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

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 $\bar{u}u+\bar{d}d$ component, and $f_0(980)$ is by the strange quark bilinear's, $s\bar{s}$.

arXiv comment15 pages, 2 figures

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