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Inclusive weak decays of heavy hadrons with power suppressed terms at NLO

Within the heavy quark expansion techniques for the heavy hadron weak decays we analytically compute the coefficient of the power suppressed dimension five chromo-magnetic operator at next-to-leading order of QCD perturbation theory with the full dependence on the final state quark mass. We present explicit expressions for the total width of inclusive semileptonic decays including the power suppressed terms and for a few moments of decay differential distributions. One of the important phenomenological applications of our results is precision analysis of the decays of bottom mesons to charmed final states and extraction of the numerical value for the CKM matrix entry |V_{cb}|.