The light meson decays of $D$ wave charmonia
Motivated by the large non-$D\bar{D}$ branching fraction of $ψ(3770)$, 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 $ψ(3770) \to ϕη$, our estimations of the branching fractions of the light meson decays of $ψ(3770)$ are consistent with the estimations in the literature. As for $ψ(3823)$, 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 $ψ(3823)$. Our estimations also indicate that $K^{(\ast)}\bar{K}^{(\ast)}$ and $ρπ$ are the dominant light meson decay modes of $ψ(3842)$, while $η_{c2}$ dominantly decays into $ρρ$, $K^\ast \bar{K}^\ast$, $ωω$ and $ϕϕ$.