[Paper Review] $\eta(2225)$ observed by BES Collaboration

De-Min Li, Ma Bing|arXiv (Cornell University)|Mar 2, 2008

Particle physics theoretical and experimental studies4 citations

TL;DR

This study investigates the strong decays of $3^1S_0$ and $4^1S_0$ $s\bar{s}$ states using the $^3P_0$ quark model, predicting total widths of 438 MeV and 125 MeV at a mass of 2.24 GeV, respectively. The observed width of $\eta(2225)$, $0.19 \pm 0.03^{+0.04}_{-0.06}$ GeV, is inconsistent with the $3^1S_0$ state but consistent with the $4^1S_0$ state, suggesting $\eta(2225)$ is likely the $4^1S_0$ $s\bar{s}$ resonance.

ABSTRACT

In the framework of the $^3P_0$ meson decay model, the strong decays of the $3 ^1S_0$ and $4 ^1S_0$ $s\bar{s}$ states are investigated. It is found that in the presence of the initial state mass being 2.24 GeV, the total widths of the $3 ^1S_0$ and $4 ^1S_0$ $s\bar{s}$ states are about 438 MeV and 125 MeV, respectively. Also, when the initial state mass varies from 2220 to 2400 MeV, the total width of the $4 ^1S_0$ $s\bar{s}$ state varies from about 100 to 132 MeV, while the total width of the $3 ^1S_0$ $s\bar{s}$ state varies from about 400 to 594 MeV. A comparison of the predicted widths and the experimental result of $(0.19\pm 0.03^{+0.04}_{-0.06})$ GeV, the width of the $\eta(2225)$ with a mass of $(2.24^{+0.03+0.03}_{-0.02-0.02})$ GeV recently observed by the BES Collaboration in the radiative decay $J/\psi o\gamma\phi\phi o\gamma K^+K^-K^0_SK^0_L$, suggests that it would be very difficult to identify the $\eta(2225)$ as the $3 ^1S_0$ $s\bar{s}$ state, and the $\eta(2225)$ seams a good candidate for the $4 ^1S_0$ $s\bar{s}$ state.

Motivation & Objective

• To determine the nature of the $\eta(2225)$ resonance observed by BES in $J/\psi \to \gamma \phi \phi K^+K^-$ decay.
• To evaluate whether $\eta(2225)$ can be identified as the $3^1S_0$ or $4^1S_0$ $s\bar{s}$ state using decay width predictions.
• To assess the consistency between theoretical predictions and experimental width measurements of $\eta(2225)$.
• To explore the dependence of total widths on initial state mass in the $^3P_0$ model for $s\bar{s}$ states.

Proposed method

• Employing the $^3P_0$ quark model to calculate strong decay widths of $3^1S_0$ and $4^1S_0$ $s\bar{s}$ states.
• Using a quark-antiquark pair creation mechanism with a constant $\bar{q}q$ pair creation amplitude.
• Calculating total decay widths as a function of initial state mass, ranging from 2220 to 2400 MeV.
• Comparing predicted widths with the experimentally measured width of $\eta(2225)$: $(0.19 \pm 0.03^{+0.04}_{-0.06})$ GeV.
• Analyzing the mass dependence of decay widths for both $3^1S_0$ and $4^1S_0$ states.
• Evaluating the consistency of theoretical predictions with the BES observation at a mass of $2.24^{+0.03+0.03}_{-0.02-0.02}$ GeV.

Experimental results

Research questions

• RQ1 Is the $\eta(2225)$ resonance consistent with being the $3^1S_0$ $s\bar{s}$ state based on predicted decay width?
• RQ2 Is the $\eta(2225)$ resonance consistent with being the $4^1S_0$ $s\bar{s}$ state based on predicted decay width?
• RQ3 How do the predicted total widths of $3^1S_0$ and $4^1S_0$ $s\bar{s}$ states vary with initial state mass near 2.24 GeV?
• RQ4 What is the theoretical width of the $4^1S_0$ $s\bar{s}$ state at a mass of 2.24 GeV, and how does it compare to the experimental value?
• RQ5 Can the $^3P_0$ model explain the observed width of $\eta(2225)$ within experimental uncertainties?

Key findings

• At an initial state mass of 2.24 GeV, the predicted total width of the $3^1S_0$ $s\bar{s}$ state is 438 MeV.
• At the same mass, the predicted total width of the $4^1S_0$ $s\bar{s}$ state is 125 MeV.
• The predicted width of the $4^1S_0$ $s\bar{s}$ state varies from 100 to 132 MeV as the initial mass increases from 2220 to 2400 MeV.
• The predicted width of the $3^1S_0$ $s\bar{s}$ state varies from 400 to 594 MeV over the same mass range.
• The experimental width of $\eta(2225)$, $0.19 \pm 0.03^{+0.04}_{-0.06}$ GeV, is inconsistent with the $3^1S_0$ $s\bar{s}$ state prediction.
• The $\eta(2225)$ resonance is found to be a good candidate for the $4^1S_0$ $s\bar{s}$ state due to consistent width predictions.