Semileptonic inclusive $B$ decays and the determination of $\left|V_{\mathrm{ub}}\right|$ from QCD sum rules

We calculate the electron spectrum of semileptonic decays of $B$ mesons into noncharmed hadrons. The shape of the spectrum obtained from QCD sum rules is in general agreement with quark model calculations. At high electron energies the decrease of the spectrum is less steep than predicted by Altarelli et al. Our analysis yields a total decay rate $\Gamma (B\to X_{u}e\overline{\nu })=(6.8\mathrm{}\pm 2.0)\times {10}^{13}{\left|V_{\mathrm{ub}}\right|}^2$ ${\mathrm{s}}^{-1\mathrm{}}$. For the spectrum integrated over electron energies in the interval $2.4 \mathrm{GeV}\le E_e\le 2.6 \mathrm{GeV}$ in the laboratory frame we obtain $\Gamma (B\to X_{u}e\overline{\nu })=(5.0\mathrm{}\pm 1.6)\times {10}^{12}{\left|V_{\mathrm{ub}}\right|}^2$ ${\mathrm{s}}^{-1\mathrm{}}$. Estimating all sorts of theoretical uncertainties, we obtain $\left|V_{\mathrm{ub}}\right|=0.003\mathrm{}\pm 0.001$ for the $b\to u$ weak transition matrix element from the new CLEO data.