Two-body Hidden Charm 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, we investigate the hidden charm decay processes of spin triplets of the $D$-wave charmonia with the meson loop mechanism. The model parameter $\alpha_\Lambda$ 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 $\psi(3770) \to \eta_c \omega$, $\psi_2(3823)/\psi_3(3842) \to J/\psi \eta$, $\psi_2(3823)/\psi_3(3842) \to \eta_c \omega$ are estimated. Our estimations find that the partial width of $\psi_2(3823) \to J/\psi \eta$ is $\left(29.64^{+4.01}_{-4.63}\right)\ \mathrm{keV}$, 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.