Lattice Calculation of Glueball Matrix Elements

Matrix elements of the form $<0\mathrm{\mid }Tr{g}^{2}GG\mathrm{\mid }G>$ are calculated using the lattice QCD Monte Carlo method. Here, $\mathrm{\mid }G>$ is a glueball state with quantum numbers $0^{++}$, $2^{++}$, $0^{-+}$ and $G$ is the gluon field strength operator. The matrix elements are obtained from the hybrid correlation functions of the fuzzy and plaquette operators performed on the ${12}^4$ and ${14}^4$ lattices at $\beta =5.9$ and $5.96$ respectively. These matrix elements are compared with those from the QCD sum rules and the tensor meson dominance model. They are the non-perturbative matrix elements needed in the calculation of the partial widths of $J\mathrm{/}\mathrm{\Psi }$ radiative decays into glueballs.