Refining New-Physics Searches in $B\rightarrow D_{\tau\nu}$ with Lattice QCD

Abstract

The semileptonic decay channel $B\rightarrow D_{\tau\nu}$ is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently, the $\textit{BABAR}$ experiment reported the first observation of the exclusive semileptonic decay $B\rightarrow D_{\tau}−\overline{\nu}$, finding an approximately $2\sigma$ disagreement with the standard-model prediction for the ratio $R(D)=BR(B\rightarrow D_{\tau\nu}/BR(B\rightarrow D\ell\nu)$, where $\ell=e,\mu$. 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 $\textit{ab initio}$ 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 by-product of our calculation, we also present the standard-model prediction for the longitudinal-polarization ratio $P_{L}(D)=0.325(4)(3)$.