Pseudoscalar glueball mass from $\eta$-$\eta'$-$G$ mixing

TL;DR

This paper estimates the pseudoscalar glueball mass using an $ ext{eta}$-$ ext{eta'}$-$G$ mixing model and recent experimental data, supporting $ ext{eta}(1405)$ as a prime glueball candidate.

Contribution

It introduces a mixing formalism based on the anomalous Ward identity to determine the glueball mass, consistent with experimental observations and insensitive to certain theoretical assumptions.

Findings

Glueball mass estimated at (1.4 ± 0.1) GeV.

Supports $ ext{eta}(1405)$ as a leading pseudoscalar glueball candidate.

Predicts decay widths for $G o ext{gamma} ext{gamma}$ and $ ext{leptons}^+ ext{leptons}^-$.

Abstract

We deduce 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, which is fairly insensitive to a range of inputs with or without Okubo-Zweig-Iizuka-rule violating effects. 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. Other relevant quantities including the anomaly and pseudoscalar density matrix elements are obtained. The decay widths for $G\to \gamma\gamma$, $\ell^+\ell^-$ are also predicted.