Existence of the $σ$-meson below 1 GeV and $f_0(1500)$ glueball
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On the basis of a simultaneous description of the isoscalar s-wave channel of the $ππ$ scattering (from the threshold up to 1.9 GeV) and of the $ππ\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV) in the model-independent approach, a confirmation of the $σ$-meson at $\sim$ 665 MeV and an indication for the glueball nature of the $f_0(1500)$ state are obtained. It is shown that the large $ππ$-background, usually obtained, combines, in reality, the influence of the left-hand branch-point and the contribution of a very wide resonance at $\sim$ 665 MeV. The coupling constants of the observed states with the $ππ$ and $K\bar{K}$ systems and lengths of the $ππ$ and $K\bar{K}$ scattering are obtained.
13 pages, 3 figures, LaTex; submitted to Physics Letters B
13 pages, 3 figures, LaTex; submitted to Physics Letters B