Study of exclusive $B\to X_u\ell \nu$ decays and extraction of $|V_{ub}|$ using full reconstruction tagging at the Belle experiment

We report the results of a study of the exclusive semileptonic decays $B^{-}\to {\pi }^0{\ell }^{-}{\overline{\nu }}_{\ell }$, ${\overline{B}}^0\to {\pi }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$, $B^{-}\to {\rho }^0{\ell }^{-}{\overline{\nu }}_{\ell }$, ${\overline{B}}^0\to {\rho }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$ and $B^{-}\to \omega {\ell }^{-}{\overline{\nu }}_{\ell }$, where $\ell$ represents an electron or a muon. The events are tagged by fully reconstructing a second $B$ meson in the event in a hadronic decay mode. The measured branching fractions are $\mathcal{B}(B^{-}\to {\pi }^0{\ell }^{-}{\overline{\nu }}_{\ell })=(0.80\pm 0.08\pm 0.04)\times {10}^{-4}$, $\mathcal{B}({\overline{B}}^0\to {\pi }^{+}{\ell }^{-}{\overline{\nu }}_{\ell })=(1.49\pm 0.09\pm 0.07)\times {10}^{-4}$, $\mathcal{B}(B^{-}\to {\rho }^0{\ell }^{-}{\overline{\nu }}_{\ell })=(1.83\pm 0.10\pm 0.10)\times {10}^{-4}$, $\mathcal{B}({\overline{B}}^0\to {\rho }^{+}{\ell }^{-}{\overline{\nu }}_{\ell })=(3.22\pm 0.27\pm 0.24)\times {10}^{-4}$, and $\mathcal{B}(B^{-}\to \omega {\ell }^{-}{\overline{\nu }}_{\ell })=(1.07\pm 0.16\pm 0.07)\times {10}^{-4}$, where the first error is statistical and the second one is systematic. The obtained branching fractions are inclusive of soft photon emission. We also determine the branching fractions as a function of the 4-momentum transfer squared to the leptonic system $q^2=(p_{\ell }+p_{\nu }{)}^2$, where $p_{\ell }$ and $p_{\nu }$ are the lepton and neutrino 4-momenta, respectively. Using the pion modes, a recent light cone sum rule calculation, lattice QCD results and a model-independent description of the hadronic form factor, a value of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|=(3.52\pm 0.29)\times {10}^{-3}$ is extracted. A structure in the two-pion invariant mass distribution near $1.3\mathrm{GeV}/c^2$, which might be dominated by the decay $B^{-}\to f_2(1270){\ell }^{-}{\overline{\nu }}_{\ell }$, $f_2\to {\pi }^{+}{\pi }^{-}$, is seen. These results are obtained from a $711{\mathrm{fb}}^{-1}$ data sample that contains $772\times {10}^6$ $B\overline{B}$ pairs, collected near the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Figure 1

Fit to the $M_{\mathrm{miss}}^2$ distributions in data for $B^{-}\to {\pi }^0{\ell }^{-}{\overline{\nu }}_{\ell }$ decays (top) and ${\overline{B}}^0\to {\pi }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays (bottom). The fit components are described in the text.

Figure 2

Fit to the $M_{\mathrm{miss}}^2$ distribution in data for $B^{-}\to {\rho }^0{\ell }^{-}{\overline{\nu }}_{\ell }$ decays (top) and ${\overline{B}}^0\to {\rho }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$ (bottom). The fit components are described in the text.

Figure 3

Fit to the $M_{\mathrm{miss}}^2$ distribution in data for $B^{-}\to \omega {\ell }^{-}{\overline{\nu }}_{\ell }$ decays where $\omega \to {\pi }^{+}{\pi }^{-}{\pi }^0$ (top) and $\omega \to {\pi }^0\gamma$ (bottom). The fit components are described in the text.

