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Measurements of the Semileptonic Decays $\Bb\to D\ell\nub$ and $\Bb\to D^*\ell\nub$ Using a Global Fit to $D X\ell\nub$ Final States

Semileptonic $\bar{B}$ decays to $DX\ell\barν$ ($\ell=e$ or $mu$) are selected by reconstructing $D0\ell$ and $D^+\ell$ combinations from a sample of 230 million $Υ(4S) \to B\bar{B}$ 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 $\mathcal{B}(B^- \to D0\ell\barν) = (2.34 \pm 0.03 \pm 0.13) %$ and $\mathcal{B}(B^- \to D^{*0}\ell\barν) = (5.40 \pm 0.02 \pm 0.21) %$,where the errors are statistical and systematic, respectively. The fit also determines form factor parameters in a HQET-based parameterization, resulting in $ρ_D2 = 1.20 \pm 0.04 \pm 0.07$ for $\bar{B} \to D\ell\barν$ and $ρ_{D^*}2 = 1.22 \pm 0.02 \pm 0.07$ for $\bar{B} \to D^*\ell\barν$ These values are used to obtain the product of the CKM matrix element $|V_{cb}|$ times the form factor at the zero recoil point for both $\bar{B} \to D\ell\barν$ decays, $\mathcal{G}(1)|V_{cb}| = (43.1 \pm 0.8 \pm 2.3)\times 10^{-3}$, and for $\bar{B} \to D^*\ell\barν$ decays, $\mathcal{F}(1)|V_{cb}| = (35.9 \pm 0.2 \pm 1.2)\times 10^{-3}$.