We apply the QCD sum rule method to study the double-gluon hybrid states with the quark-gluon contents $\bar q q gg$ ($q=u/d$) and $\bar s s gg$. We construct twenty-eight double-gluon hybrid currents, eleven of which are found to be zero due to some internal symmetries between the two gluons fields. We concentrate on the non-vanishing currents with the exotic quantum numbers $J^{ PC} = 1^{ -+}$ and $3^{ -+}$. Their masses are calculated to be $M_{ |\bar q q gg;1^{ -+}\rangle} = 4.35^{ +0.26}_{ -0.30}$ GeV, $M_{ |\bar s s gg;1^{ -+}\rangle} = 4.49^{ +0.25}_{ -0.30}$ GeV, $M_{ |\bar q q gg;3^{ -+}\rangle} = 3.02^{ +0.24}_{ -0.31}$ GeV, and $M_{ |\bar s s gg;3^{ -+}\rangle} = 3.16^{ +0.22}_{ -0.28}$ GeV. The decay behaviors of the $J^{ PC} = 3^{ -+}$ states are studied, and we propose to search for them in the $\pi a_1(1260)/\rho \omega/\phi \phi$ channels in future particle experiments.
Categories: hep-ph hep-ex hep-lat