On the structure of the pi pi invariant mass spectra of the Upsilon(4S)-->Upsilon(1S,2S) pi^+ pi^- decays

Abstract

We 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.