Scalar Mesons and Multichannel Amplitudes

Properties of scalar–isoscalar mesons are analysed in an unitary model using separable interactions in three decay channels: ππ , KK and an effective 2π2π. We obtain different solutions by fitting various data on the ππ and KK phase shifts and inelasticities including the CERN-Cracow-Munich measurements of the πp↑ → π+π−n reaction on a polarized target. Analytical structure of the meson-meson multichannel amplitudes is studied with a special emphasis on the role played by the S-matrix zeroes. S-matrix poles, located in the complex energy plane not too far from the physical region, are interpreted as scalar resonances. We see a wide f0(500) , a narrow f0(980) and a relatively narrow f0(1400) . In one of our solutions a resonance at about 1700 MeV is also found. Total, elastic and inelastic channel cross sections, branching ratios and coupling constants are evaluated and compared with available data. We construct an approximation to our model and show that the Breit-Wigner approach has a limited phenomenological applicability.