Abstract
The three flavor linear sigma model is studied as a {open_quotes}toy model{close_quotes} for understanding the role of possible light scalar mesons in the {pi}{pi}, {pi}K and {pi}{eta} 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 {pi}{pi} scattering, it is {open_quotes}not quite{close_quotes} right. A reasonable fit can be made if the renormalizability (for the effective Lagrangian) is relaxed while chiral symmetry is maintained. The occurrence of a Ramsauer-Townsend mechanism for the f{sub 0}(980) region naturally emerges. The effect of unitarization is very important and leads to {open_quotes}physical{close_quotes} masses for the scalar nonet all less than about 1 GeV. The a{sub 0}(1450) and K{sub 0}{sup *}(1430) appear to be {open_quotes}outsiders{close_quotes} in this picture and to require additional fields. Comparison is made with a scattering treatment using a more general nonlinear sigma model approach. In addition some speculative remarks and a highly simplified larger toy model are devoted to the question of the quark substructuremore » of the light scalar mesons.« less
Highlights
In the last few years there has been a revival of interest [1]- [27] in the possiblity that light scalar mesons like the sigma and kappa exist
Using Eq (1.17) we find that mBARE(κ) = 0.909 GeV, independent of whether we make the renormalizability restriction or not
The possible richness of the scalar meson system for further study is illustrated by the introduction of a larger toy model which includes two different M matrices
Summary
In the last few years there has been a revival of interest [1]- [27] in the possiblity that light scalar mesons like the sigma and kappa exist. Mann Levy two flavor linear sigma model [31] At tree level it yields essentially the same ππ scattering length which is the initial approximation in the chiral perturbation scheme. Compared to that scheme, which uses a non-linear Lagrangian of pions only [32], it is less convenient to systematically implement corrections It does contain a light scalar meson and it does provide the standard intuitive picture of spontaneous chiral symmetry breaking. Both plots of the predicted amplitudes compared with experiment and numerical. The possible richness of the scalar meson system for further study is illustrated by the introduction of a larger toy model which includes two different M matrices
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