QCD sum rule predictions on gluonic tetraquark states with $J^{PC}=0^{+-},0^{--}$ and $1^{\pm \pm}$

Abstract

In this work, we present a systematic calculation of the mass spectrum for tetraquark hybrid states, focusing on the $8_{[c\bar{c}]}\otimes 8_{[G]}\otimes 8_{[c\bar{c}]}$ color configuration, within the framework of QCD sum rules. As an extension of our previous work on $0^{++}$ and $0^{-+}$ states, we now construct 18 distinct interpolating currents with $J^{PC} = 0^{+-}$, $0^{--}$, and $1^{\pm\pm}$. Using operator product expansion (OPE) techniques and including nonperturbative contributions up to dimension six, we obtain key results: for the $0^{+-}$, $1^{--}$, and $1^{-+}$ states, the predicted masses lie in the range of $7.2-7.3$ GeV, while the $1^{+-}$ and $1^{++}$ states have slightly lower masses, between 6.9 and 7.1 GeV. These predictions provide strong support for the possible existence of an $8_{[c\bar{c}]}\otimes 8_{[G]}\otimes 8_{[c\bar{c}]}$ component within the di-$J/\psi$ structure reported by LHCb. Moreover, our analogous calculations for tetrabottom hybrid states yield mass ranges of $19.4-19.5$ GeV (for $0^{+-}$, $1^{--}$, and $1^{-+}$) and $19.2-19.3$ GeV (for $1^{+-}$ and $1^{++}$), offering crucial references for future searches.