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 αs2 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 Padé approximation. Via this method we confirm the existing results by an independent calculation.