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

• Received 27 April 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.011802