Study of B¯→Xuℓν¯ decays in BB¯ events tagged by a fully reconstructed B -meson decay and determination of |Vub|

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We report measurements of partial branching fractions for inclusive charmless semileptonic $B$ decays $\overline{B}\ensuremath{\rightarrow}{X}_{u}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ and the determination of the Cabibbo--Kobayashi--Maskawa (CKM) matrix element $|{V}_{ub}|$. The analysis is based on a sample of $467\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays recorded with the BABAR detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ storage rings. We select events in which the decay of one of the $B$ mesons is fully reconstructed and an electron or a muon signals the semileptonic decay of the other $B$ meson. We measure partial branching fractions $\ensuremath{\Delta}\mathcal{B}$ in several restricted regions of phase space and determine the CKM element $|{V}_{ub}|$ based on different QCD predictions. For decays with a charged lepton momentum ${p}_{\ensuremath{\ell}}^{*}>1.0\text{ }\text{ }\mathrm{GeV}$ in the $B$ meson rest frame, we obtain $\ensuremath{\Delta}\mathcal{B}=(1.80\ifmmode\pm\else\textpm\fi{}{0.13}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.15}_{\mathrm{sys}}\ifmmode\pm\else\textpm\fi{}{0.02}_{\mathrm{theo}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ from a fit to the two-dimensional ${M}_{X}\ensuremath{-}{q}^{2}$ distribution. Here, ${M}_{X}$ refers to the invariant mass of the final state hadron $X$ and ${q}^{2}$ is the invariant mass squared of the charged lepton and neutrino. From this measurement we extract $|{V}_{ub}|=(4.33\ifmmode\pm\else\textpm\fi{}{0.24}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.15}_{\mathrm{theo}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ as the arithmetic average of four results obtained from four different QCD predictions of the partial rate. We separately determine partial branching fractions for ${\overline{B}}^{0}$ and ${B}^{\ensuremath{-}}$ decays and derive a limit on the isospin breaking in $\overline{B}\ensuremath{\rightarrow}{X}_{u}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays.

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