Unitarized pseudoscalar meson scattering amplitudes from three flavor linear sigma models

Journal Article · Sun Jul 01 04:00:00 EDT 2001 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.64.014031· OSTI ID:40204492

Black, Deirdre; Fariborz, Amir H; Moussa, Sherif; Nasri, Salah; Schechter, Joseph

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 substructure of the light scalar mesons.

• Sponsoring Organization: (US)
• OSTI ID: 40204492
• Journal Information: Physical Review D, Journal Name: Physical Review D Journal Issue: 1 Vol. 64; ISSN 0556-2821
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
CHIRAL SYMMETRY
K MATRIX
LAGRANGIAN FUNCTION
PARTIAL WAVES
PSEUDOSCALAR MESONS
SCALAR MESONS
SCATTERING
SCATTERING AMPLITUDES
SIGMA MODEL