Measurement of the Inclusive Charmless Semileptonic Branching Ratio ofBMesons and Determination of|Vub|

We report a measurement of the inclusive charmless semileptonic branching fraction of $B$ mesons in a sample of $89\times {10}^6$ $B\overline{B}$ events recorded with the BABAR detector at the ${\rm Y}(4S)$ resonance. Events are selected by fully reconstructing the decay of one $B$ meson and identifying a charged lepton from the decay of the other $B$ meson. The number of signal events is extracted from the mass distribution of the hadronic system accompanying the lepton and is used to determine the ratio of branching fractions $\mathcal{B}(\overline{B}\to X_u\ell \overline{\nu })/\mathcal{B}(\overline{B}\to X\ell \overline{\nu })=[2.06\pm 0.25(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.23(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\pm 0.36(\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o})]\times {10}^{-2}$. Using the measured branching fraction for inclusive semileptonic $B$ decays, we find $\mathcal{B}(\overline{B}\to X_u\ell \overline{\nu })=[2.24\pm 0.27(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.26(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\pm 0.39(\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o})]\times {10}^{-3}$ and derive the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|=[4.62\pm 0.28(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.27(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\pm 0.48(\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o})]\times {10}^{-3}$.