Note on a sigma model connection with instanton dynamics

TL;DR

This paper explores a generalized linear sigma model incorporating two chiral nonets, revealing a new instanton-generated term related to scalar mesons and an excited eta' state, offering insights into low-lying meson spectra.

Contribution

It introduces a generalized linear sigma model with two chiral nonets to interpret an instanton-generated term with a novel physical meaning.

Findings

The new term is linked to an excited eta' state.

The model helps understand the spectrum of low-lying scalar mesons.

The instanton analysis produces a term with a different interpretation than the usual sigma model.

Abstract

It is well known that the instanton approach to QCD generates an effective term which looks like a three flavor determinant of quark bilinears. This has the right behavior to explain the unusual mass and mixing of the $\eta(958)$ meson, as is often simply illustrated with the aid of a linear SU(3) sigma model. It is less well known that the instanton analysis generates another term which has the same transformation property but does not have a simple interpretation in terms of this usual linear sigma model. Here we point out that this term has an interpretation in a generalized linear sigma model containing two chiral nonets. The second chiral nonet is taken to correspond to mesons having two quarks and two antiquarks in their makeup. The generalized model seems to be useful for learning about the spectrum of low lying scalar mesons which have been emerging in the last few years. The physics of the new term is shown to be related to the properties of an "excited" $\eta'$ state present in the generalized model and for which there are some experimental candidates.