Determinations of $|V_{ub}|$ from Inclusive Semileptonic $B$ Decays with Reduced Model Dependence

We report two novel determinations of $|V_{ub}|$ with reduced model dependence, based on measurements of the mass distribution of the hadronic system in semileptonic $B$ decays. Events are selected by fully reconstructing the decay of one $B$ meson and identifying a charged lepton from the decay of the other $B$ meson from ${\rm Y}(4S)\to B\overline{B}$ events. In one approach, we combine the inclusive $\overline{B}\to X_u\ell \overline{\nu }$ rate, integrated up to a maximum hadronic mass $m_X<1.67\mathrm{GeV}/c^2$, with a measurement of the inclusive $B\to X_s\gamma$ photon energy spectrum. We obtain $|V_{ub}|=(4.43\pm {0.38}_{\mathrm{stat}}\pm {0.25}_{\mathrm{syst}}\pm {0.29}_{\mathrm{theo}})\times {10}^{-3}$. In another approach we measure the total $\overline{B}\to X_u\ell \overline{\nu }$ rate over the full phase space and find $|V_{ub}|=(3.84\pm {0.70}_{\mathrm{stat}}\pm {0.30}_{\mathrm{syst}}\pm {0.10}_{\mathrm{theo}})\times {10}^{-3}$.

Figure 1

The $m_X$ distributions (without combinatorial backgrounds) for $\overline{B}\to X\ell \overline{\nu }$ candidates: (a) data (points) and fit components after the minimum-${\chi }^2$ fit, and (b) data and signal MC simulations after subtraction of the $\overline{B}\to X_c\ell \overline{\nu }$ and other backgrounds. The upper edge of the eighth bin is chosen to be at $m_X=2.5\mathrm{GeV}/c^2$. This fit result, with ${\chi }^2=10.2$ for 11 degrees of freedom, is used to extract the number of signal events below $2.5\mathrm{GeV}/c^2$.

Figure 2

$|V_{ub}|$ as a function of $\zeta$ with the LLR method (left) and for the determination with the full rate measurement (right). The error bars indicate the statistical uncertainty. They are correlated between the points and get larger for larger $\zeta$ due to larger background from $\overline{B}\to X_c\ell \overline{\nu }$. The total shaded area illustrates the theoretical uncertainty; the inner light shaded (yellow online) area indicates the perturbative share of the uncertainty. The arrow indicates $\zeta =1.67\mathrm{GeV}/c^2$.