v 1 1 0 M ar 1 99 4 Relativistic effects in the scalar meson dynamics

A separable potential formalism is used to describe the ππ and KK interactions in the I G (J P C) = 0 + (0 ++) states in the energy range from the ππ threshold up to 1.4 GeV. Introduction of relativistic propaga-tors into a system of Lippmann-Schwinger equations leads to a very good description of the data (χ 2 = 0.93 per one degree of freedom). Three poles are found in this energy region: f 0 (975) state can be interpreted as a KK bound state. The f 0 (500) state may be associated with the often postulated very broad scalar resonance under the KK threshold (sometimes called σ or ǫ meson). The scattering lengths in the ππ and KK channels have also been obtained. The relativistic approach provides qualitatively new results * Unité de Recherche des Universités Paris 11 et Paris 6 associée au CNRS 1 (for example the appearance of the f 0 (500)) in comparison with previously used nonrelativistic approach. Interactions in both channels are attractive and have short range form factors. Scalar meson spectroscopy is still far from being well understood [1–4]. Since it was difficult to explain known properties of the I G (J P C) = 0 + (0 ++) states using a standard q ¯ q picture, other models treating the four-quark states [5, 6] or meson-meson molecules [7–11] have been invented. There is also a continuous search [12, 13] for scalar gluonium states which can be mixed with the quark states of the same quantum numbers. The nature of the f 0 (975) and a 0 (980) mesons is very controversial [14–17]. Closeness of their almost degenerated masses to the KK threshold energy constitutes an argument towards their interpretation as virtual bound KK states which are unstable due to the open ππ channel [10, 18–21]. In this article we extend the coupled channel formalism of Refs [18, 19] including some relativistic effects in both the ππ and KK decay channels of the scalar mesons. We use the relativistic propagators and the separable potentials in the Lippmann–Schwinger formalism. Such an approach has already been applied in the analysis of the pion-nucleon amplitudes [22] or in the studies of the Λ(1405) resonance structure [23, 24]. Our aim is to describe quantitatively the isoscalar s-wave ππ and the KK scattering data in a wide energy range starting from the ππ threshold up to 1.4 GeV. …