Coupled-channels study of Lambda K and Sigma K states in the chiral SU(3) quark model

The $S$-wave $\Lambda K$ and $\Sigma K$ states with isospin $I=1/2$ are dynamically investigated within the framework of the chiral SU(3) quark model by solving a resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a good description of the energies of the baryon ground states, the binding energy of the deuteron, and the experimental data of the nucleon-nucleon ($NN$) and nucleon-hyperon ($NY$) scattering. Assumed not to give important contributions in the scattering processes, the s-channel quark-antiquark ($q\bar q$) annihilation interactions are not included as a first step. The results show a strong attraction between $\Sigma$ and $K$, which consequently results in a $\Sigma K$ quasi-bound state with about 17 MeV binding energy, unlike the case of $\Lambda K$ which is unbound. When the channel coupling of $\Lambda K$ and $\Sigma K$ is considered, a sharp resonance state near 1670 MeV with spin-parity $J^P=1/2^-$ is found. The narrow gap of the $\Lambda K$ and $\Sigma K$ thresholds, the strong attraction between $\Sigma$ and $K$, and the sizeable off-diagonal matrix elements of $\Lambda K$ and $\Sigma K$ are responsible for the appearance of this resonance.