Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>l</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mi>ν</mml:mi></mml:math>Form-Factor Shape and Branching Fraction, and Determination 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>with a Loose Neutrino Reconstruction Technique

We report the results of a study of the exclusive charmless semileptonic decay, ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}\ensuremath{\nu}$, undertaken with approximately $227\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected at the $\ensuremath{\Upsilon}(4S)$ resonance with the BABAR detector. The analysis uses events in which the signal $B$ decays are reconstructed with an innovative loose neutrino reconstruction technique. We obtain partial branching fractions in 12 bins of ${q}^{2}$, the momentum transfer squared, from which we extract the ${f}_{+}({q}^{2})$ form-factor shape and the total branching fraction $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}\ensuremath{\nu})=(1.46\ifmmode\pm\else\textpm\fi{}{0.07}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.08}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Based on a recent unquenched lattice QCD calculation of the form factor in the range ${q}^{2}&gt;16\text{ }\text{ }{\mathrm{GeV}}^{2}$, we find the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|$ to be $(4.1\ifmmode\pm\else\textpm\fi{}{0.2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.2}_{\mathrm{syst}}{\genfrac{}{}{0}{}{+0.6}{\ensuremath{-}0.4}}_{\mathrm{FF}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, where the last uncertainty is due to the normalization of the form factor.

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