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$V_{ub}$ from the Hadron Energy Spectrum in Inclusive Semileptonic B Decays

A measurement of the hadron energy spectrum in inclusive semileptonic $B$ decays is proposed as a viable method for extracting $|V_{ub}|$. Compared to the traditional energy spectrum of the charged lepton, the hadron energy spectrum exhibits kinematical advantages such as a wider energy window and a larger signal branching fraction. It is emphasized that the hadron energy spectrum method is most suited for symmetric $B$ factories, such as CLEO. The hadron energy distribution is calculated in the approach of the Altarelli et al. model and of the heavy-quark effective field theory. In both methods, perturbative QCD corrections, the Fermi motion of the $b$-quark in the $B$-meson, and the recoil momentum of the $B$-meson (stemming from the $Υ(4S)$ resonance) are taken into account. We have found excellent agreement between the spectra calculated in both methods, especially in the relevant kinematical region below the charmed meson threshold. The theoretical error to $|V_{ub}|$, which is dominated by the uncertainty of the $b$-quark mass, is estimated to be at the $\pm 12 \%$ level.