Parameters of scalar resonances from the combined analysis of data on processes $\pi\pi \to K\overline{K}, \eta\eta$ and J/ψ decays

A combined analysis of data on the isoscalar S -wave processes π π → π π , K K ¯ , η η and on decays J / ψ → ϕ π π , ϕ K K ¯ from the DM2, Mark III, and BES II Collaborations is performed to study f 0 mesons. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. In the analysis limited only to the multichannel π π -scattering data, two possible sets of parameters of the f 0 ( 500 ) were found: In both cases the mass was about 700 MeV but the total width was either about 680 or 1040 MeV. The extension of the analysis using only the DM2 and Mark III data on the J / ψ decays does not allow us to choose between these sets. However, the data from BES II on the di-pion mass distribution in the decay J / ψ → ϕ π + π − clearly prefer the wider f 0 ( 500 ) state. Spectroscopic implications from the results of the analysis are also discussed.