QCD corrections to charged Higgs-mediated $b\to c\tau \nu$ decay

We calculate the $O({\alpha }_s)$ corrections to the charged Higgs mediated inclusive semi-tauonic $B$ decay. By working in the Landau gauge, we demonstrate how to obtain the charged Higgs contributions (both direct and interference terms) from the known QCD corrections to $t\to b{H}^{+}$. Combining our results with $O(1\mathrm{/}{m}_b^2)$ corrections to the spectator model and comparing the theoretical prediction with the recent experimental measurements, we find a model-independent $2\sigma$ upper bound on the ratio of Higgs vacuum expectation values, $\tan \beta <0.52(m_H\mathrm{/}1GeV)$.