  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.
