ExtractingVbuVbcfrom semileptonicBdecays

Recent CLEO and ARGUS results for charmless semileptonic decays of $B$ mesons are compared to several models for exclusive channels under the assumption that the $\pi$, $\rho$, $D$, and $D^{*}$ saturate the region of high electron momentum of interest in determining $\frac{V_{\mathrm{bu}}}{V_{\mathrm{bc}}}$. The effect of current-algebra-inspired $\pi \pi$ backgrounds and threshold constraints in the $\rho$ channel, as well as the error made by the narrow-width approximation, are examined with a view to estimating the model dependence inherent in extracting $\frac{V_{\mathrm{bu}}}{V_{\mathrm{bc}}}$ from the data. Total semileptonic rates to $\pi$ and $\rho$ differ widely, model to model, while rates to $D$ and $D^{*}$ final states have much less model dependence. Model dependence is somewhat smaller when only high lepton energies are concerned. $V_{\mathrm{bc}}$ calculated from exclusive semileptonic decay to $D$ and $D^{*}$ final states vary about 25% and 10%, respectively, model to model. The model dependence of $\frac{V_{\mathrm{bu}}}{V_{\mathrm{bc}}}$ is also considerable. The narrow-width approximation in the $\rho$ channel can be a 20% effect in the determination of this ratio because of the sensitivity of the high-energy region to the lowest mass of the final hadronic system. If current-algebra-inspired backgrounds are present, $\frac{V_{\mathrm{bu}}}{V_{\mathrm{bc}}}$ may be considerably smaller than suggested by many models. If the $D^{**}$ component of $b$ to $c$ is as large as recent CLEO data suggest, $\frac{V_{\mathrm{bu}}}{V_{\mathrm{bc}}}$ may be 16% larger than expected by models that ignore this contribution. Electron spectra for various models are presented, illustrating the high variation of shape features in the end-point region.