Scattering of $Λ_{c}Λ_{c}$ and $Λ_{c}\barΛ_{c}$ in chiral effective field theory

Abstract

We investigate the $S$-wave scatterings of $Λ_cΛ_c$ and $Λ_{c}\bar Λ_{c}$ 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 $Λ_cΛ_c$ scattering phase shift at an unphysical pion mass. After extrapolating to the physical pion mass, we find a repulsive interaction in the $I(J^P)=0(0^{+})$ $Λ_cΛ_c$ channel, consistent with the lattice QCD simulation. On the $Λ_{c}\bar Λ_{c}$ side, using the fitted contact low-energy constants, we predict the phase shifts and potentials for $Λ_c \barΛ_c$ 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 $0(1^{--})$ $Λ_c \barΛ_c$ 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 $0(1^{--})$ $Λ_c \barΛ_c$ channels.

Figures (6)

• Figure 1: Two-pion-exchange diagrams for the $\Lambda_{c}\Lambda_{c}$ system: the planar box diagram and the crossed box diagram. The thin, thick, and dashed lines denote the $\Lambda_{c}$, $\Sigma_{c}$, and $\pi$, respectively.
• Figure 2: $0(0^+)$$\Lambda_c\Lambda_c$ scattering phase shifts as a function of $aE_{\rm cm}$. The blue and red dots denote the LQCD data from Ref. Xing:2025uai for the F32P30 and F48P30 ensembles, respectively. The gray-blue and light-red bands correspond to our ChEFT fits of the F32P30 and F48P30 ensembles, respectively, obtained by varying the cutoff $\Lambda$ from 0.56 to 0.66 GeV.
• Figure 3: $0(0^+)$$\Lambda_{c}\Lambda_{c}$ scattering phase shifts as a function of the kinetic energy in the center-of-mass frame at the physical pion mass. The gray-blue and light-red bands correspond to our ChEFT fits of the F32P30 and F48P30 ensembles, respectively, obtained by varying the cutoff $\Lambda$ from 0.56 to 0.66 GeV.
• Figure 4: $0(0^{+})$$\Lambda_{c}\Lambda_{c}$ effective potentials in coordinate space at the physical pion mass, with cutoff $\Lambda = 0.60$ GeV. Here we set $C_{a} = -3.65~\mathrm{GeV}^{-2}$ from Table \ref{['fit']}.
• Figure 5: $0(0^{-+})$ and $0(1^{--})$$\Lambda_{c}\bar{\Lambda}_{c}$ scattering phase shifts as a function of the kinetic energy $E$ in the center-of-mass frame at the physical pion mass, with cutoff $\Lambda = 0.60$ GeV. The blue dashed line and light-red solid line represent the results for the $0(0^{-+})$ and $0(1^{--})$ channels using the fitted values $C_{a} = -3.71~\mathrm{GeV}^{-2}$ (F32P30 ensemble) and $C_{a} = -3.65~\mathrm{GeV}^{-2}$ (F48P30 ensemble) from Table \ref{['fit']}, respectively.