Combined analysis of processes ππ → ππ, KK, ηη and J=ψ decays and parameters of scalar mesons

The coupled processes - the ππ scattering, ππ → KK, ππ → ηη and J=ψ → θππ;θKK - are considered in the 2- and 3-channel approaches for studying f0-mesons. An applied modelindependent method of analysis is based on analyticity and unitarity and uses an uniformization procedure. It is shown that for obtaining correct values of the f0-meson parameters a one-channel dispersive equation (Roy's equations) analysis of the ππ scattering is not enough, even for the f0(600) which is in the elastic region of the ππ scattering below the thresholds of coupled channels. At least, the combined 3-channel analysis of data on coupled processes ππ →ππ;KK;ηη is needed, which is carried out adding the data on decays J=ψ →θππ;θKK from Mark III , DM2 and BES Collaborations. The latter allows us considerably to diminish possible scenarios of the resonance representations on the Riemann surface of the S-matrix, which give the similar description of the multi-channel ππ scattering and, however, the quite different parameters of some resonances. There are changed most considerably parameters of the f₀(600) - now the obtained mass is in some accordance with prediction by S. Weinberg on the basis of mended symmetry. Some spectroscopic implications from results of the analysis are discussed.