We have measured the inclusive semileptonic branching fractions of $D^0$, $D^{+}$, and $D_s^{+}$ mesons. For these measurements, we have used the full CLEO-c open-charm data samples, $818{\mathrm{pb}}^{-1}$ at $E_{\mathrm{CM}}=3.774\mathrm{GeV}$, giving $D^0{\overline{D}}^0$ and $D^{+}{D}^{-}$ events, and $602{\mathrm{pb}}^{-1}$ at $E_{\mathrm{CM}}=4.170\mathrm{GeV}$, giving $D_s^{*\pm }{D}_s^{\mp }$ events. We obtain $\mathcal{B}(D^0\to X{e}^{+}{\nu }_e)=(6.46\pm 0.09\pm 0.11)\%$, $\mathcal{B}(D^{+}\to X{e}^{+}{\nu }_e)=(16.13\pm 0.10\pm 0.29)\%$, and $\mathcal{B}(D_s^{+}\to X{e}^{+}{\nu }_e)=(6.52\pm 0.39\pm 0.15)\%$, where the first uncertainties are statistical and the second are systematic. From these and lifetimes obtained elsewhere, we obtain the ratios of semileptonic decay widths $\Gamma (D^{+}\to X{e}^{+}{\nu }_e)/\Gamma (D^0\to X{e}^{+}{\nu }_e)=0.985\pm 0.015\pm 0.024$ and $\Gamma (D_s^{+}\to X{e}^{+}{\nu }_e)/\Gamma (D^0\to X{e}^{+}{\nu }_e)=0.828\pm 0.051\pm 0.025$. The ratio of $D^{+}$ and $D^0$ is consistent with the isospin symmetry prediction of unity, and the ratio of $D_s^{+}$ and $D^0$ differs from unity, as expected.

• Received 21 December 2009

DOI:https://doi.org/10.1103/PhysRevD.81.052007