Two- and three-gluon glueballs of $C=+$

Abstract

We study two- and three-gluon glueballs of $C=+$ using the method of QCD sum rules. We systematically construct their interpolating currents, and find that all the spin-1 currents of $C=+$ vanish. This suggests that the ``ground-state'' spin-1 glueballs of $C=+$ do not exist within the relativistic framework. We calculate masses of the two-gluon glueballs with $J^{PC} = 0^{\pm+}/2^{\pm+}$ and the three-gluon glueballs with $J^{PC} = 0^{\pm+}/2^{\pm+}$. We propose to search for the $J^{PC} = 0^{-+}/2^{-\pm}/3^{\pm-}$ three-gluon glueballs in their three-meson decay channels in future BESIII, GlueX, LHC, and PANDA experiments.