V_{ub} from the Hadronic Invariant Mass Spectrum in Semileptonic B Decay

The hadronic invariant mass spectrum for the inclusive charmless semileptonic decay $B\to X_{u}e{\bar{\nu }}_e$ is studied. Particular attention is paid to the region $s_H<m_D^2$, which may be useful for extracting the value of $\mathrm{\mid }{V}_{ub}\mathrm{\mid }$. The sensitivity of the spectrum to the parameter $\bar{\mathrm{\Lambda }}\equiv m_B-m_b$ is explored. Perturbative QCD corrections to $d\mathrm{\Gamma }\mathrm{/}d{s}_H$ of order ${\alpha }_s^2{\beta }_0$ are calculated. For $s_H\sim \bar{\mathrm{\Lambda }}{m}_b$ nonperturbative QCD effects are important and the shape of the invariant mass spectrum is controlled by the B meson matrix element of an infinite sum of local operators. The utility of the hadronic mass spectrum for extracting $\mathrm{\mid }{V}_{ub}\mathrm{\mid }$ is explored.