2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/195968We perform a model-independent analysis for recently reported data of the $π^+π^-$ invariant mass spectra in the $Υ(4S)\toΥ(1S,2S)π^+π^-$ decays and point out that there does exist a broad peak below 0.6 GeV in the data of the $Υ(4S)\toΥ(1S)π^+π^-$ decay, which is analogous to that in the $Υ(3S)\toΥ(1S)π^+π^-$ decay. With the data of $Υ(4S)$ decays, we further test our model developed for studying the puzzle in the $Υ(3S)\toΥ(1S)π^+π^-$ decay. The result shows that with such a model, all the $π^+π^-$ invariant mass spectra of $Υ(4S)$ decays can be described. We also predict the $\cosθ_π^*$ distributions of $Υ(4S)\toΥ(1S,2S)π^+π^-$ decays, which can be used to justify our model prediction.11 pages, 5 figures. Extended to include new data; title changed. Version accepted for publication in Phys. Lett. BHigh Energy Physics - PhenomenologyHigh Energy Physics - Experimenttext