The effect of multi-channel pion-pion scattering in decays of the $\hat{I}\yen$-family mesons

Abstract

The effect of isoscalar S-wave multi-channel pion-pion scattering ($\ddot{I}€\ddot{I}€\to \ddot{I}€\ddot{I}€,K\bar{K},\hat{I}\cdot \hat{I}\cdot$) is considered in the analysis of data on decays of the $\hat{I}\yen$-meson family -- $\hat{I}\yen (2S)\to \hat{I}\yen (1S)\ddot{I}€\ddot{I}€$, $\hat{I}\yen (3S)\to \hat{I}\yen (1S)\ddot{I}€\ddot{I}€$ and $\hat{I}\yen (3S)\to \hat{I}\yen (2S)\ddot{I}€\ddot{I}€$. The analysis, which aims at studying the scalar mesons, is performed jointly considering the multi-channel pion-pion scattering, which is described in our model-independent approach based on analyticity and unitarity and using an uniformizing variable method, and the charmonium decay processes $J/\ddot{I}ˆ\to \ddot{I}•(\ddot{I}€\ddot{I}€,K\bar{K})$, $\ddot{I}ˆ(2S)\to J/\ddot{I}ˆ(\ddot{I}€\ddot{I}€)$. Results of the analysis confirm all our earlier conclusions on the scalar mesons. It is also shown that in the final states of the $\hat{I}\yen$-meson family decays (except for the $\ddot{I}€\ddot{I}€$ scattering) the contribution of the coupled processes, e.g., $K\bar{K}\to \ddot{I}€\ddot{I}€$, is important even if these processes are energetically forbidden. This is in accordance with our previous conclusions on the wide resonances: If a wide resonance cannot decay into a channel which opens above its mass but the resonance is strongly connected with this channel (e.g. the $f_0(500)$ and the $K\bar}$ channel), one should consider this resonance as a multi-channel state with allowing for the indicated channel taking into account the Riemann-surface sheets related to the threshold branch-point of this channel and performing the combined analysis of the considered and coupled channels.

Talk at the HSQCD 2014 -- Hadron Structure and QCD: from LOW to HIGH energies, Gatchina, Russia, July 1 -- 5, 2014. 11 pages, 24 figures, 3 tables