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Possible $Λ_c\barΛ_c$ molecular states and their productions in nulceon-antinulceon collision

In this work, a study of possible molecular states from the $Λ_c\barΛ_c$ 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 $Λ_c\barΛ_c$ interaction which is described by the light meson exchanges. However, the result does not support the assignment of experimentally observed $Y(4630)$ as a $Λ_c\barΛ_c$ molecular state because it is hard to obtain a peak near experimental mass of the $Y(4630)$ which is far above the $Λ_c\barΛ_c$ 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 $Λ_c\barΛ_c$ threshold in the $D^*\bar{D}^*$ channel at an order of amplitude of 10 $μ$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 $Λ_c\barΛ_c$ molecular state with $1^{--}$ is suggested in process $N\bar{N}\to D^*\bar{D}^*$, which is accessible at $\rm \bar{P}ANDA$.