Document Type
Article
Date
12-21-2000
Language
English
Disciplines
Physics
Description/Abstract
The three flavor linear sigma model is studied as a ``toy model'' 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 scatteirng, it is ``not quite'' right. A reasonable fit can be made if the renormalizability (for the {\it 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.
Recommended Citation
Schechter, Joseph; Black, Deirdre; Fariborz, Amir H.; Moussa, Sherif; and Nasri, Salah, "Unitarized Pseudoscalar Meson Scattering Amplitudes in Three Flavor Linear Sigma Models" (2000). Physics - All Scholarship. 287.
https://surface.syr.edu/phy/287
Source
Harvested from Arxiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
Submitted to Phys. Rev. D. 45 pages, 12 figures More information available at http://arxiv.org/abs/hep-ph/0012278