Pseudoscalar glueball and $\eta-\eta^\prime$ mixing

TL;DR

This paper analyzes the mixing of pseudoscalar mesons and glueballs using an effective theory, concluding that the pseudoscalar glueball likely has a mass over 2000 MeV and significantly influences the $ a^ extprime$.

Contribution

It provides an analytical approach to pseudoscalar mixing, emphasizing mechanisms that align theoretical predictions with experimental data without predicting exact glueball masses.

Findings

Glueball mass estimated to be greater than 2000 MeV.

Significant glue content in the $ a^ extprime$ meson.

Mixing angles consistent with previous studies.

Abstract

We have performed a dynamical analysis of the mixing in the pseudoscalar channel with the goal of understanding the existence and behavior of the pseudoscalar glueball. Our philosophy has not been to predict precise values of the glueball mass but to exploit an adequate effective theory to the point of breaking and to analyze which kind of mechanisms restore compatibility with data. Our study has lead to analytical solutions which allow a clear understanding of the phenomena. The outcome of our calculation leads to a large mass glueball $M_\Theta>2000$ MeV, to a large glue content of the $\eta^\prime$ and to mixing angles in agreement with previous numerical studies.