Improving constraints on tan(beta)/m_H using B to D tau bar{nu}

We study the q^2 dependence of the exclusive decay mode B \to D tau \bar{nu} in type II two Higgs doublet models 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)\bar{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 GeV^{-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 2\sigma upper bound on tan(beta)/m_H of 0.07 GeV^{-1} or could differentiate at the 4.6\sigma level between a 2HDM with tan(beta)/m_H = 0.1 GeV^{-1} and the SM.