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Single $Λ_c^+$ hypernuclei within quark mean-field model

The quark mean-field (QMF) model is applied to study the single $Λ^+_c$ hypernuclei. The charm baryon, $Λ^+_c$, is constructed by three constituent quarks, $u, ~d$, and $c$, confined by central harmonic oscillator potentials. The confinement potential strength of charm quark is determined by fitting the experimental masses of charm baryons, $Λ^+_c,~Σ^+_c$, and $Ξ^{++}_{cc}$. The effects of pions and gluons are also considered to describe the baryons at the quark level. The baryons in $Λ^+_c$ hypernuclei interact with each other through exchanging the $σ,~ω$, and $ρ$ mesons between the quarks confined in different baryons. The $Λ^+_c N$ potential in the QMF model is strongly dependent on the coupling constant between $ω$ meson and $Λ^+_c$, $g_{ωΛ^+_c}$. When the conventional quark counting rule is used, i. e., $g_{ωΛ^+_c}=2/3g_{ωN}$, the massive $Λ^+_c$ hypernucleus can exist, whose single $Λ^+_c$ binding energy is smaller with the mass number increasing due to the strong Coulomb repulsion between $Λ^+_c$ and protons. When $g_{ωΛ^+_c}$ is fixed by the latest lattice $Λ^+_c N$ potential, the $Λ^+_c$ hypernuclei only can exist up to $A\sim 50$.