Improving constraints ontanβ/mHusingB→Dτν¯

We study the $q^2$ dependence of the exclusive decay mode $B\to D\tau \overline{\nu }$ in type-II two Higgs doublet models (2HDM’s) and show that this mode may be used to put stringent bounds on $\tan \beta {/m}_H.$ There are currently rather large theoretical uncertainties in the $q^2$ distribution, but these may be significantly reduced by future measurements of the analogous distribution for $B\to D(e,\mu )\overline{\nu }.$ We estimate that this reduction in the theoretical uncertainties would eventually (i.e., with sufficient data) allow one to push the upper bound on $\tan \beta {/m}_H$ down to about $0.06{\mathrm{GeV}}^{\mathrm{-}1}.$ This would represent an improvement on the current bound by about a factor of 7. We then apply the method of optimized observables which allows us to estimate the reach of an experiment with a given number of events. We thus find that an experiment with, for example, ${10}^3$ events could set a 2σ upper bound on $\tan \beta {/m}_H$ of $0.07{\mathrm{GeV}}^{\mathrm{-}1}$ or could differentiate at the 4.6σ level between a 2HDM with $\tan \beta {/m}_H=0.1\mathrm{}{\mathrm{GeV}}^{\mathrm{-}1}$ and the standard model.