The light meson decays of $D$ wave charmonia

Motivated by the large non-$D\bar{D}$ branching fraction of $\psi (3770)$, we investigate the light meson decays of the $D$-wave charmonia in the present work with the meson loop mechanism. With the parameter range determined by $\psi (3770)\to \phi \eta$, our estimations of the branching fractions of the light meson decays of $\psi (3770)$ are consistent with the estimations in the literature. As for $\psi (3823)$, the partial widths of $K^{\ast }{\bar{K}}^{\ast }$ channel is estimated to be around 200 keV, which is the the predominant light meson decay channel of $\psi (3823)$. Our estimations also indicate that $K^{(\ast )}{\bar{K}}^{(\ast )}$ and $\rho \pi$ are the dominant light meson decay modes of $\psi (3842)$, while ${\eta }_{c2}$ dominantly decays into $\rho \rho$, $K^{\ast }{\bar{K}}^{\ast }$, $\omega \omega$ and $\phi \phi$.