Peak shifts due to $B^{(*)}-\bar{B}^{(*)}$ rescattering in $\Upsilon(5S)$ dipion transitions

TL;DR

This paper investigates how final state rescattering affects the energy distributions in $S$ dipion transitions, predicting a shift in resonance peaks that can test the rescattering mechanism in heavy quarkonium decays.

Contribution

It introduces a model analyzing energy shifts in $S$ dipion transitions due to rescattering, providing specific predictions for experimental verification.

Findings

Resonance peaks shift upward by 7-20 MeV in dipion transitions.

Energy distributions differ significantly from direct $S$ decays.

Predictions enable testing of rescattering effects in heavy quarkonia.

Abstract

We study the energy distributions of dipion transitions $\Upsilon(5S)$ to $\Upsilon(1S,2S,3S)\pi^+\pi^-$ in the final state rescattering model. Since the $\Upsilon(5S)$ is well above the open bottom thresholds, the dipion transitions are expected to mainly proceed through the real processes $\Upsilon(5S)\to B^{(*)}\bar{B}^{(*)}$ and $B^{(*)}\bar{B}^{(*)}\to \Upsilon(1S,2S,3S)\pi^+\pi^-$. We find that the energy distributions of $\Upsilon(1S,2S,3S)\pi^+\pi^-$ markedly differ from that of $\Upsilon(5S)\to B^{(*)}\bar{B}^{(*)}$. In particular, the resonance peak will be pushed up by about 7-20 MeV for these dipion transitions relative to the main hadronic decay modes. These predictions can be used to test the final state rescattering mechanism in hadronic transitions for heavy quarkonia above the open flavor thresholds.