Pinpointing Physical Solutions in Y(4230) Decays

TL;DR

This paper develops a method to identify the physically meaningful solutions among multiple experimental ambiguities for the Y(4230) particle decays, impacting theoretical models and predictions.

Contribution

It introduces a $ ext{chi}^2$ minimization approach with constraints to resolve solution ambiguities in Y(4230) decay channels.

Findings

Identifies the physical solution for Y(4230) → π+π− J/ψ as the largest among four experimental options.

Predicts the product of electronic width and branching ratio for Y(4230) → π+π− ψ(2S), with large uncertainties.

Reveals that the physical solution can significantly alter theoretical input parameters.

Abstract

To resolve ambiguities from multiple solutions in experimental measurements, we construct a $\chi^2$ function incorporating constraints such as isospin conservation and amplitude relations. By minimizing the global $\chi^2$, we identify physical solutions for seven hidden-charm decay channels of $Y(4230)$. Crucially, the physical solution for $Y(4230) \to \pi^{+}\pi^{-} J/\psi$ corresponds to the largest among four experimental solutions, potentially modifying inputs for theoretical calculations. Additionally, we predict $\Gamma_{ee} B(Y(4230) \to \pi^{+}\pi^{-} \psi(2S))$ based on our results, acknowledging substantial uncertainties in current measurements.