Inverse Mass Hierarchy of Light Scalar Mesons Driven by AnomalyInduced 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 antiquark ($q\bar{q}$ mesons). The source is provided by the SU(3)flavor symmetrybreaking induced by U(1) axial anomaly. In particular, the anomaly term including the explicitchiral symmetrybreaking 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 anomalyinduced explicitchiral symmetrybreaking 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, $s\bar{s}$.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.09146
 Bibcode:
 2019arXiv191009146K
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 15 pages, 2 figures