Measurement of the relative branching fractions ofB¯→D/D*/D**l−ν¯ldecays in events with a fully reconstructedBmeson

We determine the relative branching fractions of semileptonic $B$ decays to charmed final states. The measurement is performed on the recoil from a fully reconstructed $B$ meson in a sample of $362\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the BABAR detector. A simultaneous fit to a set of discriminating variables is performed on a sample of $\overline{B}\to DX{\ell }^{-}{\overline{\nu }}_{\ell }$ decays to determine the contributions from the different channels. We measure $\Gamma (B^{-}\to D{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (B^{-}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.227\pm 0.014\pm 0.016$, $\Gamma (B^{-}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (B^{-}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.582\pm 0.018\pm 0.030$, and $\Gamma (B^{-}\to D^{**}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (B^{-}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.191\pm 0.013\pm 0.019$ for the charged $B$ sample, and $\Gamma (\overline{B^0}\to D{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (\overline{B^0}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.215\pm 0.016\pm 0.013$, $\Gamma (\overline{B^0}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (\overline{B^0}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.537\pm 0.031\pm 0.036$, and $\Gamma (\overline{B^0}\to D^{**}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (\overline{B^0}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.248\pm 0.032\pm 0.030$ for the neutral $B$ sample, where uncertainties are statistical and systematic, respectively.