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

TL;DR

This paper develops a potential model for charmed baryon-nucleon interactions, predicts bound states, and explores three-body systems, contributing to understanding of charmed baryon interactions in nuclear physics.

Contribution

The paper introduces a new potential model combining meson exchange and quark exchange for charmed baryon-nucleon interactions, predicting bound states and extending to three-body systems.

Findings

Bound $ ext{Λ}_c N$ states with $J^ ext{π}=0^+$ and $1^+$ are predicted.

Effective $ ext{Λ}_c N$ potential constructed for many-body calculations.

Predicted bound states in the $ ext{Λ}_c NN$ three-body system with $J=1/2$ and $3/2$.

Abstract

A potential model for the interaction between a charmed baryon ($\Lambda_c$, $\Sigma_c$, and $\Sigma_c^*$) 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 $\Lambda_c N$ states with $J^\pi= 0^+$ and $1^+$ once the channel couplings among $\Lambda_c$, $\Sigma_c$ and $\Sigma_c^*$ are taken into account. One can also investigate many-body problems with the model. Here, we construct an effective $\Lambda_c N$ one-channel potential with the parameter set (d) and apply it to the 3-body $\Lambda_c NN$ system. The bound states with $J=1/2$ and $3/2$ are predicted.