Existence of the sigma-meson below 1 GeV and the f0(1500) glueball

The isoscalar s-waves of the pi pi scattering (from the threshold up to 1.9 GeV) and of the pi pi --> K (K) over bar process (from the threshold to si milar to 1.46 GeV) are analyzed simultaneously in the model-independent app roach. A confirmation of the sigma -meson at similar to 665 MeV and an indi cation for the glueball nature of the f(o)(1500) state are obtained. It is shown that the large pi-pi -background, usually obtained, combines, in real ity, the influence of the left-hand branchpoint and the contribution of a w ide resonance at similar to 665 MeV. A minimum scenario of the simultaneous description of the processes pi pi --> pi pi, K (K) over bar does wihtout the f(o)(1370) resonance. A version including this state is also considered . In this case the f(o)(1370) resonance has the dominant s (s) over bar com ponent (the ratio of its coupling constant with the pi pi channel to the on e with the K (K) over bar channel is 0.12). The coupling constants of the o bserved states with the pi pi and K (K) over bar systems and the pi pi and K (K) over bar scattering lengths are obtained.