Semileptonic Decays on theDMeson

Abstract

The electron energy spectrum in the process $e^{+}{e}^{-}\to {\psi }^{\prime \prime }\mathrm{}\left(3770\right)\mathrm{}\to e^{\pm }+(>\mathrm{}2\mathrm{} \mathrm{charged}\mathrm{particles})$ 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 $b(D\to \mathrm{Xe}\nu )=0.080\mathrm{}\pm 0.015$ and the state $X$ is dominated by $K$ and $K\pi$. The fraction of $K\pi e\nu$ is (37 ± 16)% if the $K\pi$ system is entirely $K^{*}\mathrm{}\left(890\right)\mathrm{}$, or (55 ± 21)% if the $K\pi$ system is nonresonant. Within the assumptions of the analysis, the $D$ lifetime is calculated to be (2.5 ± 1.6) × ${10}^{-13\mathrm{}}$ sec.