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

Abstract

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, $\varphi \to {\pi }^0{\pi }^0\gamma$ 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 $-5m_{\pi }^2<s<0.64$ GeV${}^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.

Comments: Published version: a few clarifications are added, the Editors corrections are taken into account