We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ using the decay $B\to D\ell {\nu }_{\ell }$ ($\ell =e,\mu$) based on $711{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}\to \mathrm{\Upsilon }(4S)$ data recorded by the Belle detector and containing $772\times {10}^6$ $B\overline{B}$ pairs. One $B$ meson in the event is fully reconstructed in a hadronic decay mode, while the other, on the signal side, is partially reconstructed from a charged lepton and either a $D^{+}$ or $D^0$ meson in a total of 23 hadronic decay modes. The isospin-averaged branching fraction of the decay $B\to D\ell {\nu }_{\ell }$ is found to be $\mathcal{B}(B^0\to D^{-}{\ell }^{+}{\nu }_{\ell })=(2.31\pm 0.03(\mathrm{stat})\pm 0.11(\mathrm{syst}))\%$. Analyzing the differential decay rate as a function of the hadronic recoil with the parametrization of Caprini, Lellouch, and Neubert and using the form-factor prediction $\mathcal{G}(1)=1.0541\pm 0.0083$ calculated by FNAL/MILC, we obtain ${\eta }_{\mathrm{EW}}|V_{cb}|=(40.12\pm 1.34)\times {10}^{-3}$, where ${\eta }_{\mathrm{EW}}$ is the electroweak correction factor. Alternatively, assuming the model-independent form-factor parametrization of Boyd, Grinstein, and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD collaborations, we find ${\eta }_{\mathrm{EW}}|V_{cb}|=(41.10\pm 1.14)\times {10}^{-3}$.

• Received 14 October 2015

DOI:https://doi.org/10.1103/PhysRevD.93.032006