Measurement of the decay $Bto Dell u_ell$ in fully reconstructed events and determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$

We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ using the decay $Bto Dell u_ell$ ($ell=e,mu$) based on 711 fb$^{-1}$ of $e^+e^-to Upsilon(4S)$ data recorded by the Belle detector and containing $772 times 10^6$ $Bbar{B}$ 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 $Bto Dell u_ell$ is found to be $mathcal{B}(B^0 to D^- ell^+ u_{ell})=(2.31pm 0.03(mathrm{stat})pm 0.11(mathrm{syst}))%$. Analyzing the differential decay rate as a function of the hadronic recoil with the parameterization of Caprini, Lelouch and Neubert and using the form-factor prediction $mathcal{G}(1)=1.0541pm 0.0083$ calculated by FNAL/MILC, we obtain $eta_mathrm{EW}|V_{cb}|=(40.12pm 1.34)times 10^{-3}$, where $eta_mathrm{EW}$ is the electroweak correction factor. Alternatively, assuming the model-independent form-factor parameterization of Boyd, Grinstein and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD collaborations, we find $eta_mathrm{EW}|V_{cb}|=(41.10 pm 1.14)times 10^{-3}$.