Measurement of the $B\to \pi l\nu$ Branching Fraction and Determination of $|V_{ub}|$ with Tagged $B$ Mesons

We report a measurement of the $B\to \pi \ell \nu$ branching fraction based on $211{\mathrm{fb}}^{-1}$ of data collected with the BABAR detector. We use samples of $B^0$ and $B^{+}$ mesons tagged by a second $B$ meson reconstructed in a semileptonic or hadronic decay and combine the results assuming isospin symmetry to obtain $\mathcal{B}(B^0\to {\pi }^{-}{\ell }^{+}\nu )=(1.33\pm {0.17}_{\mathrm{stat}}\pm {0.11}_{\mathrm{syst}})\times {10}^{-4}$. We determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ by combining the partial branching fractions measured in ranges of the momentum transfer squared and theoretical calculations of the form factor. Using a recent lattice QCD calculation, we find $|V_{ub}|=(4.5\pm {0.5}_{\mathrm{stat}}\pm {0.3}_{\mathrm{syst}}{\genfrac{}{}{0ex}{}{+0.7}{-0.5}}_{\mathrm{FF}})\times {10}^{-3}$, where the last error is due to the normalization of the form factor.

Figure 1

Distributions of ${cos}^2{\varphi }_B$ of the (a) $B^0\to {\pi }^{-}{\ell }^{+}\nu$ and (b) $B^{+}\to {\pi }^0{\ell }^{+}\nu$ candidates. The points with error bars and the shaded histograms are the data in the $D$ mass peak and sideband, respectively. The curves are the fit results representing the total (solid), background (dashed), and “cmb” (dotted) components defined in the text. The fits were performed in bins of $q^2$, but the results shown are for the complete $q^2$ range.

Figure 2

Distributions of $m_{\mathrm{miss}}^2$ of the (a) $B^0\to {\pi }^{-}{\ell }^{+}\nu$ and (b) $B^{+}\to {\pi }^0{\ell }^{+}\nu$ candidates. The points with error bars are the data. The histograms represent, from the lightest to the darkest, the MC simulation of the $B\to \pi \ell \nu$ signal, $b\to u\ell \nu$, $b\to c\ell \nu$, and other backgrounds. The arrows indicate the regions in which the signals are extracted.