Investigation of $cs\bar c\bar s$ tetraquark in the chiral quark model

Inspired by the recent observation of exotic resonances $X(4140)$, $X(4274)$, $X(4350)$, $X(4500)$ and $X(4700)$ reported by several experiment collaborations, we investigated the four-quark system $cs\bar c\bar s$ with quantum numbers $J^{PC}=1^{++}$ and $0^{++}$ in the framework of the chiral quark model. Two configurations, diquark-antidiquark and meson-meson, with all possible color structures are considered. The results show that no molecular state can be formed, but the resonance may exist if the color structure of meson-meson configuration is $8\otimes8$. In the present calculation, the $X(4274)$ can be assigned as the $cs\bar c\bar s$ tetraquark states with $J^{PC}=1^{++}$, but the energy of $X(4140)$ is too low to be regarded as the tetraquark state. $X(4350)$ can be a good candidate of compact tetraquark state with $J^{PC}=0^{++}$. When the radial excitation is taken into account, the $X(4700)$ can be explained as the $2S$ radial excited tetraquark state with $J^{PC}=0^{++}$. As for $X(4500)$, there is no matching state in our calculation.