Spectrum of the S-wave fully-heavy tetraquark states

In present work, spectrum of the $S$-wave fully-heavy tetraquark states $QQ\bar{Q}\bar{Q}$ ($Q=c,b$), i.e., $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$, $cc\bar{b}\bar{b}$/$bb\bar{c}\bar{c}$, $bc\bar{c}\bar{c}$/ $cc\bar{b}\bar{c}$, $bb\bar{c}\bar{b}$/$cb\bar{b}\bar{b}$, and $bc\bar{b}\bar{c}$ are systematically investigated within an nonrelativistic constituent quark model, in which the Instanton-induced and one-gluon-exchange interactions are taken into account as the residual spin-dependent hyperfine interaction. Our results show that the states with $cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$ components could be located around $6500$ MeV and $19200$ MeV, respectively. Based on our calculations, the new $X(6900)$ state observed by LHCb may be not a ground $cc\bar{c}\bar{c}$ tetraquark state, while it could be an orbitally or radially excited state of $cc\bar{c}\bar{c}$ system. On the other hand, the recently reported $X(6600)$ state by CMS and ATLAS can be explained as a ground $cc\bar{c}\bar{c}$ tetraquark state with spin-parity $J^{PC}=0^{++}$.