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

TL;DR

This paper constructs a comprehensive analytical model for the $CC$ scattering amplitude that aligns with experimental data and supports the four-quark structure of light scalar mesons like $CC$ and $f_0(980)$, integrating multiple theoretical approaches.

Contribution

It develops a regular analytical $CC$ scattering amplitude that incorporates data, meson mixing, and chiral symmetry considerations, advancing understanding of light scalar mesons.

Findings

Amplitude agrees with experimental data on scattering and decay processes.

Supports the four-quark nature of $CC$ and $f_0(980)$ mesons.

Consistent with chiral expansion, dispersion relations, and Roy equations.

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, $\phi\to\pi^0\pi^0\gamma$ 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.