Refining New-Physics Searches in $B\rightarrow D_{\tau u}$ with Lattice QCD
Jon A. Bailey, Alexei Bazavov, C. Bérnard, Chris Bouchard, Carleton DeTar, Dongsheng Du, Aida X El-Khadra, Justin Foley, E. D. Freeland, E. Gámiz, Steven Gottlieb, Urs M. Heller, J. Kim, Andreas S. Kronfeld, J. Laiho, L. Levkova, P. B. Mackenzie, Yannick Meurice, E. T. Neil, M. B. Oktay · IUScholarWorks (Indiana University) · 2012
The semileptonic decay channel $B\\rightarrow D_{\\tau\ u}$ 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 $B\\rightarrow D_{\\tau}−\\overline{\ u}$, finding an approximately $2\\sigma$ disagreement with the standard-model prediction for the ratio $R(D)=BR(B\\rightarrow D_{\\tau\ u}/BR(B\\rightarrow D\\ell\ u)$, 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 $P_{L}(D)=0.325(4)(3)$.