Scalar and Pseudoscalar Glueballs Revisited

TL;DR

This paper revisits the structure of scalar and pseudoscalar glueballs, using meson mixing models and experimental data to identify the nature of certain mesons and estimate the pseudoscalar glueball mass around 1.4 GeV, challenging lattice QCD results.

Contribution

It provides a detailed analysis of scalar meson mixing and estimates the pseudoscalar glueball mass using experimental data, proposing $ ext{eta}(1405)$ as a prime candidate.

Findings

$f_0(1500)$ is a pure SU(3) octet and degenerate with $a_0(1450)$

$f_0(1370)$ is mainly an SU(3) singlet with slight glueball mixing

Pseudoscalar glueball mass estimated around 1.4 GeV

Abstract

Using two simple and robust inputs to constrain the mixing matrix of the isosinglet scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$, we have shown that in the SU(3) symmetry limit, $f_0(1500)$ becomes a pure SU(3) octet and is degenerate with $a_0(1450)$, while $f_0(1370)$ is mainly an SU(3) singlet with a slight mixing with the scalar glueball which is the primary component of $f_0(1710)$. These features remain essentially unchanged even when SU(3) breaking is taken into account. We have deduced the mass of the pseudoscalar glueball $G$ from an $\eta$-$\eta'$-$G$ mixing formalism based on the anomalous Ward identity for transition matrix elements. With the inputs from the recent KLOE experiment, we find a solution for the pseudoscalar glueball mass around $(1.4\pm 0.1)$ GeV. This affirms that $\eta(1405)$, having a large production rate in the radiative $J/\psi$ decay and not seen in $\gamma\gamma$ reactions, is indeed a leading candidate for the pseudoscalar glueball. It is much lower than the results from quenched lattice QCD ($>2.0$ GeV).