We present measurements of the inclusive branching fractions for the decays $D^{+}\to X{e}^{+}{\nu }_e$ and $D^0\to X{e}^{+}{\nu }_e$, using $281{\mathrm{pb}}^{-1}$ of data collected on the $\psi (3770)$ resonance with the CLEO-c detector. We find $\mathcal{B}(D^0\to X{e}^{+}{\nu }_e)=(6.46\pm 0.17\pm 0.13)\%$ and $\mathcal{B}(D^{+}\to X{e}^{+}{\nu }_e)=(16.13\pm 0.20\pm 0.33)\%$. Using the known $D$ meson lifetimes, we obtain the ratio ${\Gamma }_{D^{+}}^{\mathrm{sl}}/{\Gamma }_{D^0}^{\mathrm{sl}}=0.985\pm 0.028\pm 0.015$, confirming isospin invariance at the level of 3%. The positron momentum spectra from $D^{+}$ and $D^0$ have consistent shapes.

• Received 21 April 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.251801