Figure 4

Data/MC comparison for (a) $B^{-}\to {\rho }^0{\ell }^{-}{\overline{\nu }}_{\ell }$, (b) $B^{-}\to {\pi }^0{\ell }^{-}{\overline{\nu }}_{\ell }$ and (c) $B^{-}\to \omega {\ell }^{-}{\overline{\nu }}_{\ell }$ decays, where corresponding components are scaled according to the result of the fit to the $M_{\mathrm{miss}}^2$ distribution. Where present, the hatched region shows the selection criterion on the corresponding variable. In each case $M_{\mathrm{miss}}^2$ is required to be close to zero, and all other selection criteria are applied except the one on the variable plotted.

Figure 5

Projection onto the $M_{\mathrm{miss}}^2$ axis of the fitted distribution to data for $B^{-}\to {\pi }^0{\ell }^{-}{\overline{\nu }}_{\ell }$ decay, for 7 bins in $q^2$.

Figure 6

Projection onto the $M_{\mathrm{miss}}^2$ axis of the fitted distribution to data for ${\overline{B}}^0\to {\pi }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$ decay, for 13 bins in $q^2$.

Figure 7

Projection onto the $M_{\mathrm{miss}}^2$ axis of the fitted distribution to data for $B^{-}\to {\rho }^0{\ell }^{-}{\overline{\nu }}_{\ell }$ decay, for 11 bins in $q^2$.

Figure 8

Projection onto the $M_{\mathrm{miss}}^2$ axis of the fitted distribution to data for ${\overline{B}}^0\to {\rho }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$ decay, for 6 bins in $q^2$.

Figure 9

Projection onto the $M_{\mathrm{miss}}^2$ axis of the fitted distribution to data for $B^{-}\to \omega {\ell }^{-}{\overline{\nu }}_{\ell }$ decay, for 3 bins in $q^2$.

Figure 10

Detection efficiency for ${\overline{B}}^0\to {\pi }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$ decay as a function of the total emitted energy carried by photons.

Figure 11

Projection of the fitted distribution to data for the $\overline{B}\to \rho {\ell }^{-}{\overline{\nu }}_{\ell }$ decay onto the $M_{\pi \pi }$ axis. The top plot shows $B^{-}\to {\rho }^0{\ell }^{-}{\overline{\nu }}_{\ell }$; the bottom plot shows ${\overline{B}}^0\to {\rho }^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$. The inclusive component $\overline{B}\to X_u(\pi \pi ){\ell }^{-}{\overline{\nu }}_{\ell }$ predicted by MC is shown on the top of the stack. Vertical lines show the bins in invariant mass used during the fit procedure. The hatched region shows the actual selection criterion on the invariant mass.

Figure 12

Comparison of $q\overline{q}$ MC and off-peak data, using loose $B^{-}\to {\rho }^0{\ell }^{-}{\overline{\nu }}_{\ell }$ decay selection criteria.

Figure 13

Fit to data obtained in this analysis, LQCD points and the LCSR prediction at $q^2=0$ using the BCL parametrization, with the number of free parameters $N=4$. The shaded regions represent the uncertainties of the fit.

Figure 14

The combined fit to the most recent data and theory inputs using the BCL parametrization with the number of free parameters $N=6$ using untagged Belle [13] and BABAR [12] and tagged (this study) data. Shaded regions represent the uncertainties of the fit.

Figure 15

The comparison of $|V_{ub}|$ values obtained with the BCL form factor parametrization with the number of terms in expansion $K=3$, using LCSR and LQCD inputs for tagged (this analysis), untagged Belle [13] and BABAR [12] data as well as a combined fit with those three data sets. The value of $|V_{ub}|$ based on inclusive semileptonic decays of $B$ mesons is taken from the recent PDG [5] review. The CKMfitter [40] and UTfit [41] estimates of $|V_{ub}|$ are from global fits where $|V_{ub}|$ related inputs are excluded. The dashed lines represent $|V_{ub}|$ values quoted in the original papers.