Model-independent approach as a tool of studying chiral symmetry

A simultaneous analysis (in the model-independent approach) of the $\pi\pi$ scattering (from the threshold to 1.9 GeV) and of the $\pi\pi\to K\overline{K}$ process (from the threshold to $\sim$ 1.46 GeV) is carried out in channel with $I^GJ^{PC}=0^+0^{++}$. The existence of the $f_0(665)$ state with properies of the $\sigma$-meson is proved. An indication for the glueball nature of the $f_0(1500)$ is obtained. A minimum scenario of the simultaneous description of the processes $\pi\pi\to\pi\pi,K\overline{K}$ does without the ${f_0}(1370)$ resonance. A version including this state is also considered. In this case the ${f_0}(1370)$ resonance has the dominant $s{\bar s}$ component (the ratio of its coupling constant with the $\pi\pi$ channel to the one with the $K\overline{K}$ channel is 0.12). The coupling constants of the observed states with the $\pi\pi$ and $K\overline{K}$ systems and the $\pi\pi$ and $K\overline{K}$ scattering lengths are obtained. A parameterless description of the $\pi\pi$ background is given by allowance for the left-hand branch-point in the uniformizing variable. On the basis of this and of the fact that all the adjusted parameters for the $\pi\pi$ scattering are only the positions of poles describing resonances, it is concluded that our model-independent approach is a valuable tool for studying the realization schemes of chiral symmetry. The existence of the $f_0(665)$ state and the obtained $\pi\pi$-scattering length ($a_0^0\approx 0.27 m_{\pi^+}^{-1}$) seem to suggest the linear realization of chiral symmetry.