B→Dτνbranching ratios: Opportunity for lattice QCD and hadron colliders

In the standard model, scalar contributions to leptonic and semileptonic decays are helicity suppressed. The hypothesis of additional physical neutral/charged Higgses can enhance such scalar contributions and give detectable effects especially in $B$ physics. For the charged Higgs, experimental information on both $\mathrm{Br}(B\to D\tau \nu )$ and $\mathrm{Br}(B\to \tau \nu )$ has already become available, and in particular, the $B\to D\tau \nu$ branching ratio measurements will be further improved in the coming years. Hadronic uncertainties of scalar contributions in semileptonic decays are already in much better shape than the ones plaguing the helicity-suppressed leptonic decays $B\to \tau \nu$. Combining existing experimental information from the $B$ factories, we explore which existing and future lattice estimates will be useful to directly address new physics effects from measurements of $\mathrm{Br}(B_{u,d,s}\to D_{u,d,s}\tau \nu )$, which can be performed also at hadron colliders.