Further study of \(c\bar{c}c\bar{c}\) system within a chiral quark model

Inspired by the recent ATLAS and CMS experiments on the invariant mass spectrum of \(J/\psi J/\psi \), we systematically study the \(c\bar{c}c\bar{c}\) system of \(J^{P}=0^{+}\). In the framework of chiral quark model, we have carried out bound-state calculation and resonance-state calculation respectively by using Real-scaling method. The results of bound-state calculation show that there are no bound states in the \(c\bar{c}c\bar{c}\) with \(0^{+}\) system. The resonance-state calculation shows that there are four possible resonances: R(6923), R(6996), R(7060) and R(7159). R(6923) and R(7159) are experimental candidates for X(6900) and X(7200), whose main decay channel is \(J/\psi J/\psi \). It is important to note that the another major decay channel of R(7159) is \(\chi _{c0} \chi _{c0}\), and the \(\chi _{c0} \chi _{c0}\) is also the main decay channel of R(6996), R(7060). Therefore, we propose to search experimentally for these two predicted resonances in the \(\chi _{c0} \chi _{c0}\) invariant mass spectrum.