Investigation of csc¯s¯ tetraquark in the chiral quark model

Abstract

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 $cs\overline{c}\overline{s}$ 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 the meson-meson configuration is $8\ensuremath{\bigotimes}8$. In the present calculation, the $X(4274)$ can be assigned as the $cs\overline{c}\overline{s}$ 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 the 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.