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$O(α_s)$ perturbative and nonperturbative corrections to polarized semileptonic $Λ_b$ decay distributions

In this paper we calculate first order radiative QCD corrections to the decay process $b\to cW^-(\to\ell^-\barν_\ell)$ of a polarized bottom quark. Taking into account both the bottom and charm quark masses, the analytical expressions given in this paper allow for a detailed analysis of the differential decay rate of the polarized quark in dependence on the polar and azimuthal angles of the lepton pair and the angle of the polarization vector of the quark relative to the momentum direction of the $W$ boson. The results are given for different polarization states of the charged lepton. In addition, we calculated nonperturbative corrections and estimated their contribution.