Towards heavy double-gluon hybrid mesons with exotic quantum numbers in QCD sum rules

The double-gluon hybrid meson configuration was recently proposed and investigated within QCD sum rules. In this talk, we discuss the color structures of the double-gluon hybrid meson and construct current operators with exotic quantum numbers $J^{PC}=1^{-+}$ and $2^{+-}$ for two of the structures. In the framework of QCD sum rules, we consider the condensates up to dimension-8 at the leading order of ${\alpha }_s$ for both charmonium and the bottomonium systems. The results indicate that the masses of the $1^{-+}$ and $2^{+-}$ charmonium double-gluon hybrid mesons are approximately $6.1-7.2$ GeV and $6.3-6.4$ GeV, respectively. As for the bottomonium systems, their masses fall within the range of $13.7-14.3$ GeV and $12.6-13.3$ GeV for the $1^{-+}$ and $2^{+-}$ channels, respectively. Additionally, the charmonium hybrids could be produced in the radiative decays of bottomonium mesons in BelleII experiment.