Measurement of the Partial Branching Fraction for Inclusive Charmless\n Semileptonic B Decays and Extraction of $|V_{ub}|$

Charmless semileptonic decays, ${\\bar{B}} \\to X_u \\ell \\bar{\\nu}$, are\nstudied in a sample of 232 million $B\\bar{B}$ decays recorded with the BaBar\ndetector, in events where the decay of the second $B$ meson is fully\nreconstructed. Inclusive charmless decays are selected in kinematic regions\nwhere the dominant background from semileptonic B decays to charm is reduced by\nrequirements on the hadronic mass $M_X$ and the momentum transfer $q^2$. The\npartial branching fraction for ${\\bar{B}} \\to X_u \\ell \\bar{\\nu}$ decays for\n$M_X<1.7$ GeV/c^2 and $q^2>8$ Gev^2/c^4 is measured to be\n$\\Delta{\\cal{B}}({\\bar{B}} \\to X_u \\ell \\bar{\\nu}) = (0.87 \\pm 0.09_{\\rm\nstat}\\pm 0.09_{\\rm sys}\\pm 0.01_{\\rm th})\\times 10^{-3}$. The CKM matrix\nelement $|V_{ub}|$ is determined by using theoretical calculations of phase\nspace acceptances. Theoretical uncertainties in this extrapolation are reduced\nby using the inclusive $b \\to s \\gamma$ photon spectrum and moments of the $b\n\\to c \\ell \\bar{\\nu}$ lepton energy and hadronic invariant mass.\n