Glueball Matrix Elements on Anisotropic Lattices

TL;DR

This study computes glueball-to-vacuum matrix elements of gluonic operators on anisotropic lattices to aid in experimental identification of glueballs, demonstrating small lattice spacing dependence and reliable continuum extrapolation.

Contribution

It introduces improved gluonic operators and performs a detailed lattice study to determine glueball matrix elements with controlled systematic effects.

Findings

Small lattice spacing dependence observed.

Continuum limits reliably extrapolated.

Results aid in predicting glueball decay patterns.

Abstract

The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing in the range 0.1fm -- 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/\psi$ radiative decays which will help to identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check, and the finite volume effects are also studied. The lattice spacing dependence of our results is very small and the continuum limits are reliably extrapolated.