The hadron decays of D wave charmonia

The experimental observations of $\psi_2(3823)$ and $\psi_3(3842)$ make $D$ wave charmonia family abundant. In the present work, 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. The model parameter $\alpha$ is determined by reproducing the branching fraction of $\psi(3770) \to J/\psi\eta$. With this range of model parameter values, the branching fractions (partial widths) of $\psi_1(3770) \to \eta_c\omega$,$ \psi_2(3823)/\psi_3(3842) \to J/\psi\eta$, $\psi_2(3823)/\psi_3(3842) \to \eta_c\omega$ are estimated. Our estimations find that the partial width of $\psi_2(3823) \to J/\psi\eta$ is $29.64^{+4.01}_{−4.63}$keV, and the partial width ratio of $\psi_2(3823) \to J/\psi\eta$ relative to $\psi_2(3823) \to \gamma \chi_{c1}$ is about $10\%$, which could be tested by further precise measurements from the BESIII, Belle II and LHCb Collaborations.In the same way, with the parameter range determined by $\psi(3770) → \phi\eta$, 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 $K^∗\bar{K}^∗$ 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 $K^{(∗)}\bar{K}^{(∗)}$ and $\rho\pi$ are the dominant light meson decay modes of $\psi(3842)$, while $\eta_{c2}$ dominantly decays into $\rho\rho, K^{∗}\bar{K}^{∗} , \omega\omega$ and $\phi\phi$.