A model of charmed baryon-nucleon potential and 2- and 3-body bound states with charmed baryon

A potential model for the interaction between a charmed baryon (${\mathrm{\Lambda }}_c$, ${\mathrm{\Sigma }}_c$, and ${\mathrm{\Sigma }}_c^{\ast }$) and the nucleon ($N$) is constructed. The model contains a long-range meson ($\pi$ and $\sigma$) exchange part and a short-distance quark exchange part. The quark cluster model is used to evaluate the short-range repulsion and a monopole type form factor is introduced to the long-range potential to reflect the extended structure of hadrons. We determine the cutoff parameters in the form factors by fitting the $NN$ scattering data with the same approach and we obtain four sets of parameters (a – d). The most attractive potential (d) leads to bound ${\mathrm{\Lambda }}_{c}N$ states with $J^{\pi }=0^{+}$ and $1^{+}$ once the channel couplings among ${\mathrm{\Lambda }}_c$, ${\mathrm{\Sigma }}_c$ and ${\mathrm{\Sigma }}_c^{\ast }$ are taken into account. One can also investigate many-body problems with the model. Here, we construct an effective ${\mathrm{\Lambda }}_{c}N$ one-channel potential with the parameter set (d) and apply it to the 3-body ${\mathrm{\Lambda }}_{c}NN$ system. The bound states with $J=1\mathrm{/}2$ and $3\mathrm{/}2$ are predicted.