Unitarized pseudoscalar meson scattering amplitudes from three flavor linear sigma models - art. no. 014031

The three flavor linear sigma model is studied as a "toy model" for underst anding the role of possible light scalar mesons in the pi pi. piK and pi et a scattering channels. The approach involves computing the tree level parti al wave amplitude for each channel and unitarizing by a simple K-matrix pre scription which does not introduce any new parameters. If the renormalizabl e version of the model is used there is only one free parameter. While this highly constrained version has the right general structure to explain pi p i scattering, it is "not quite" right. A reasonable fit can be made if the renormalizability (for the effective Lagrangian) is relaxed while chiral sy mmetry is maintained. The occurrence of a Ramsauer-Townsend mechanism for t he f(o)(980) region naturally emerges. The effect of unitarization is very important and leads to "physical" masses for the scalar nonet all less than about 1 GeV. The a(o)(1450) and K-o*(1430) appear to be "outsiders" in thi s picture and to require additional fields. Comparison is made with a scatt ering treatment using a more general nonlinear sigma model approach. In add ition some speculative remarks and a highly simplified larger toy model are devoted to the question of the quark substructure of the light scalar meso ns.