Global aspects of the scalar meson puzzle

TL;DR

This paper uses a generalized linear sigma model to explore the quark structure of scalar and pseudoscalar mesons, revealing that lighter scalars have significant four-quark components while pseudoscalars are mainly quark-antiquark pairs, with detailed SU(3) flavor breaking effects.

Contribution

It introduces a model that predicts the quark content of mesons without prior assumptions, highlighting the contrasting quark structures of scalars and pseudoscalars and analyzing SU(3) flavor breaking effects.

Findings

Lighter pseudoscalars are primarily quark-antiquark states.

Lighter scalars have large four-quark admixtures.

SU(3) flavor breaking effects refine but do not change the overall quark structure pattern.

Abstract

A generalized linear sigma model for low energy QCD is employed to study the quark structure of eight low lying scalar isomultiplets as well as eight low lying pseudoscalar isomultiplets. The model, building on earlier work, assumes the possible mixing of quark anti-quark states with others made of two quarks and two antiquarks. No {\it a priori} assumption is made about the quark contents of the states, which emerge as predictions. An amusing and contrasting pattern for the quark structure is found; the lighter conventional pseudoscalars are, as expected, primarily of two quark type whereas the lighter scalars have very large four quark admixtures. The new feature of the present paper compared to earlier ones in this series involves the somewhat subtle and complicated effects of SU(3) flavor breaking. They do not alter the general pattern of two quark vs. four quark mixing obtained in the SU(3)symmetric case but, of course, give a more detailed picture.