Mass effects in muon and semileptonic b -> c decays

Quantum chromodynamics (QCD) effects in the semileptonic decay b -> c l nu are evaluated to the second order in the coupling constant, O(alpha_s^2), and to several orders in the expansion in quark masses, m_c/m_b. Corrections are calculated for the total decay rate as well as for the first two moments of the lepton energy and the hadron system energy distributions. Applied to the muon decay, they decrease its predicted rate by -0.43 ppm.