Existence of the $\sigma$-meson below 1 GeV and $f_0(1500)$ glueball

Abstract

On the basis of a simultaneous description of the isoscalar s-wave channel of the $\pi \pi$ scattering (from the threshold up to 1.9 GeV) and of the $\pi \pi \to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV) in the model-independent approach, a confirmation of the $\sigma$-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 $\pi \pi$-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 $\pi \pi$ and $K\bar{K}$ systems and lengths of the $\pi \pi$ and $K\bar{K}$ scattering are obtained.

Comments: 13 pages, 3 figures, LaTex; submitted to Physics Letters B