Analytical properties of the $\pi \pi$ scattering amplitude and the light scalar mesons

The $\pi \pi$ scattering amplitude with regular analytical properties in the $s$ complex plane has been constructed. It describes simultaneously the data on the $\pi \pi$ scattering, $\varphi \to {\pi }^0{\pi }^0\gamma$ decay and $\pi\pi\to K\bar K$reaction\mathrm{.}Thechiralshieldingofthe$\sigma (600)$ meson and it’s mixing with the $f_0(980)$ meson are taken into account also. The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons. The amplitude in the range $-5m_{\pi }^2<s<0.64$ GeV${}^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations and the Roy equations.