute the imaginary part of the four-loop diagrams contributing to the corresponding fermion propagator in the limit of small external momentum. The on-shell condition is obtained with the help of a conformal mapping and Pad\'e approximation. Via this method we confirm the existing results by an independent calculation. |**M. Steinhauser and T. Seidensticker** | |** Physics Letters B 467 271-278 1999 ** | | {{preprints:1999:ttp99-38.pdf|PDF}} {{preprints:1999:ttp99-38.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9909436|arXiv]] | | |