The analytical $\pi\pi$ scattering amplitude and the light scalars

In this work we construct the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, which describes simultaneously the data on the $\pi\pi$ scattering, $\phi\to\pi^0\pi^0\gamma$ decay, and $\pi\pi\to K\bar K$ reaction. The chiral shielding of the $\sigma (600)$ meson and its mixing with the $f_0(980)$ meson are also taken into account. The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons. The amplitude in the range $-5 m_\pi^2 < s < 0.64$ GeV$^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.