Searching for higher charmonium members in $J/\psi$ family through reaction $e^+e^- \to \Lambda_c \bar{\Lambda}_c$.

In this work, we investigate the open-charm decay of $\psi\to\Lambda_c\bar{\Lambda}_c$ via a hadronic loop mechanism, where $\psi$ is higher vector charmonium above $\Lambda_c\bar{\Lambda}_c$ in $J/\psi$ family. The branching fractions of these vector charmonium states to $\Lambda_c\bar{\Lambda}_c$ are estimated. Our numerical results support the charmonium explanation of $Y(4630)$ observed in $e^+e^- \to \Lambda_c\bar{\Lambda}_c$. Furthermore, for the predicted higher vector charmonia above 4.7 GeV, the branching fractions $\mathcal{B}[\psi(nS)\to\Lambda_c\bar{\Lambda}_c]$ with $n=7,8,9$ are found to be of the order of $10^{-4}-10^{-3}$ and $\mathcal{B}[\psi(mD)\to\Lambda_c\bar{\Lambda}_c]$ with $m=6,7,8$ are of the order of $10^{-3}-10^{-2}$. The experimental signals of these missing charmonium states are discussed. The search for them may be an interesting topic in the future BESIII and BelleII experiments.