Measurement of the Cabibbo-Kobayashi-Maskawa Matrix Element $|V_{ub}|$ with $B\to \rho e\nu$ Decays

We present a measurement of the branching fraction for the rare decays $B\to \rho e\nu$ and extract a value for the magnitude of $V_{ub}$, one of the smallest elements of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix. The results are given for five different calculations of form factors used to parametrize the hadronic current in semileptonic decays. Using a sample of $55\times {10}^6$ $B\overline{B}$ meson pairs recorded with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring, we obtain $\mathcal{B}(B^0\to {\rho }^{-}{e}^{+}\nu )=(3.29\pm 0.42\pm 0.47\pm 0.55)\times {10}^{-4}$ and $|V_{ub}|=(3.64\pm 0.22\pm {0.25}_{-0.56}^{+0.39})\times {10}^{-3}$, where the uncertainties are statistical, systematic, and theoretical, respectively.

Figure 1

Continuum-subtracted data distributions (points with error bars) and fit projections (histograms) for $M_{\pi \pi }$ (top plots) and $\Delta E$ (bottom plots) for the $B^0\to {\rho }^{-}{e}^{+}\nu$ channel in the low-$E_e$ (left plots) and high-$E_e$ regions (right plots). The fit results are shown for the ISGW2 model. The histograms correspond to the true and cross feed components of the signal (open histogram, above and below the dashed line, respectively), the background from other $b\to ue\nu$ decays (dark shaded region), and $b\to ce\nu$ and other backgrounds (light shaded region).

Figure 2

The branching fraction $\mathcal{B}(B^0\to {\rho }^{-}{e}^{+}\nu )/{10}^{-4}$ results using five different form-factors calculations. The uncertainties shown are statistical, systematic, and (for the combined result) theoretical, successively added in quadrature. The combined result is the unweighted mean of the five form-factor results.

Figure 3

$|V_{ub}|/{10}^{-3}$ determined using five different form-factor calculations. Only theoretical error bars are shown. The combined result is also shown at the bottom with statistical, systematic, and theoretical uncertainties successively added in quadrature.