Measurement ofB→ρlνdecay and|Vub|

Using a sample of $3.3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ events collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR), we measure $\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\rho}l\ensuremath{\nu}),$ $|{V}_{\mathrm{ub}}|,$ and the partial rate $(\ensuremath{\Delta}\ensuremath{\Gamma})$ in three bins of ${q}^{2}\ensuremath{\equiv}{(p}_{B}\ensuremath{-}{p}_{\ensuremath{\rho}}{)}^{2}.$ We find $\mathcal{B}{(B}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{l}^{+}\ensuremath{\nu})=(2.69\ifmmode\pm\else\textpm\fi{}{0.41}_{\ensuremath{-}0.40}^{+0.35}\ifmmode\pm\else\textpm\fi{}0.50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4},$ $|{V}_{\mathrm{ub}}|=(3.23\ifmmode\pm\else\textpm\fi{}{0.24}_{\ensuremath{-}0.26}^{+0.23}\ifmmode\pm\else\textpm\fi{}0.58)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3},$ $\ensuremath{\Delta}\ensuremath{\Gamma}(0l{q}^{2}l7{\mathrm{GeV}}^{2}{/c}^{4})=(7.6\ifmmode\pm\else\textpm\fi{}{3.0}_{\ensuremath{-}1.2}^{+0.9}\ifmmode\pm\else\textpm\fi{}3.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}{\mathrm{ns}}^{\ensuremath{-}1},$ $\ensuremath{\Delta}\ensuremath{\Gamma}(7l{q}^{2}l14{\mathrm{GeV}}^{2}{/c}^{4})=(4.8\ifmmode\pm\else\textpm\fi{}{2.9}_{\ensuremath{-}0.8}^{+0.7}\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}{\mathrm{ns}}^{\ensuremath{-}1},$ and $\ensuremath{\Delta}\ensuremath{\Gamma}(14l{q}^{2}l21{\mathrm{GeV}}^{2}{/c}^{4})=(7.1\ifmmode\pm\else\textpm\fi{}{2.1}_{\ensuremath{-}1.1}^{+0.9}\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}{\mathrm{ns}}^{\ensuremath{-}1}.$ Here, $l=e$ or $\ensuremath{\mu},$ but not both, and the errors are statistical, systematic, and theoretical. The method is sensitive primarily to $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\rho}l\ensuremath{\nu}$ decays with leptons in the energy range above 2.3 GeV. Averaging with the previously published CLEO results for $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\rho}l\ensuremath{\nu},$ we obtain $\mathcal{B}{(B}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{l}^{+}\ensuremath{\nu})=(2.57\ifmmode\pm\else\textpm\fi{}{0.29}_{\ensuremath{-}0.46}^{+0.33}\ifmmode\pm\else\textpm\fi{}0.41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $|{V}_{\mathrm{ub}}|=(3.25\ifmmode\pm\else\textpm\fi{}{0.14}_{\ensuremath{-}0.29}^{+0.21}\ifmmode\pm\else\textpm\fi{}0.55)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}.$