Fully strange tetra- and penta-quarks in a chiral quark model

Motivated by the recently reported resonant structure $X(2300)$, a strong candidate for a fully strange tetraquark with positive parity, we perform a systematic study of fully strange tetra- and penta-quark systems within a chiral quark model. Low-lying $S$-wave configurations of the $ss\bar s\bar s$ and $ssss\bar s$ systems are investigated using the Gaussian Expansion Method (GEM) combined with the Complex Scaling Method (CSM), which allows for a unified treatment of bound, resonant, and scattering states. For tetraquarks, all possible configurations: meson-meson, diquark-antidiquark, and K-type structures, with complete color bases, are incorporated, while baryon-meson and diquark-diquark-antiquark configurations are considered for pentaquarks. Several weakly bound states and narrow resonances are identified in both sectors. In particular, a compact fully strange tetraquark with $J^P=1^+$ is found near $2.3\,\text{GeV}$, providing a natural interpretation of the $X(2300)$ resonance. Additional exotic states with dominant hidden-color and K-type components are predicted in the mass ranges $1.6-3.1$ GeV for tetraquarks and $2.6-3.2$ GeV for pentaquarks. The internal structure of these states is analyzed through their sizes, magnetic moments, and wave-function compositions, highlighting the essential role of channel coupling and exotic color configurations. Finally, promising two-body strong decay channels are proposed to facilitate future experimental searches.