Study of $B \to \pi \ell \nu$ and $B \to \rho \ell \nu$ Decays and Determination of $|V_{ub}|$

We present an analysis of exclusive charmless semileptonic B- meson decays based on 343 million $B\bar{B}$ pairs recorded with the {\it B{\footnotesize A}B{\footnotesize AR}} detector at the $\Upsilon(4S)$ resonance. We measure branching fractions ${\cal B}(B \to \pi \ell \nu)$ and ${\cal B}(B \to \rho \ell \nu)$. We compare the measured distribution in $q^2$, the momentum- transfer squared, with theoretical predictions for the form factors from lattice QCD, light-cone sum rules, and quark model calculations. We also extract the CKM matrix element $|V_{ub}|$ from the measurement of $B \to \pi \ell \nu$ decays.