Recent Results on QCD Corrections to Semileptonic $b$-Decays

We summarize recent results on QCD corrections to various observables in semileptonic $b$ quark decays. For massless leptons in the final state we present effects of such corrections on triple differential distribution of leptons which are important in studies of polarized $b$ quark decays. Analogous formulas for distributions of neutrinos are applicable in decays of polarized $c$ quarks. In the case of decays with a $τ$ lepton in the final state mass effect of $τ$ has to be included. In this case we concentrate on corrections to the total decay width.

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