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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.21042 |
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Table of Contents:
- The $ψ(3686)$ is identified as the radial excitation of the $J/ψ$. Based on perturbative QCD, the branching ratio of the $ψ(3686)$ into some final hadron state should be approximately 13% of the branching ratio of the $J/ψ$ to that same hadron final state. This is called the "13\% rule". However, certain decay channels such as the $ρπ$ severely violate this 13% rule. Using the extended Linear Sigma Model, we study the effect a small mixing angle between the $ψ(3686)$ and the vector glueball can have on the 13% rule. We show that in a simple model the mixing can already suppress $ψ(3686)$ decays sufficiently to match the $ρπ$ observation, but to fully describe the data a more sophisticated model is necessary. We also show that matching to data can tell us about the magnitude of glueball decay widths.