Investigation of fully heavy tetraquark within chiral quark model

In the framework of the Chiral quark model (ChQM), we investigate the fully charmed and fully bottomed tetraquark with $J^{PC}=2^{++}$ including two structures: $Q\bar{Q}-Q\bar{Q}$ and $QQ-\bar{Q}\bar{Q}$. The bound-state calculation shows that there is no bound state in either $cc\bar{c}\bar{c}$ or $bb\bar{b}\bar{b}$ systems. However, by using the real-scaling method, some resonance states are obtained. For the $cc\bar{c}\bar{c}$ system, when the channel-coupling includes only three $S$-wave channels, two resonant states are obtained: one with a mass around $7002$ MeV and decay width near $54$ MeV, and another with a mass around $7227$ MeV and a decay width near $66$ MeV. The former can be regarded as a candidate for the $X(6900)$, and the latter can be considered as a candidate for the $X(7200)$. Upon adding the $\chi_{c0}\chi_{c2}$, $\chi_{c1}\chi_{c1}$, $\chi_{c1}\chi_{c2}$, $\chi_{c2}\chi_{c2}$ channels, both resonant states still remain. For the $bb\bar{b}\bar{b}$ system, only one resonant state is obtained, regardless of whether the four channels composition of the excited mesons are included or excluded. The mass and width of this resonant state are around $19743$ MeV and $67$ MeV, respectively. We suggest that future experiments search for the possible resonance state in the invariant mass spectrum of $\Upsilon \Upsilon$ or $\Upsilon \Upsilon(2S)$.