The analytical $ππ$ scattering amplitude and the light scalars

In this work we construct the $ππ$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, which describes simultaneously the data on the $ππ$ scattering, $ϕ\toπ^0π^0γ$ decay, and $ππ\to K\bar K$ reaction. The chiral shielding of the $σ(600)$ 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 $σ(600)$ and $f_0(980)$ mesons. The amplitude in the range $-5 m_π^2 < s < 0.64$ GeV$^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.

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