Pinpointing Physical Solutions in Y(4230) Decays

Abstract

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

4 pages, 1 figure, 3 tables; in the updated version a missing factor has been considered and the conclusion is changed