Order 1/m_b^3 corrections to B\to X_c\ell\bar\nu decay and their implication for the measurement of \bar\Lambda and \lambda_1

Abstract

We compute the order 1/m_b^3 nonperturbative contributions to the inclusive differential B\to X_c\ell\bar\nu decay rate. They are parametrized by the expectation values of two local and four nonlocal dimension-six operators. We use our results to estimate part of the theoretical uncertainties in the extraction of matrix elements \bar\Lambda and \lambda_1 from the lepton spectrum in the inclusive semileptonic B decay and find them to be very large. We also compute the 1/m_b^3 corrections to the moments of the hadronic invariant mass spectrum in this decay, and combine them with the extracted values of \bar\Lambda and \lambda_1 to put an upper bound on the branching fraction Br(B\to D^{**}\ell\bar\nu).