Possible $\Lambda_c\bar{\Lambda}_c$ molecular states and their productions in nulceon-antinulceon collision

In this work, a study of possible molecular states from the $\Lambda_c\bar{\Lambda}_c$ interaction and their productions in nucleon-antinucleon collision is performed in a quasipotential Bethe-Salpeter equation approach. Two bound states with quantum numbers $J^{PC}=0^{-+}$ and $1^{--}$ are produced with almost the same binding energy from the $\Lambda_c\bar{\Lambda}_c$ interaction which is described by the light meson exchanges. However, the result does not support the assignment of experimentally observed $Y(4630)$ as a $\Lambda_c\bar{\Lambda}_c$ molecular state because it is hard to obtain a peak near experimental mass of the $Y(4630)$ which is far above the $\Lambda_c\bar{\Lambda}_c$ threshold. The possibility to search these states in nucleon-antinucleon collision is studied by including couplings to $N\bar{N}$ and $D^{(*)}\bar{D}^{(*)}$ channels. The peaks can be found obviously near the $\Lambda_c\bar{\Lambda}_c$ threshold in the $D^*\bar{D}^*$ channel at an order of amplitude of 10 $\mu$b. Too small width of state with $0^{-+}$ may lead to the difficulty to be observed in experiment. Based on the results in the current work, search for the $\Lambda_c\bar{\Lambda}_c$ molecular state with $1^{--}$ is suggested in process $N\bar{N}\to D^*\bar{D}^*$, which is accessible at $\rm \bar{P}ANDA$.