Pinpointing Physical Solutions in Y(4230) Decays
Jie Yuan, Yadi Wang, Kai Zhu
TL;DR
The paper addresses ambiguities arising from multiple amplitude solutions in e+e- cross sections for Y(4230) decays by constructing a global $χ^2$ function that enforces isospin constraints and amplitude relations across seven hidden-charm channels. By evaluating all solution combinations and minimizing the global $χ^2$, the authors identify a physical solution with a minimum $χ^2$ of $1.17$ at a strange-quark fraction $f=δ/\,\sqrt{1+δ^2}\approx 0.043$, selecting the largest $Y(4230)\to \pi^{+}\pi^{-}J/\psi$ amplitude as physical. They also provide predictions for $\Gamma_{ee} \mathcal{B}(Y(4230) \to \pi^{+}\pi^{-} \psi(2S))$ (≈ $0.3 \pm 0.1$ eV) and relate other branching ratios through η–η' mixing and light–strange quark mixing, while noting that long-range meson-loop effects are not included in these constraints. The study yields a more coherent set of inputs for theory by resolving the multi-solution ambiguity and highlighting the dominant π+π−J/ψ contribution, with caveats about potential meson-loop contributions and the similarity of results for different $f$ values. Overall, it narrows down the physical interpretation of Y(4230) decays and provides concrete numerical inputs for future phenomenological work.}
Abstract
To resolve ambiguities from multiple solutions in experimental measurements, we construct a $χ^2$ function incorporating constraints such as isospin conservation and amplitude relations. By minimizing the global $χ^2$, we identify physical solutions for seven hidden-charm decay channels of $Y(4230)$. Crucially, the physical solution for $Y(4230) \to π^{+}π^{-} J/ψ$ corresponds to the largest among four experimental solutions, potentially modifying inputs for theoretical calculations. Additionally, we predict $Γ_{ee} B(Y(4230) \to π^{+}π^{-} ψ(2S))$ based on our results, acknowledging substantial uncertainties in current measurements.