Three channel model of meson-meson scattering and scalar meson spectroscopy

New solutions on the scalar – isoscalar $\pi \pi$ phase shifts are analysed together with previous $K\bar{K}$ results using a separable potential model of three coupled channels ($\pi \pi$, $K\bar{K}$ and an effective $2\pi 2\pi$ system). Model parameters are fitted to two sets of solutions obtained in a recent analysis of the CERN-Cracow-Munich measurements of the $\pi^- p_{\uparrow} \to \pi^+ \pi^- n$ reaction on a polarized target. A relatively narrow (90 – 180 MeV) scalar resonance $f_0(1400-1460)$ is found, in contrast to a much broader ($\mathrm{\Gamma }\approx 500$ MeV) state emerging from the analysis of previous unpolarized target data.