Measurements of Partial Branching Fractions for $\bar B \to X_u \ell \bar \nu$ and Determination of $|V_{ub}|$ at BaBar

We present partial branching fractions for inclusive charmless semileptonic $B$ decays $\bar B \to X_u \ell \bar \nu$, and the determination of the CKM matrix element $|V_{ub}|$. The analysis is based on a sample of 383 million Y(4S) decays into $B \bar B$ pairs collected with the BaBar detector at the PEP-II $e^+ e^-$ storage rings. $\Upsilon(4S) \to B\bar B$ events are tagged by the full reconstruction of a hadronic decay of one of the $B$ mesons. Signal $\bar B \to X_u \ell \bar \nu$ is then identified looking at several kinematic variables. The corresponding value of $|V_{ub}|$ is extracted.