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In this paper we calculate first order radiative QCD corrections to the decayprocess $b\to cW^-(\to\ell^-\bar\nu_\ell)$ of a polarized bottom quark. Takinginto account both the bottom and charm quark masses, the analytical expressionsgiven in this paper allow for a detailed analysis of the differential decayrate of the polarized quark in dependence on the polar and azimuthal angles ofthe lepton pair and the angle of the polarization vector of the quark relativeto the momentum direction of the $W$ boson. The results are given for differentpolarization states of the charged lepton. In addition, we calculatednonperturbative corrections and estimated their contribution.

$O(\alpha_s)$ perturbative and nonperturbative corrections to polarized semileptonic $\Lambda_b$ decay distributions