Relativistic Effects in the Scalar Meson Dynamics

Abstract

A separable potential formalism is used to describe the $\pi \pi$ and $K\overline{K}$ interactions in the scalar-isoscalar states in the energy range from the $\pi \pi$ threshold up to 1.4 GeV. Introduction of relativistic propagators into a system of Lippmann-Schwinger equations leads to a very good description of the data (${\chi }^2=0.93$ per one degree of freedom). Three poles are found in this energy region: fo(500) ($M=506\pm 10$ MeV, $\Gamma =494\pm 5$ MeV), fo(975) ($M=973\pm 2$ MeV, $\Gamma =29\pm 2$ MeV) and fo(1400) ($M=1430\pm 5$ MeV, $\Gamma =145\pm 25$ MeV). The fo(975) state can be interpreted as a $K\overline{K}$ bound state. The fo(500) state may be associated with the often postulated very broad scalar resonance under the $K\overline{K}$ threshold (sometimes called $\sigma$ or $ϵ$ meson). The scattering lengths in the $\pi \pi$ and $K\overline{K}$ channels have also been obtained. The relativistic approach provides qualitatively new results (e.g. the appearance of the fo(500)) in comparison with previously used nonrelativistic approach.

Comments: 30 pages in LaTeX + 5 figures available on request. Preprint Orsay No IPNO/TH 93-31