Study of the $q^2$ dependence of $\overrightarrow{B}\pi \mathcal{l}\nu$ and of $\overrightarrow{B}\rho \left(\omega \right)\mathcal{l}\nu$ and extraction of $|V_{\mathrm{ub}}|$

We report on determinations of $|V_{\mathrm{ub}}|$ resulting from studies of the branching fraction and $q^2$ distributions in exclusive semileptonic B decays that proceed via the $\overrightarrow{b}u$ transition. Our data set consists of the $9.7\times {10}^6$ $B\overline{B}$ meson pairs collected at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance with the CLEO II detector. We measure $\mathcal{B}{(B}^0\to {\pi }^{-}{\mathcal{l}}^{+}\nu )=(1.33\mathrm{}\pm 0.18\pm 0.11\pm 0.01\pm 0.07)\times {10}^{-4}$ and $\mathcal{B}{(B}^0\to {\rho }^{-}{\mathcal{l}}^{+}\nu )=(2.17\mathrm{}\pm {0.34}_{-0.54}^{+0.47\mathrm{}}\pm 0.41\pm 0.01)\times {10}^{-4},$ where the errors are statistical, experimental systematic, systematic due to residual form-factor uncertainties in the signal, and systematic due to residual form-factor uncertainties in the cross-feed modes, respectively. We also find $\mathcal{B}{(B}^{+}\to \eta {\mathcal{l}}^{+}\nu )=(0.84\mathrm{}\pm 0.31\pm 0.16\pm 0.09)\times {10}^{-4},$ consistent with what is expected from the $\overrightarrow{B}\pi \mathcal{l}\nu$ mode and quark model symmetries. We extract $|V_{\mathrm{ub}}|$ using light-cone sum rules for $0<~q^2<16\mathrm{}{\mathrm{GeV}}^2$ and lattice QCD for $16{\mathrm{GeV}}^2<~q^2<q_{\max }^2.$ Combining both intervals yields $|V_{\mathrm{ub}}|=(3.24\mathrm{}\pm 0.22\pm {0.13}_{-0.39}^{+0.55\mathrm{}}\pm 0.09)\times {10}^{-3}$ for $\pi \mathcal{l}\nu ,$ and $|V_{\mathrm{ub}}|=(3.00\mathrm{}\pm {0.21}_{-0.35-0.38}^{+0.29+0.49\mathrm{}}\pm 0.28)\times {10}^{-3}$ for $\rho \mathcal{l}\nu ,$ where the errors are statistical, experimental systematic, theoretical, and ρlν form-factor shape, respectively. Our combined value from both decay modes is $|V_{\mathrm{ub}}|=(3.17\mathrm{}\pm {0.17}_{-0.17-0.39}^{+0.16+0.53\mathrm{}}\pm 0.03)\times {10}^{-3}.$