Third order corrections to the semileptonic b →c and the muon decays

We compute corrections of order α${}^3$${}_s$ to the decay b→cℓ¯ν taking into account massive charm quarks. In the on-shell scheme large three-loop corrections are found. However, in the kinetic scheme the three-loop corrections are below 1% and thus perturbation theory is well under control. We furthermore provide results for the order α${}^3$${}_s$corrections to b→uℓ¯ν and the third-order QED corrections to the muon decay which will be important input for reducing the uncertainty of the Fermi coupling constant
G${}_F$.