Paper detail

The effect of multi-channel pion-pion scattering in decays of the $Υ$-family mesons

The effect of isoscalar S-wave multi-channel pion-pion scattering ($ππ\toππ,K\bar{K},ηη$) is considered in the analysis of data on decays of the $Υ$-meson family -- $Υ(2S)\toΥ(1S)ππ$, $Υ(3S)\toΥ(1S)ππ$ and $Υ(3S)\toΥ(2S)ππ$. 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 $J/ψ\toϕ(ππ, K\bar{K})$, $ψ(2S)\to J/ψ(ππ)$. Results of the analysis confirm all our earlier conclusions on the scalar mesons. It is also shown that in the final states of the $Υ$-meson family decays (except for the $ππ$ scattering) the contribution of the coupled processes, e.g., $K\bar{K}\toππ$, 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.