Abstract
A measurement of the hadron energy spectrum in inclusive semileptonic $B$ decays is proposed as a viable method for extracting ${|V}_{\mathrm{ub}}|$. 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. The hadron energy distribution is calculated in the approach of the model of Altarelli et al. 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 $\ensuremath{\Upsilon}(4S)$ resonance] are taken into account. We find excellent agreement between the spectra calculated in both methods, especially in the relevant kinematical region below the charmed meson threshold. The theoretical error to ${|V}_{\mathrm{ub}}|$, which is dominated by the uncertainty of the $b$-quark mass, is estimated to be at the $\ifmmode\pm\else\textpm\fi{}12%$ level. Experimental techniques utilized in the recent measurement of exclusive semileptonic $b\ensuremath{\rightarrow}u$ decays point to the feasibility of the present proposal both at CLEO and at future $B$ factories.
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