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

TL;DR

This paper systematically calculates the mass spectrum of gluonic tetraquark states with various quantum numbers using QCD sum rules, predicting their masses and supporting their possible existence in experimental data.

Contribution

It extends previous work by constructing 18 new interpolating currents for specific quantum numbers and providing mass predictions for both charmonium-like and bottomonium-like tetraquark states.

Findings

Predicted masses for charmonium-like states range from 6.9 to 7.3 GeV.

Predicted masses for bottomonium-like states range from 19.2 to 19.5 GeV.

Results support the potential existence of gluonic tetraquark components in experimental observations.

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.