Measurement of BF($B^0\to\pi^-\ell^+\nu$) and BF($B^0\to\rho^-\ell^+\nu$) using neutrino reconstruction

We present an analysis of exclusively reconstructed charmless semileptonic $B$-meson decays based on 88 million $B \overline{B}$ pairs recorded with the BaBar detector at the PEP-II $e^+e^-$ storage rings. We study the four decay modes $B \rightarrow H_u \ell \nu$, where $H_u$ represents a $\pi^\pm, \pi^0, \rho^\pm$, or $\rho^0$, and $\ell$ is an electron or muon. The neutrino kinematics are inferred from the missing momentum and energy in the $B \overline{B}$ event. An extended maximum-likelihood fit is perfomed in bins of the three variables $\Delta E$, the reconstructed minus the expected $B$-meson energy; $m_{ES}$, the beam-energy substituted $B$~mass; and $q^2$, the squared four-momentum transfer, to determine the branching fractions $\mathcal{B} (B^0 \rightarrow \pi^- \ell^+ \nu)$ and $\mathcal{B} (B^0 \rightarrow \rho^- \ell^+ \nu)$ using isospin symmetry. The measured $q^2$ spectra are used to fit the $q^2$ dependence of the $B \rightarrow \pi (\rho) \ell \nu$ decay form factors and compare with theoretical predictions from light-cone sum rules, quark models and recent lattice QCD calculations. We extract the CKM matrix element $|V_{ub}|$ using the various theoretical calculations.