Glueball Spectrum and Matrix Elements on Anisotropic Lattices

TL;DR

This study numerically investigates glueball-to-vacuum matrix elements on anisotropic lattices, providing essential data for experimental glueball identification and demonstrating weak lattice spacing dependence for reliable continuum extrapolation.

Contribution

It introduces improved local gluonic operators and performs a detailed analysis of their matrix elements, masses, and finite volume effects on anisotropic lattices.

Findings

Weak lattice spacing dependence of matrix elements

Reliable continuum limit extrapolation achieved

Updated glueball mass spectrum provided

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 ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/\psi$ radiative decays which will help 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 studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.