Measurement of the inclusive charmless semileptonic branching fraction of B meson using the full reconstruction tag

We present a preliminary measurement of the inclusive charmless semileptonic branching fraction of the B meson, based on $140 fb^{-1}$ of data collected by the Belle detector at the KEKB $e^+e^-$ asymmetric collider. Events are tagged by fully reconstructing one of the B mesons, produced in pairs from $\Upsilon(4S)$. The signal for $b \to u$ semileptonic decay is distinguished from the $b \to c$ semileptonic background using the hadronic and leptonic invariant mass distributions $M_X$ and $q^2$. We find the partial branching fraction for the kinematical region given by $M_X < 1.7 GeV/c^2$ and $q^2>8 {GeV}^2/c^2$, $\Delta{\cal{B}}(B \to X_u \ell \nu) = [0.99 \pm 0.15 (stat) \pm 0.18 (syst) \pm 0.04 (b\to u) \pm 0.07 (b\to c)]\times 10^{-3}$. Using a theoretical prediction for the extrapolation to the full range of $M_X$ and $q^2$ variables, we obtain ${\cal{B}}(B \to X_u \ell \nu) = [3.37 \pm 0.50 (stat)\pm 0.60 (syst) \pm 0.14 (b\to u) \pm 0.24 (b\to c) \pm 0.50 (f_u error)] \times 10^{-3}$. From this measurement, the magnitude of the the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ is $|V_{ub}|= [5.54 \pm 0.42 (stat) \pm 0.50 (syst) \pm 0.12 (b\to u) \pm 0.19 (b\to c) \pm 0.42 (f_u error) \pm 0.27 ({\cal{B}} \to |V_{ub}| error)] \times 10^{-3}$.