Effect of coupled channels of the multi-channel pion-pion scattering in two-pion transitions of the $\Upsilon$ mesons

TL;DR

This paper analyzes how coupled-channel effects in multichannel pion-pion scattering influence the dipion mass spectra in bottomonium decays, confirming the role of scalar mesons through a unified scattering mechanism.

Contribution

It demonstrates that the dipion spectra in bottomonium decays can be explained by a unified multichannel scattering mechanism consistent with previous analyses of meson scattering and charmonia decays.

Findings

Dipion spectra explained by multichannel $\pi ext{ extpi}$ scattering

Results confirm earlier conclusions on scalar mesons

Multichannel amplitudes remain consistent across different processes

Abstract

The effect of isoscalar S-wave processes $\pi\pi\to\pi\pi,K\overline{K},\eta\eta$ is considered in the analysis of data (from the ARGUS, CLEO, CUSB, Crystal Ball, Belle, BABAR collaborations) on the bottomonia decays --- $\Upsilon(mS)\to\Upsilon(nS)\pi\pi$ ($m>n, m=2,3,4,5, n=1,2,3$). It is shown that the dipion mass spectra of these decays are explained by the unified mechanism related to the contribution of the multichannel $\pi\pi$ scattering in the final states of these reactions. Since in the analysis the multichannel $\pi\pi$-scattering amplitudes did not change in comparison with the ones in our combined analysis of data on the multichannel $\pi\pi$ scattering and on the charmonia decays --- $J/\psi\to\phi(\pi\pi, K\overline{K})$ and $\psi(2S)\to J/\psi(\pi\pi)$ (from the Crystal Ball, DM2, Mark II, Mark III, and BES II) --- the results confirm all our earlier conclusions on the scalar mesons.