[Paper Review] Scalar glueball: seeking help from $\eta\eta'$ decays

Jean‐Marie Frère, Julian Heeck|arXiv (Cornell University)|Jun 15, 2015

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates the scalar glueball's mixing with isosinglet mesons $f_0(1370)$, $f_0(1500)$, and $f_0(1710)$ using an effective Hamiltonian and a two-angle mixing scheme for $\eta$ and $\eta'$, finding that $f_0(1710)$ has the largest glueball component and a sizable branching ratio into $\eta\eta'$, making it testable at BESIII.

ABSTRACT

We study the mixing of the scalar glueball into the isosinglet mesons $f_0 (1370)$, $f_0(1500)$, and $f_0(1710)$ to describe the two-body decays to pseudoscalars. We use an effective Hamiltonian and employ the two-angle mixing scheme for $\eta$ and $\eta'$. In this framework, we analyse existing data and look forward to new data into $\eta$ and $\eta'$ channels. For now, the $f_0 (1710)$ has the largest glueball component and a sizable branching ratio into $\eta\eta'$, testable at BESIII.

Motivation & Objective

• To understand the scalar glueball's composition by studying its mixing with isosinglet mesons $f_0(1370)$, $f_0(1500)$, and $f_0(1710)$.
• To analyze two-body decays of these mesons into pseudoscalars using an effective Hamiltonian framework.
• To apply a two-angle mixing scheme for $\eta$ and $\eta'$ to improve the description of $\eta\eta'$ final states.
• To assess the potential for experimental verification of the glueball component in $f_0(1710)$ via $\eta\eta'$ decays at BESIII.
• To interpret existing data and guide future measurements in $\eta$ and $\eta'$ decay channels.

Proposed method

• Employ an effective Hamiltonian to describe the decay amplitudes of $f_0$ states into pseudoscalar pairs.
• Implement a two-angle mixing scheme for $\eta$ and $\eta'$, allowing for a more accurate parametrization of their quark content.
• Use the mixing framework to compute branching ratios for $f_0$ decays into $\eta\eta'$, focusing on the glueball admixture.
• Fit the model to existing experimental data on $f_0$ decays to constrain the glueball component in each state.
• Predict the branching ratio of $f_0(1710)$ into $\eta\eta'$ as a key observable for future experiments.
• Assess the sensitivity of the results to the choice of mixing angles and model parameters.

Experimental results

Research questions

• RQ1 What is the relative glueball component in the $f_0(1710)$ state, and how does it compare to $f_0(1500)$ and $f_0(1370)$?
• RQ2 How well can the two-angle mixing scheme for $\eta$ and $\eta'$ describe the $\eta\eta'$ decay modes of scalar mesons?
• RQ3 What is the predicted branching ratio of $f_0(1710)$ into $\eta\eta'$, and is it measurable at BESIII?
• RQ4 How do existing data on $f_0$ decays constrain the glueball mixing parameters?
• RQ5 What experimental signatures in $\eta$ and $\eta'$ channels can confirm the glueball nature of $f_0(1710)$?

Key findings

• The $f_0(1710)$ state has the largest glueball component among the three isosinglet scalar mesons studied.
• The $f_0(1710)$ exhibits a sizable branching ratio into the $\eta\eta'$ final state, making it a prime candidate for experimental verification.
• The two-angle mixing scheme for $\eta$ and $\eta'$ provides a consistent framework for analyzing $\eta\eta'$ decays of scalar mesons.
• Existing data are consistent with the model, supporting the glueball interpretation of $f_0(1710)$.
• The $f_0(1500)$ and $f_0(1370)$ have smaller glueball components, with $f_0(1500)$ being a less dominant glueball candidate.
• The $\eta\eta'$ decay mode of $f_0(1710)$ is testable at BESIII, offering a clear experimental pathway to probe its glueball content.