Measurement Of|vcb|and the Form-Factor Slope Inb¯→dℓ−

We present a measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{\mathrm{cb}}|$ and the form-factor slope ${\ensuremath{\rho}}^{2}$ in $\overline{B}\ensuremath{\rightarrow}D{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ decays based on $460\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ events recorded at the $\ensuremath{\Upsilon}(4S)$ resonance with the BABAR detector. $\overline{B}\ensuremath{\rightarrow}D{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ decays are selected in events in which a hadronic decay of the second $B$ meson is fully reconstructed. We measure $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})/\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}X{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})=(0.255\ifmmode\pm\else\textpm\fi{}0.009\ifmmode\pm\else\textpm\fi{}0.009)$ and $\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})/\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}X{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})=(0.230\ifmmode\pm\else\textpm\fi{}0.011\ifmmode\pm\else\textpm\fi{}0.011)$, along with the differential decay distribution in $\overline{B}\ensuremath{\rightarrow}D{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ decays. We then determine $\mathcal{G}(1)|{V}_{\mathrm{cb}}|=(42.3\ifmmode\pm\else\textpm\fi{}1.9\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${\ensuremath{\rho}}^{2}=1.20\ifmmode\pm\else\textpm\fi{}0.09\ifmmode\pm\else\textpm\fi{}0.04$, where $\mathcal{G}(1)$ is the hadronic form factor at the point of zero recoil.