  The semileptonic decay channel B -> D tau nu is sensitive to the presence of
a scalar current, such as that mediated by a charged-Higgs boson. Recently the
BaBar experiment reported the first observation of the exclusive semileptonic
decay B -> D tau nu, finding an approximately 2-sigma disagreement with the
Standard-Model prediction for the ratio R(D)=BR(B->D tau nu)/BR(B->D l nu),
where l=e,mu. We compute this ratio of branching fractions using hadronic form
factors computed in unquenched lattice QCD and obtain R(D) = 0.316(12)(7),
where the errors are statistical and total systematic, respectively. This
result is the first Standard-Model calculation of R(D) from ab initio full QCD.
Its error is smaller than that of previous estimates, primarily due to the
reduced uncertainty in the scalar form factor f_0(q^2). Our determination of
R(D) is approximately 1-sigma higher than previous estimates and, thus, reduces
the tension with experiment. We also compute R(D) in models with electrically
charged scalar exchange, such as the type II two-Higgs doublet model. Once
again, our result is consistent with, but approximately 1-sigma higher than,
previous estimates for phenomenologically relevant values of the scalar
coupling in the type II model. As a byproduct of our calculation, we also
present the Standard-Model prediction for the longitudinal polarization ratio
P_L (D)= 0.325(4)(3).
