Measurement of $\overrightarrow{B}\rho l\nu$ decay and $|V_{\mathrm{ub}}|$

Using a sample of $3.3\times {10}^6$ ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}\to B\overline{B}$ events collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR), we measure $\mathcal{B}\left(\overrightarrow{B}\rho l\nu \right),$ $|V_{\mathrm{ub}}|,$ and the partial rate $\left(\Delta \Gamma \right)$ in three bins of $q^2\equiv {(p}_B-p_{\rho }{)}^2.$ We find $\mathcal{B}{(B}^0\to {\rho }^{-}{l}^{+}\nu )=(2.69\mathrm{}\pm {0.41}_{-0.40}^{+0.35\mathrm{}}\pm 0.50)\times {10}^{-4},$ $|V_{\mathrm{ub}}|=(3.23\mathrm{}\pm {0.24}_{-0.26}^{+0.23\mathrm{}}\pm 0.58)\times {10}^{-3},$ $\Delta \Gamma (0<q^2<7\mathrm{}{\mathrm{GeV}}^2{/c}^4)=(7.6\mathrm{}\pm {3.0}_{-1.2}^{+0.9\mathrm{}}\pm 3.0)\times {10}^{-2}{\mathrm{ns}}^{-1},$ $\Delta \Gamma (7<q^2<14\mathrm{}{\mathrm{GeV}}^2{/c}^4)=(4.8\mathrm{}\pm {2.9}_{-0.8}^{+0.7\mathrm{}}\pm 0.7)\times {10}^{-2}{\mathrm{ns}}^{-1},$ and $\Delta \Gamma (14<q^2<21\mathrm{}{\mathrm{GeV}}^2{/c}^4)=(7.1\mathrm{}\pm {2.1}_{-1.1}^{+0.9\mathrm{}}\pm 0.6)\times {10}^{-2}{\mathrm{ns}}^{-1}.$ Here, $l=e$ or $\mu ,$ but not both, and the errors are statistical, systematic, and theoretical. The method is sensitive primarily to $\overrightarrow{B}\rho l\nu$ decays with leptons in the energy range above 2.3 GeV. Averaging with the previously published CLEO results for $\overrightarrow{B}\rho l\nu ,$ we obtain $\mathcal{B}{(B}^0\to {\rho }^{-}{l}^{+}\nu )=(2.57\mathrm{}\pm {0.29}_{-0.46}^{+0.33\mathrm{}}\pm 0.41)\times {10}^{-4}$ and $|V_{\mathrm{ub}}|=(3.25\mathrm{}\pm {0.14}_{-0.29}^{+0.21\mathrm{}}\pm 0.55)\times {10}^{-3}.$