Inverse Mass Hierarchy of Light Scalar Mesons Driven by Anomaly-Induced Flavor Breaking

TL;DR

This paper introduces a new mechanism involving anomaly-induced flavor breaking to explain the inverse mass hierarchy of light scalar mesons below 1 GeV, aligning theoretical predictions with observed spectra.

Contribution

It develops a linear sigma model incorporating anomaly-induced explicit-chiral symmetry-breaking to reproduce the inverse hierarchy of scalar meson masses.

Findings

Successfully reproduces the inverse mass hierarchy of light scalar mesons.

Predicts the quark content of f0(500) and f0(980) mesons.

Highlights the role of U(1) axial anomaly in meson mass spectrum.

Abstract

We propose a novel mechanism to reproduce the observed mass hierarchy for the scalar mesons lighter than 1 GeV (called the inverse hierarchy) regarding them as mesons made of a quark and an anti-quark ($q\bar{q}$ mesons). The source is provided by the SU(3)-flavor symmetry-breaking induced by U(1) axial anomaly. In particular, the anomaly term including the explicit-chiral symmetry-breaking plays a significant role for the light scalar meson spectrum. To be concrete, we construct a linear sigma model for the scalar mesons of $q\bar{q}$ type together with their pseudoscalar chiral partners, including an anomaly-induced explicit-chiral symmetry-breaking term. We find that, due to the proposed mechanism, the inverse hierarchy, i.e., $m\left[ a_0 (980) \right] \simeq m\left[ f_0 (980) \right] > m \left[ K_0^\ast (700) \right] > m \left[ f_0(500) \right]$ is indeed realized. Consequently, the quark content of $f_0 (500)$ is dominated by the isoscalar $\bar uu+ \bar dd$ component, and $f_0 (980)$ is by the strange quark bilinear's, $s\bar{s}$.