Three - Meson Resonances in a Relativistic Faddeev - Type Approach

Three-body resonances are studied within the framework of a relativistic version of the Faddeev equations, in which the input two-body amplitudes are assumed to be separable. A first discussion concerns the simplest πππ and KK̄π systems in which only the ρ(765 MeV) or the K*(890 MeV) resonance is taken into account. Compared to preceding works on a similar subject, more flexible parametrizations are used, allowing us to consider a larger class of two-body interactions and to better understand the influence of the main parameters involved in the model. A more satisfactory agreement with experiment is also found in the three-pion case and this for more realistic two-body amplitudes. The success is less convincing for the KK̄π case, but this might be due to the neglect of the two-body KK̄ interaction. Finally the study of the Kππ case gives an insight into the constructive and destructive interference effects which can be observed when more than one two-body resonance is taken into account. We add in the Appendix some comments about the properties one can reasonably require for the input separable two-body amplitudes owing to potential theory or its relativistic generalizations.