Improving constraints on tan(beta)/mₕ using B → D tau nu

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We study the q² dependence of the exclusive decay mode B → D tau nu in type II two Higgs doublet models and show that this mode may be used to put stringent bounds on tan(beta)/mₕ. There are currently rather large theoretical uncertainties in the q² distribution, but these may be significantly reduced by future measurements of the analogous distribution for B → D(e,mu)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)/mₕ 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, 10³ events could set a 2σupper bound on tan(beta)/mₕ of 0.07 GeV⁻¹ or could differentiate at the 4.6σlevel between a 2HDM with tan(beta)/mₕ = 0.1 GeV⁻¹ and the SM.