Scattering of $\Lambda_{c}\Lambda_{c}$ and $\Lambda_{c}\bar{\Lambda}_{c}$ in chiral effective field theory

Abstract

We investigate the $S$-wave scatterings of $\Lambda_c\Lambda_c$ and $\Lambda_{c}\bar \Lambda_{c}$ systems within a unified chiral effective field theory framework up to next-to-leading order. The contact low-energy coupling constants are determined by fitting to the lattice QCD results for the $\Lambda_c\Lambda_c$ scattering phase shift at an unphysical pion mass. After extrapolating to the physical pion mass, we find a repulsive interaction in the $I(J^P)=0(0^{+})$ $\Lambda_c\Lambda_c$ channel, consistent with the lattice QCD simulation. On the $\Lambda_{c}\bar \Lambda_{c}$ side, using the fitted contact low-energy constants, we predict the phase shifts and potentials for $\Lambda_c \bar\Lambda_c$ scattering in the $I(J^{PC})=0(0^{-+})$ and $0(1^{--})$ channels. Attractive interactions are found in both channels, each allowing for the formation of bound states. In particular, the attraction in the $0(1^{--})$ $\Lambda_c \bar\Lambda_c$ channel is stronger. In addition, our analysis reveals that the spin-spin term caused by the two-pion exchange contributes significantly to the interactions, leading to a distinct mass splitting between the $0(0^{-+})$ and $0(1^{--})$ $\Lambda_c \bar\Lambda_c$ channels.