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 JPC=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
Nearby in the stack
αs
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.