Measurements of $B\to \{\pi ,\eta ,{\eta }^{\prime }\}l{\nu }_l$ Branching Fractions and Determination of $|V_{ub}|$ with Semileptonically Tagged $B$ Mesons

We report measurements of branching fractions for the decays $B\to P\ell {\nu }_{\ell }$, where $P$ are the pseudoscalar charmless mesons ${\pi }^{-}$, ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$, based on $348{\mathrm{fb}}^{-1}$ of data collected with the BABAR detector, using $B^0$ and $B^{+}$ mesons found in the recoil of a second $B$ meson decaying as $B\to D^{(*)}\ell {\nu }_{\ell }$. Assuming isospin symmetry, we combine pionic branching fractions to obtain $\mathcal{B}(B^0\to {\pi }^{-}{\ell }^{+}{\nu }_{\ell })=(1.54\pm {0.17}_{(\mathrm{stat})}\pm {0.09}_{(\mathrm{syst})})\times {10}^{-4}$; we find $3.2\sigma$ evidence of the decay $B^{+}\to \eta {\ell }^{+}{\nu }_{\ell }$ and measure its branching fraction to be $(0.64\pm {0.20}_{(\mathrm{stat})}\pm {0.03}_{(\mathrm{syst})})\times {10}^{-4}$, and determine $\mathcal{B}(B^{+}\to {\eta }^{\prime }{\ell }^{+}{\nu }_{\ell })<0.47\times {10}^{-4}$ to 90% confidence level. Using partial branching fractions for the pionic decays in ranges of the momentum transfer and a variety of form factor calculation, we obtain values of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ in ranging from $3.6\times {10}^{-3}$ to $4.1\times {10}^{-3}$.