Inclusive Semitauonic $B$ Decays to Order ${\cal O} (\Lambda_{QCD}^3/m_b^3)$

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 $\Lambda_{QCD}^3/m_b^3$ 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 $\bar B \to (D, D^*, D^{**}) \tau \bar \nu_\tau$ 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.