Existence and Properties of the $f_0(665)$ State and Chiral Symmetry

Abstract

On the basis of a simultaneous description of the isoscalar s-wave of $ππ$ scattering (from the threshold up to 1.9 GeV) and of $ππ\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV) in the model-independent approach, it is shown that there exists the $f_0(665)$ state with properies of the $σ$-meson, the glueball nature of $f_0(1500)$ is indicated, and the $f_0(1370)$ is assigned mainly to $s{\bar s}$ state. The coupling constants of the observed states with $ππ$ and $K\bar{K}$ systems and scattering lengths $a_0^0(ππ)$ and $a_0^0(K\bar{K})$ are calculated. The existence of the $f_0(665)$ state and the obtained $ππ$-scattering length ($a_0^0\approx 0.27 m_{π^+}^{-1}$) seem to suggest the linear realization of chiral symmetry.