We present partial branching fractions for inclusive charmless semileptonic $B$ decays $\overline{B}\to X_u\ell \overline{\nu }$, and the determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$. The analysis is based on a sample of $383\times {10}^6$ ${\rm Y}(4S)$ decays into $B\overline{B}$ pairs collected with the BABAR detector at the SLAC PEP-II $e^{+}{e}^{-}$ storage rings. We select events using the invariant mass $M_X$ of the hadronic system, the invariant mass squared, $q^2$, of the lepton and neutrino pair, the kinematic variable $P_{+}$, or one of their combinations. We then determine partial branching fractions in limited regions of phase space: $\Delta \mathcal{B}=(1.18\pm {0.09}_{\mathrm{stat}}\pm {0.07}_{\mathrm{syst}}\pm {0.01}_{\mathrm{theor}})\times {10}^{-3}$ ($M_X<1.55\mathrm{GeV}/c^2$), $\Delta \mathcal{B}=(0.95\pm {0.10}_{\mathrm{stat}}\pm {0.08}_{\mathrm{syst}}\pm {0.01}_{\mathrm{theor}})\times {10}^{-3}$ ($P_{+}<0.66\mathrm{GeV}/c$), and $\Delta \mathcal{B}=(0.81\pm {0.08}_{\mathrm{stat}}\pm {0.07}_{\mathrm{syst}}\pm {0.02}_{\mathrm{theor}})\times {10}^{-3}$ ($M_X<1.7\mathrm{GeV}/c^2$, $q^2>8{\mathrm{GeV}}^2/c^4$). Corresponding values of $|V_{ub}|$ are extracted using several theoretical calculations.

• Received 28 August 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.171802