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

Abstract

Peculiarities of obtaining parameters for broad multi-channel resonances from data are discussed analyzing the experimental data on processes $\pi \pi \to \pi \pi ,K\bar{K}$ in the $I^G{J}^{PC}=0^{+}{0}^{++}$ 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 $\pi \pi$ scattering data from the threshold to 1.89 GeV with parameters of resonances cited in the PDG tables as preferred. However, in this case, first, representation of the $\pi \pi$ background is unsatisfactory; second, the data on the coupled process $\pi \pi \to K\bar{K}$ are not well described even qualitatively above 1.15 GeV when using the resonance parameters from the only $\pi \pi$ scattering analysis. The combined analysis of these coupled processes is needed, which is carried out satisfactorily. Then both above-indicated flaws, related to the analysis of solely the $\pi \pi$-scattering, are cured. The most remarkable change of parameters with respect to the values of only $\pi \pi$ scattering analysis appears for the mass of the $f_0(600)$ which is now in some accordance with the Weinberg prediction on the basis of mended symmetry and with an analysis using the large-$N_c$ consistency conditions between the unitarization and resonance saturation. The obtained $\pi \pi$-scattering length $a_0^0$ in case when we restrict to the analysis of the $\pi \pi$ scattering or consider so-called A-solution (with a lower mass and width of $f_0(600)$ meson) agrees well with prediction of chiral perturbation theory (ChPT) and with data extracted at CERN by the NA48/2 Collaboration from the analysis of the $K_{e4}$ decay and by the DIRAC Collaboration from the measurement of the ${\pi }^{+}{\pi }^{-}$ lifetime.

21 pages, 3 figures, 6 tables

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• Improvement of multichannel amplitudes for the pion-pion scattering using the dispersion relations
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• The interference effects of multi-channel pion-pion scattering contributions to the final states of $\Psi$- and ${\rm Y}$-meson family decays