Inclusive Semitauonic $B$ Decays to Order $\mathcal{O}({\mathrm{\Lambda }}_{QCD}^3\mathrm{/}{m}_b^3)$

We calculate the decay width and the $\tau$-lepton energy distribution as well as relevant moments for inclusive $\bar{B}\to X_c\tau {\bar{\nu }}_{\tau }$ process including power corrections up to order ${\mathrm{\Lambda }}_{QCD}^3\mathrm{/}{m}_b^3$ and QCD corrections to the partonic level. We compare the result with the sum of the standard-model predictions of the branching fractions of the exclusive semileptonic $\bar{B}\to (D,D^{\ast },D^{\ast \ast })\tau {\bar{\nu }}_{\tau }$ decays as well as with the relevant experimental data. Our prediction is in agreement with the LEP measurement and is consistent with the standard-model calculation of the exclusive modes. We discuss the impact from physics beyond the Standard Model.