Fierz analyses on the decay properties of two- and 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 $η(2370)$ 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 $ππω$ and $K\bar{K}φ$ channels, and the three-gluon glueball with $J^{PC} = 1^{+-}$ in the $ππω$, $ππφ$, and $K\bar{K}φ$ channels. This study enhances our understanding of the gluonic structure of exotic hadrons and will assist future experimental searches in high-energy physics.

Figures (2)

• Figure 1: Diagram (a) illustrates the schematic diagram of a two-gluon glueball decaying into two mesons via a single Fierz rearrangement, while Diagram (b) depicts the schematic diagram of a three-gluon glueball decaying into three mesons through two successive Fierz rearrangements.
• Figure 2: Relative branching ratios of two-gluon glueballs with $J^{PC}=0^{++}/0^{-+}$ and three-gluon glueballs with $J^{PC}=0^{++}/1^{+-}$, derived via the Fierz rearrangement, where $\sigma$ denotes $f_0(500)$, $\kappa$ denotes $K_0^*(700)$, $f_0$ denotes $f_0(980)$, and $K^*$ denotes $K^*(892)$.