Third order corrections to the semi-leptonic boldmath{bto c} and the muon decays
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We compute corrections of order $\alpha_s^3$ to the decay $b \to c \ell \bar\nu$ 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 $\alpha_s^3$ corrections to $b \to u \ell \bar\nu$ and the third-order QED corrections to the muon decay which will be important input for reducing the uncertainty of the Fermi coupling constant $G_F$.
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