Masses and widths of scalar–isoscalar multi-channel resonances from data analysis

Abstract

The peculiarities of obtaining parameters for broad multi-channel resonances from data are discussed, analyzing the experimental data on processes in the IGJPC = 0+0++ channel in a model-independent approach based on analyticity and unitarity, and using an uniformization procedure. We show that it is possible to obtain a good description of the ππ scattering data from the threshold to 1.89 GeV with parameters of resonances cited in the Particle Data Group tables as preferred. However, in this case, first, the representation of the ππ background is unsatisfactory; second, the data on the coupled process are not well described even qualitatively above 1.15 GeV when using the resonance parameters from only the ππ scattering analysis. The combined analysis of these coupled processes is needed, and is carried out satisfactorily. Then, both of the above-indicated issues related to the analysis of ππ scattering only are overcome. The most remarkable change of parameters with respect to the values of the ππ scattering only analysis appears for the mass of the f0(600), which is now in some accordance with the Weinberg prediction on the basis of mended symmetry and with an analysis using the large-Nc consistency conditions between the unitarization and resonance saturation. The obtained ππ scattering length , in the case where we are restricted to the analysis of the ππ scattering or where we consider the so-called A-solution (with a lower mass and width of f0(600) meson), agrees well with the prediction of the chiral perturbation theory and with data extracted at CERN by the NA48/2 collaboration from the analysis of the Ke4 decay and by the DIRAC collaboration from the measurement of the π+π− lifetime.