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Semi-inclusive decays Lambda_b -> X_c + D_s^* at O(alpha_s) including Lambda_b and D_s^* polarization effects

In the leading order of the (1/m_b)-expansion in HQET the dominant contribution to the semi-inclusive decays of polarized Lambda_b baryons into the charm-strangeness mesons D_s and D_s^* is given by the partonic process b(up) -> c + (D_s^-, D_s^{*-}). Using standard values for the parameters of the process one expects a rather large branching ratio of approx. 8% into these two channels. In the factorization approximation the semi-inclusive decay of a polarized Lambda_b is governed by three unpolarized and four polarized structure functions for which we determine the nonperturbative O(1/m_b^2) corrections and the O(alpha_s) radiative corrections. We find that the perturbative and nonperturbative corrections amount to approx. 10% and approx. 3%, respectively. The seven structure functions can be measured through an analysis of the joint decay distributions of the process involving the polarization of the Lambda_b and the decays D_s^{*-} -> D_s^- + gamma and D_s^{*-} -> D_s^- + pi^0 for which we provide explicit forms. We also provide numerical results for the Cabibbo suppressed semi-inclusive decays Lambda_b -> X_u + (D_s, D_s^*).