Measurement of the $B^0\to {\pi }^{-}{l}^{+}\nu$ Form-Factor Shape and Branching Fraction, and Determination of $|V_{ub}|$ with a Loose Neutrino Reconstruction Technique

We report the results of a study of the exclusive charmless semileptonic decay, $B^0\to {\pi }^{-}{\ell }^{+}\nu$, undertaken with approximately $227\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ 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 $\mathcal{B}(B^0\to {\pi }^{-}{\ell }^{+}\nu )=(1.46\pm {0.07}_{\mathrm{stat}}\pm {0.08}_{\mathrm{syst}})\times {10}^{-4}$. Based on a recent unquenched lattice QCD calculation of the form factor in the range $q^2>16{\mathrm{GeV}}^2$, we find the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ to be $(4.1\pm {0.2}_{\mathrm{stat}}\pm {0.2}_{\mathrm{syst}}{\genfrac{}{}{0ex}{}{+0.6}{-0.4}}_{\mathrm{FF}})\times {10}^{-3}$, where the last uncertainty is due to the normalization of the form factor.