Fully Charmed Tetraquark States in $8_{[c\bar{c}]}\otimes8_{[c\bar{c}]}$ Color Structure via QCD Sum Rules

Stimulated by the recent experimental results on the fully-charm tetraquark states, we systematically calculate the mass spectra of the fully-charm tetraquark states in $8_{[c\bar{c}]}\otimes8_{[c\bar{c}]}$ color configuration via QCD sum rules. By constructing nine $8_{[c\bar{c}]}\otimes8_{[c\bar{c}]}$ type currents with quantum numbers $J^{PC}=0^{-+},0^{--},1^{-+},1^{+-},1^{--}$ and $2^{++}$, we perform analytic calculation up to dimension six in the Operator Product Expansion (OPE). We find the fully-charm tetraquark states with $J^{PC}=1^{+-},2^{++}$ lie around 6.48 $\sim$ 6.62 GeV while the fully-charm tetraquark states with $J^{PC}=0^{-+},0^{--},1^{--},1^{-+}$ are about 6.85 $\sim$ 7.02 GeV. Notably, the mass predictions for the $c\bar{c}c\bar{c}$ tetraquarks, specifically those with $J^{PC}=2^{++}$, align with the broad structure identified by LHCb. Moreover, the masses of fully-charm tetraquarks with $J^{PC}=0^{-+}$ and $1^{-+}$ are anticipated to match closely with the mass of X(6900), considering the margin of error. Such findings hint at the presence of some $8_{[c\bar{c}]}\otimes8_{[c\bar{c}]}$ components within the di-$J/\psi$ structures observed by LHCb. The predictions for tetraquark states with $J^{PC}=0^{--},1^{+-},1^{--}$ may be accessible in the future BelleII, Super-B, PANDA, and LHCb experiments.