We investigate the "family" relationship of a possible scalar nonet composed of the a 0 (980), the f 0 (980) and the σ and κ type states found in recent treatments of ππ and πK scattering. We work in the effective Lagrangian framework, starting from terms which yield "ideal mixing" according to Okubo's original formulation. It is noted that there is another solution corresponding to dual ideal mixing which agrees with Jaffe's picture of scalars as qqqq states rather than qq states. At the Lagrangian level there is no difference in the formulation of the two cases (other than the numerical values of the coefficients). In order to agree with experiment, additional mass and coupling terms which break ideal mixing are included. The resulting model turns out to be closer to dual ideal mixing than to conventional ideal mixing; the scalar mixing angle is roughly −17 • in a convention where dual ideal mixing is 0 • .

A generalized linear sigma model for low energy QCD is employed to study the quark structure of eight low lying scalar isomultiplets as well as eight low lying pseudoscalar isomultiplets. The model, building on earlier work, assumes the possible mixing of quark anti-quark states with others made of two quarks and two antiquarks. No a priori assumption is made about the quark contents of the states, which emerge as predictions. An amusing and contrasting pattern for the quark structure is found; the lighter conventional pseudoscalars are, as expected, primarily of two quark type whereas the lighter scalars have very large four quark admixtures. The new feature of the present paper compared to earlier ones in this series involves the somewhat subtle and complicated effects of SU (3) flavor breaking. They do not alter the general pattern of two quark vs. four quark mixing obtained in the SU(3)symmetric case but, of course, give a more detailed picture.

We study scattering in a model which starts from the tree diagrams of a non-linear chiral Lagrangian including appropriate resonances. Previously, models of this type were applied to and K scattering and were seen to require the existence of light scalar (560) and (900) mesons and to be consistent with the f 0 (980). The present calculation extends this to include the a 0 (980), thereby completing a possible nonet of light scalars, all ''seen'' in the same manner. We note that, at the initial level, the channel is considerably cleaner than the and K channels for the study of light scalars. This is because the large competing effects of vector meson exchange and ''current-algebra'' contact terms are absent. The simplicity of this channel enables us to demonstrate the closeness of our exactly crossing symmetric amplitude to a related exactly unitary amplitude. The calculation is also extended to higher energies in order to let us discuss the role played by the a 0 (1450) resonance.

The three flavor linear sigma model is studied as a "toy model" for understanding the role of possible light scalar mesons in the ππ, πK and πη scattering channels. The approach involves computing the tree level partial wave amplitude for each channel and unitarizing by a simple K-matrix prescription which does not introduce any new parameters. If the renormalizable version of the model is used there is only one free parameter. While this highly constrained version has the right general structure to explain ππ scatteirng, it is "not quite" right. A reasonable fit can be made if the renormalizability (for the effective Lagrangian) is relaxed while chiral symmetry is maintained.The occurence of a Ramsauer Townsend mechanism for the f 0 (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 0 (1450) and K * 0 (1430) appear to be "outsiders" in this picture and to require additional fields. Comparison is made with a scattering treatment using a more general non-linear sigma model approach. In addition some speculative remarks and a highly simplified larger toy model are devoted to the question of the quark substructure of the light scalar mesons.