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

New solutions on the scalar – isoscalar ππ phase shifts are analysed together with previous KK results using a separable potential model of three coupled channels (ππ , KK and an effective 2π2π system). Model parameters are fitted to two sets of solutions obtained in a recent analysis of the CERN-Cracow-Munich measurements of the πp↑ → π +π−n reaction on a polarized target. A relatively narrow (90 – 180 MeV) scalar resonance f0(1400 − 1460) is found, in contrast to a much broader (Γ ≈ 500 MeV) state emerging from the analysis of previous unpolarized target data. The spectrum of scalar mesons is still not well known [1, 2]. The J = 0 meson nonet is not free from ambiguities and the internal structure of scalar mesons is rather controversial. Recently, many papers have been devoted to the study of the lowest scalar glueball [3–6]. In these articles properties of the f0(1500) resonance, observed recently by the Crystal Barrel Collaboration in pp̄ annihilations [7, 8], are analysed and interpreted. Furthermore, lattice QCD calculations predict the mass of the lowest scalar glueball to fall between 1500 and 1700 MeV [9, 10]. One should also mention increasing evidence for a broad scalar– isoscalar resonance σ [11–14] below 1000 MeV. This state reappeared as f0(400− 1200) in the last edition of the Particle Data Group [1], after 22 years of absence.