Two chiral nonet model with massless quarks

TL;DR

This paper introduces a linear sigma model with two chiral nonets to explain the nature of light scalar mesons as four-quark states and their chiral partners, providing insights into low energy QCD phenomena.

Contribution

It presents a novel two nonet chiral model that accounts for mixing between two and four quark states, explaining the properties of light scalar mesons.

Findings

Light scalars have a large four quark content.

One light isosinglet scalar is exceptionally light.

Pion-pion scattering matches current algebra predictions.

Abstract

We present a detailed study of a linear sigma model containing one chiral nonet transforming under U(1)$_A$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-anti diquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an "excited" pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.