Measurement of the decay $B^0\to {\pi }^{-}{\ell }^{+}\nu$ and determination of $|V_{ub}|$

We present a measurement of the charmless semileptonic decay $B^0\to {\pi }^{-}{\ell }^{+}\nu$ using a data sample containing $657\times {10}^6$ $B\overline{B}$ events collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider operating near the ${\rm Y}(4S)$ resonance. We determine the total branching fraction of the decay, $\mathcal{B}(B^0\to {\pi }^{-}{\ell }^{+}\nu )=(1.49\pm 0.04(\mathrm{stat})\pm 0.07(\mathrm{syst}))\times {10}^{-4}$. We also report a new precise measurement of the differential decay rate and extract the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ using model-independent and model-dependent approaches. From a simultaneous fit to the measured differential decay rate and lattice QCD results, we obtain $|V_{ub}|=(3.43\pm 0.33)\times {10}^{-3}$, where the error includes both experimental and theoretical uncertainties.

Figure 1

Fit projections (a, b) in $\Delta E$ with $M_{\mathrm{bc}}>5.27\mathrm{GeV}/c^2$, and (c, d) in $M_{\mathrm{bc}}$ with $|\Delta E|<0.125\mathrm{GeV}$. The projections (a, c) and (b, d) show the regions $q^2<16{\mathrm{GeV}}^2/c^2$ and $q^2>16{\mathrm{GeV}}^2/c^2$, respectively. The points with error bars are ${\rm Y}(4S)$ data, the histograms are (from top to bottom) $B^0\to {\pi }^{-}{\ell }^{+}\nu$ signal (open), $B\to X_u\ell \nu$ (cross-hatched), $B\to X_c\ell \nu$ (hatched), and continuum background (black-filled). The smaller error bars are statistical only while the larger ones include systematic uncertainties.

Figure 2

Distribution of the partial branching fraction as a function of $q^2$ after unfolding (closed circles). The error bars show the statistical and the total uncertainty on the data. The curve is the result of a fit of the BK form factor parameterization [36] to our data. The four histograms (dashed:ISGW2; plain:HPQCD; dotted:FNAL; dot-dashed:LCSR) show various form factor predictions.

Figure 3

$|V_{ub}|$ extraction from a simultaneous fit of experimental (closed circles) and FNAL/MILC lattice QCD results (open circles) [9]. The error for each experimental data point is the total experimental uncertainty. The smaller error bars of the lattice QCD results are statistical only while the larger ones also include systematic uncertainties.