On the nature of $f_0$ mesons below 1.9 GeV and lower scalar nonets

Abstract

The combined 3-channel analysis of experimental data on the coupled processes $\pi\pi\to\pi\pi,K\bar{K},\eta\eta$ is carried out in the channel with the vacuum quantum numbers. An approach, using only first principles (analyticity and unitarity) and the uniformizing variable, is applied. Definite indications of the QCD nature of the $f_0$ resonances below 1.9 GeV are obtained, among them a surprising indication for $f_0(980)$ to be the $\eta\eta$ bound state. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.