Semileptonic decays on the D meson

The electron energy spectrum in the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\psi}}^{\ensuremath{'}\ensuremath{'}}(3770)\ensuremath{\rightarrow}{e}^{\ifmmode\pm\else\textpm\fi{}}+(g2 \mathrm{charged}\mathrm{particles})$ has been used to determine the $D(56%{D}^{0}+44%{D}^{+})$ semileptonic branching ratio. Assuming the Glashow-Iliopoulos-Maiani model, it is found that the inclusive branching ratio is $b(D\ensuremath{\rightarrow}\mathrm{Xe}\ensuremath{\nu})=0.080\ifmmode\pm\else\textpm\fi{}0.015$ and the state $X$ is dominated by $K$ and $K\ensuremath{\pi}$. The fraction of $K\ensuremath{\pi}e\ensuremath{\nu}$ is (37 \ifmmode\pm\else\textpm\fi{} 16)% if the $K\ensuremath{\pi}$ system is entirely ${K}^{*}(890)$, or (55 \ifmmode\pm\else\textpm\fi{} 21)% if the $K\ensuremath{\pi}$ system is nonresonant. Within the assumptions of the analysis, the $D$ lifetime is calculated to be (2.5 \ifmmode\pm\else\textpm\fi{} 1.6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}13}$ sec.