Lattice Calculation of Glueball Matrix Elements

TL;DR

This paper uses lattice QCD to compute glueball matrix elements, providing essential non-perturbative data for understanding glueball properties and their role in particle decays.

Contribution

It presents the first lattice QCD calculations of specific glueball matrix elements for various quantum states, comparing results with QCD sum rules and models.

Findings

Matrix elements obtained for different glueball states.

Comparison with sum rules and models shows consistency.

Results aid in calculating glueball decay widths.

Abstract

Matrix elements of the form $ <0| Tr \; g^{2}GG |G> $ are calculated using the lattice QCD Monte Carlo method. Here, $|G>$ 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 $J/\Psi$ radiative decays into glueballs.