Low-lying bound states of three gluons: Their spectrum and production and decay properties

Abstract

In a potential model for glueballs, with a dynamical gluon mass $m\simeq 500$ MeV, the masses of the low-lying three-gluon glueballs (with $J^{\mathrm{PC}}=0^{-+}, 1^{--}, \mathrm{and} 3^{--}$) are found to be approximately degenerate $\simeq 4.8m\simeq 2.4$ GeV. The ${\eta }_c\to \eta \pi \pi$, $\psi \to \rho \pi$ decays are used to extract mixing of three-gluon $0^{-+}$ and $1^{--}$ glueballs with ${\eta }_c$ and $\psi$, respectively. The decays $\psi \left({\psi }^{\prime }\right)\to h+X$ ($h=\pi \pi ,\eta ,{\eta }^{\prime }$) are suggested for experimentally studying the three-gluon continuum and three-gluon bound states. The three-gluon glueballs production rate via that mechanism as well as in $\mathrm{pp}$, $\gamma p$, and $\gamma \gamma$ collisions is estimated. The $1^{--}$ decays dominantly into $\rho \pi$, but also has reasonable decay widths for $K^{*}\overline{K}$ channels. The $0^{-+}$ glueball state decays dominantly into $\mathrm{VV}$ ($V=\rho ,\omega ,\phi$). Its other important decay modes are found to be $\delta \pi$, $V\gamma$, and $\gamma \gamma$.