Measurements of B→{π,η,η′}lνl Branching Fractions and Determination of |Vub| with Semileptonically Tagged B Mesons

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We report measurements of branching fractions for the decays $B\ensuremath{\rightarrow}P\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$, where $P$ are the pseudoscalar charmless mesons ${\ensuremath{\pi}}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$, based on $348\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected with the BABAR detector, using ${B}^{0}$ and ${B}^{+}$ mesons found in the recoil of a second $B$ meson decaying as $B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$. Assuming isospin symmetry, we combine pionic branching fractions to obtain $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})=(1.54\ifmmode\pm\else\textpm\fi{}{0.17}_{(\mathrm{stat})}\ifmmode\pm\else\textpm\fi{}{0.09}_{(\mathrm{syst})})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$; we find $3.2\ensuremath{\sigma}$ evidence of the decay ${B}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ and measure its branching fraction to be $(0.64\ifmmode\pm\else\textpm\fi{}{0.20}_{(\mathrm{stat})}\ifmmode\pm\else\textpm\fi{}{0.03}_{(\mathrm{syst})})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, and determine $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})<0.47\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ 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 $3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ to $4.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

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