Third order corrections to the semileptonic b -> c and the muon decays

We compute corrections of order alpha(3)(s) to the decay b -> b -> cl ( nu) over bar taking into account massive charm quarks. In the on-shell scheme large three-loop corrections are found. However, in the kinetic scheme the three-loop corrections are below 1% and thus perturbation theory is well under control. We furthermore provide results for the order alpha(3)(s) corrections to b -> cl (nu ) over bar and the third-order QED corrections to the muon decay which will be important input for reducing the uncertainty of the Fermi coupling constant G(F).