Selecting the physical solution via $η$-$η'$ mixing

Based on $η$-$η'$ mixing analysis, we propose a novel method to extract the physical solutions for the hadronic properties of the $Y(4230)$ resonance from the experimental data. Experimentally, multiple solutions have been reported in the decays of $Y(4230) \to ηJ/ψ$ and $Y(4230) \to η' J/ψ$. Utilizing our method, we determine a unique solution for the process $Y(4230) \to η' J/ψ$. Likewise, two solutions for the process $Y(4230) \to ηJ/ψ$ are preferred among the originally reported three solutions under the assumption that $Y(4230)$ dose not take an $s\bar{s}$ component.

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