Order ${1/m}_b^3$ corrections to $B\to X_c\mathcal{l}\overline{\nu }$ decay and their implication for the measurement of $\overline{\Lambda }$ and ${\lambda }_1$

We compute the order ${1/m}_b^3$ nonperturbative contributions to the inclusive differential $B\to X_c\mathcal{l}\overline{\nu }$ 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 $\overline{\Lambda }$ 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 $\overline{\Lambda }$ and ${\lambda }_1$ to put an upper bound on the branching fraction $B(B\to D^{**}\mathcal{l}\overline{\nu })$.