Existence of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>meson below 1 GeV and chiral symmetry

Abstract

On the basis of a simultaneous description of the isoscalar s-wave channel of $\ensuremath{\pi}\ensuremath{\pi}$ scattering (from the threshold up to 1.9 GeV) and the $\ensuremath{\pi}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}}K\overline{K}$ process (from the threshold to $\ensuremath{\sim}1.4$ GeV where the 2-channel unitarity is valid), a confirmation of the $\ensuremath{\sigma}$ meson at $\ensuremath{\sim}665$ MeV and an indication for the glueball nature of the ${f}_{0}(1500)$ state are obtained. These results are achieved in the model-independent approach consisting of the immediate application of such general principles as analyticity and unitarity to the analysis of experimental data. A parameterless description of the $\ensuremath{\pi}\ensuremath{\pi}$ background is first given by allowance for the left-hand branch point in the proper uniformizing variable. It is shown that the large $\ensuremath{\pi}\ensuremath{\pi}$ background, usually obtained, combines, in reality, the influence of the left-hand branch point and the contribution of a wide resonance at $\ensuremath{\sim}665$ MeV. The coupling constants of the observed states with the $\ensuremath{\pi}\ensuremath{\pi}$ and $K\overline{K}$ systems and lengths of the $\ensuremath{\pi}\ensuremath{\pi}$ and $K\overline{K}$ scattering are obtained. The existence of the ${f}_{0}(665)$ state and the obtained $\ensuremath{\pi}\ensuremath{\pi}$-scattering length ${(a}_{0}^{0}=0.27\ifmmode\pm\else\textpm\fi{}0.06,[{m}_{{\ensuremath{\pi}}^{+}}^{\ensuremath{-}1}])$ seem to suggest the linear realization of chiral symmetry.