Study of exclusive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>u</mml:mi></mml:msub><mml:mi>ℓ</mml:mi><mml:mi>ν</mml:mi></mml:math>decays and extraction of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:math>using full reconstruction tagging at the Belle experiment

We report the results of a study of the exclusive semileptonic decays ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$, ${\overline{B}}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$, ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$, ${\overline{B}}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$, where $\ensuremath{\ell}$ represents an electron or a muon. The events are tagged by fully reconstructing a second $B$ meson in the event in a hadronic decay mode. The measured branching fractions are $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})=(0.80\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})=(1.49\ifmmode\pm\else\textpm\fi{}0.09\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})=(1.83\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})=(3.22\ifmmode\pm\else\textpm\fi{}0.27\ifmmode\pm\else\textpm\fi{}0.24)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, and $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})=(1.07\ifmmode\pm\else\textpm\fi{}0.16\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, where the first error is statistical and the second one is systematic. The obtained branching fractions are inclusive of soft photon emission. We also determine the branching fractions as a function of the 4-momentum transfer squared to the leptonic system ${q}^{2}=({p}_{\ensuremath{\ell}}+{p}_{\ensuremath{\nu}}{)}^{2}$, where ${p}_{\ensuremath{\ell}}$ and ${p}_{\ensuremath{\nu}}$ are the lepton and neutrino 4-momenta, respectively. Using the pion modes, a recent light cone sum rule calculation, lattice QCD results and a model-independent description of the hadronic form factor, a value of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|=(3.52\ifmmode\pm\else\textpm\fi{}0.29)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ is extracted. A structure in the two-pion invariant mass distribution near $1.3\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, which might be dominated by the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{f}_{2}(1270){\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$, ${f}_{2}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, is seen. These results are obtained from a $711\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data sample that contains $772\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs, collected near the $\ensuremath{\Upsilon}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider.