Fierz analyses on the decay properties of two- and three-gluon glueballs

TL;DR

This paper uses Fierz rearrangement to analyze decay properties of two- and three-gluon glueballs, deriving decay ratios that help identify gluonic components in certain mesons and proposing experimental channels for observing specific glueballs.

Contribution

It applies Fierz analysis to calculate decay ratios of glueballs, providing nearly one hundred ratios and suggesting experimental signatures for gluonic states.

Findings

$f_0(1710)$ and $ ext{eta}(2370)$ likely have significant gluon content.

Small gluon component in $f_0(1500)$.

Proposed experimental channels for observing specific three-gluon glueballs.

Abstract

The Fierz rearrangement, based on the various internal symmetries of hadrons, can be used to study their decay properties in a largely model-independent way. In this Letter we apply this method to calculate the relative branching ratios of two-gluon glueballs with $J^{PC} = 0^{++}/0^{-+}$ and three-gluon glueballs with $J^{PC} = 0^{++}/1^{+-}$. In total, we derive nearly one hundred ratios for these glueballs. Our results suggest that the $f_0(1710)$ and $\eta(2370)$ likely contain a significant gluon component, whereas the gluon component in $f_0(1500)$ appears to be small. Furthermore, we propose observing the three-gluon glueball with $J^{PC} = 0^{++}$ in the $\pi\pi\omega$ and $K\bar{K}\phi$ channels, and the three-gluon glueball with $J^{PC} = 1^{+-}$ in the $\pi\pi\omega$, $\pi\pi\phi$, and $K\bar{K}\phi$ channels. This study enhances our understanding of the gluonic structure of exotic hadrons and will assist future experimental searches in high-energy physics.