The Inclusive $\bar B\to \tau \bar\nu X$ Decay in Two Higgs Doublet Models

We calculate in the framework of two Higgs doublet models the differential decay rate for inclusive $\bar B\to\tau\,\bar\nu\,X$ transitions to order $1/m_b^2$ in the heavy quark expansion, for both polarized and unpolarized tau leptons. In contrast to the situation in the standard model, we find sizeable $1/m_b^2$ corrections. A systematic heavy quark expansion significantly reduces the theoretical uncertainties in the calculation compared to the existing free quark decay model results. From the experimental measurement of the branching ratio, we derive the bound $\tan\beta < 0.51\, m_{H^\pm}\,[{\rm GeV}]$. We point out that the tau polarization is potentially a more sensitive probe of multi scalar models than the branching ratio itself.