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 ${J}^{PC}={0}^{\ifmmode\pm\else\textpm\fi{}+}/{2}^{\ifmmode\pm\else\textpm\fi{}+}$ and the three-gluon glueballs with ${J}^{PC}={0}^{\ifmmode\pm\else\textpm\fi{}+}/{2}^{\ifmmode\pm\else\textpm\fi{}+}$. We propose searching for the ${J}^{PC}={0}^{\ensuremath{-}+}/{2}^{\ensuremath{-}\ifmmode\pm\else\textpm\fi{}}/{3}^{\ifmmode\pm\else\textpm\fi{}\ensuremath{-}}$ three-gluon glueballs in their three-meson decay channels in the future BESIII, GlueX, LHC, and PANDA experiments.