Type: Article
Publication Date: 2006-12-21
Citations: 37
DOI: https://doi.org/10.1103/physrevlett.97.251801
We present measurements of the inclusive branching fractions for the decays ${D}^{+}\ensuremath{\rightarrow}X{e}^{+}{\ensuremath{\nu}}_{e}$ and ${D}^{0}\ensuremath{\rightarrow}X{e}^{+}{\ensuremath{\nu}}_{e}$, using $281\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of data collected on the $\ensuremath{\psi}(3770)$ resonance with the CLEO-c detector. We find $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}X{e}^{+}{\ensuremath{\nu}}_{e})=(6.46\ifmmode\pm\else\textpm\fi{}0.17\ifmmode\pm\else\textpm\fi{}0.13)%$ and $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}X{e}^{+}{\ensuremath{\nu}}_{e})=(16.13\ifmmode\pm\else\textpm\fi{}0.20\ifmmode\pm\else\textpm\fi{}0.33)%$. Using the known $D$ meson lifetimes, we obtain the ratio ${\ensuremath{\Gamma}}_{{D}^{+}}^{\mathrm{sl}}/{\ensuremath{\Gamma}}_{{D}^{0}}^{\mathrm{sl}}=0.985\ifmmode\pm\else\textpm\fi{}0.028\ifmmode\pm\else\textpm\fi{}0.015$, confirming isospin invariance at the level of 3%. The positron momentum spectra from ${D}^{+}$ and ${D}^{0}$ have consistent shapes.