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.
Categories: hep-ph