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 Fade approximation. Via this method we confirm the existing results by an independent calculation. (C) 1999 Published by Elsevier Science B.V. All rights reserved.