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

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

Comments: 8 pages, 6 figures. The talk given by A.V. Kiselev at the International Seminar "Quarks-2010", Kolomna, Russia, June 6-12, 2010