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

TL;DR

This paper constructs a comprehensive analytical model of the $$ scattering amplitude that aligns with experimental data and theoretical frameworks, supporting the four-quark nature of certain light scalar mesons.

Contribution

It develops an amplitude with regular analytical properties that simultaneously describes multiple scattering processes and decay data, incorporating meson mixing and chiral effects.

Findings

Data supports the four-quark structure of $$ mesons.

Amplitude matches results from chiral expansion, dispersion relations, and Roy equations.

The model describes scattering and decay processes consistently across a broad energy range.

Abstract

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, $\phi\to\pi^0\pi^0\gamma$ decay and $\pi\pi\to K\bar K$ reaction. The chiral shielding of the $\sigma (600)$ meson and 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 $-5 m_\pi^2 < s < 0.64$ GeV$^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations and the Roy equations.