Measurements of the Semileptonic Decays $\text{Bb}\to D\mathrm{\ell }\text{nub}$ and $\text{Bb}\to D^{\ast }\mathrm{\ell }\text{nub}$ Using a Global Fit to $DX\mathrm{\ell }\text{nub}$ Final States

Semileptonic $\bar{B}$ decays to $DX\mathrm{\ell }\bar{\nu }$ ($\mathrm{\ell }=e$ or $mu$) are selected by reconstructing $D0\mathrm{\ell }$ and $D^{+}\mathrm{\ell }$ combinations from a sample of 230 million $\mathrm{{\rm Y}}(4S)\to B\bar{B}$ decays recorded with the BaBar detector at the PEPII $e^{+}{e}^{-}$ collider at SLAC. A global fit to these samples in a 3-dimensional space of kinematic variables is used to determine the branching fractions $\mathcal{B}(B^{-}\to D0\mathrm{\ell }\bar{\nu })=(2.34\pm 0.03\pm 0.13)$ and $$\mathcal{B}$(B^- \to D^{0}\ell\bar{\nu}) = (5.40 \pm 0.02 \pm 0.21) %$,where the errors are statistical and systematic, respectively. The fit also determines form factor parameters in a HQET-based parameterization, resulting in ${\rho }_{D}2=1.20\pm 0.04\pm 0.07$ for $\bar{B}\to D\mathrm{\ell }\bar{\nu }$ and ${\rho }_{D^{\ast }}2=1.22\pm 0.02\pm 0.07$ for $\bar{B}\to D^{\ast }\mathrm{\ell }\bar{\nu }$ These values are used to obtain the product of the CKM matrix element $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ times the form factor at the zero recoil point for both $\bar{B} \to D\ell\bar{\nu}$decays,$$\mathcal{G}$(1)|V_{cb}| = (43.1 \pm 0.8 \pm 2.3)\times 10^{-3}$,andfor$\bar{B} \to D^\ell\bar{\nu}$decays,$$\mathcal{F}$(1)|V_{cb}| = (35.9 \pm 0.2 \pm 1.2)\times 10^{-3}$.