Double-gluon charmonium hybrid states with various (exotic) quantum numbers

We study the double-gluon charmonium hybrid states with various quantum numbers, each of which is composed of one valence charm quark and one valence charm antiquark as well as two valence gluons. We concentrate on the exotic quantum numbers $J^{PC} =0^{--}/0^{+-}/1^{-+}/2^{+-}/3^{-+}$ that the conventional $\bar q q$ mesons can not reach. We apply the QCD sum rule method to calculate their masses to be $7.28^{+0.38}_{-0.43}$ GeV, $5.19^{+0.36}_{-0.46}$ GeV, $5.46^{+0.41}_{-0.62}$ GeV, $4.48^{+0.25}_{-0.31}$ GeV, and $5.54^{+0.35}_{-0.43}$ GeV, respectively. We study their possible decay patterns and propose to search for the $J^{PC}=2^{+-}/3^{-+}$ states in the $D^*\bar D^{(*)}/D^{*}_s \bar D^{(*)}_s/\Sigma_c^* \bar \Sigma_c^{(*)}/\Xi_c^* \bar \Xi_c^{(\prime,*)}$ channels. Experimental investigations on these states and decay channels can be useful in classifying the nature of the hybrid state, thus serving as a direct test of QCD in the low energy sector.