Study of $B\to X_{u}\ell\nu$ Decays on the Recoil of Fully Reconstructed $B$ Mesons with the BaBar Experiment

We present a study of charmless semileptonic $B$ decays performed on the recoil of $B$ candidates fully reconstructed in hadronic decay modes. The semileptonic decays of the second $B$ meson are identified by the presence of an electron or a muon. The hadronic invariant mass, $m_{X}$, and the mass of the lepton pair, $q^2$ are used to discriminate charmless $B$ decays from charmed background. From this event sample the inclusive semileptonic branching fraction for charged and neutral $B$ mesons for $B\to X_{u}\ell\nu$ is measured and the CKM matrix element $|V_{ub}|$ is extracted. In addition, the unfolding of the hadronic mass spectrum and the measurement of several exclusive charmless semileptonic decays is discussed.