Measurement of the inclusive semielectronic $D^0$ branching fraction

Using the angular correlation between the ${\pi }^{+}$ emitted in a $D^{*+}\to D^0{\pi }^{+}$ decay and the $e^{+}$ emitted in the subsequent $D^0\to X{e}^{+}\nu$ decay, we have measured the branching fraction for the inclusive semielectronic decay of the $D^0$ meson to be $\mathcal{B}(D^0\to X{e}^{+}\nu )=[6.64\mathrm{}\pm 0.18(\mathrm{stat})\pm 0.29(\mathrm{syst}\left)\right]\%$. The measurement uses 1.7 ${\mathrm{fb}}^{-1\mathrm{}}$ of $e^{+}{e}^{-}$ collisions recorded by the CLEO II detector located at the Cornell Electron Storage Ring (CESR). Combining this result with previous CLEO results we find $\frac{\mathcal{B}(D^0\to X{e}^{+}\nu )}{\mathcal{B}(D^0\to K^{-}{\pi }^{+})}=1.684\mathrm{}\pm 0.056\left(\mathrm{stat}\right)\pm 0.093\left(\mathrm{syst}\right)$ and $\frac{\mathcal{B}(D^0\to K^{-}{e}^{+}\nu )}{\mathcal{B}(D^0\to X{e}^{+}\nu )}=0.581\mathrm{}\pm 0.023\left(\mathrm{stat}\right)\pm 0.028\left(\mathrm{syst}\right)$. The difference between this inclusive rate and the sum of the measured exclusive branching fractions (measured at CLEO and other experiments) is also presented.