Measurements of the Partial Branching Fraction for B->Xulnu and the Determination of Vub

Abstract

We measure partial branching fractions for the inclusive charmless semileptonic decay of $\Bxulnu$, and present determinations of the CKM matrix element $\Vub$. This analysis is based on a sample of 467 million $\FourS$ decays into $\BB$ pairs, collected with the \babar\ detector at the PEP-II $e^{+} e^{-}$ storage rings. We select events where one of the B mesons is fully reconstructed in a hadronic decay mode and the other B decays semileptonically into an electron or a muon. We then use the invariant mass, $\mx$, of the hadronic system, the invariant mass squared, $q^{2}$, of the lepton and neutrino pair, the lepton momentum in the in the $B$ meson rest frame $\Pl$, the kinematic variable $P_{+}$ or one of their combinations as discriminating variables to isolate $\Bxulnu$ decays from the background. We then measure the partial branching fractions in various regions of phase space These partial branching fractions are translated into values of $\Vub$ using several theoretical calculations. An estimate based on the most inclusive analysis gives $\Vub = (4.31\pm 0.35) \times 10^{-3}$. Furthermore, we place a limit on isospin breaking in $B\to X_u\ell\nu$ decays of 9% at 90% C.L. using separate measurements of partial branching ratios for $B^0$ and $B^+$.