Chiral Nonet Mixing in pi pi Scattering

TL;DR

This paper models pi pi scattering using a generalized linear sigma model with two scalar and pseudoscalar nonets, incorporating mixing and unitarity to match experimental data up to 1 GeV, revealing insights into scalar meson poles.

Contribution

It introduces a model with two scalar and pseudoscalar nonets and studies their mixing and scattering amplitudes, providing a more realistic description of scalar mesons compared to traditional models.

Findings

Identification of the sigma meson pole around 500 MeV.

Observation of the f0(980) pole near 1 GeV.

Detection of additional poles in the 1-2 GeV region.

Abstract

Pion pion scattering is studied in a generalized linear sigma model which contains two scalar nonets (one of quark-antiquark type and the other of diquark-antidiquark type) and two corresponding pseudoscalar nonets. An interesting feature concerns the mixing of the four isosinglet scalar mesons which yield poles in the scattering amplitude. Some realism is introduced by enforcing exact unitarity via the K-matrix method. It is shown that a reasonable agreement with experimental data is obtained up to about 1 GeV. The poles in the unitarized scattering amplitude are studied in some detail. The lowest pole clearly represents the sigma meson (or f0(600)) with a mass and decay width around 500 MeV. The second pole invites comparison with the f0(980) which has a mass around 1 GeV and decay width around 100 MeV. The third and fourth poles, resemble some of the isosinglet state in the complicated 1-2 GeV region. Some comparison is made to the situation in the usual SU(3) linear sigma model with a single scalar nonet.