Role of U$_{A}$(1) breaking term in dynamical chiral symmetry breaking of chiral effective theories

TL;DR

This paper investigates how the U$_{A}$(1) anomaly influences spontaneous chiral symmetry breaking in effective theories, deriving mass relations and constraining sigma meson mass in the presence of anomaly-driven symmetry breaking.

Contribution

It demonstrates the role of the U$_{A}$(1) anomaly in spontaneous chiral symmetry breaking and derives a mass relation among flavor singlet mesons within effective models.

Findings

Large U$_{A}$(1) anomaly contribution can induce spontaneous chiral symmetry breaking.

Derived a mass relation among eta0 and sigma0 mesons in the linear sigma model.

Sigma0 meson mass should be less than about 800 MeV under anomaly-driven symmetry breaking.

Abstract

The spontaneous breaking of chiral symmetry is examined by chiral effective theories, such as the linear sigma model and the Nambu Jona-Lasinio (NJL) model. Indicating that sufficiently large contribution of the UA(1) anomaly can break chiral symmetry spontaneously, we discuss such anomaly driven symmetry breaking and its implication. We derive a mass relation among the SU(3) flavor singlet mesons, eta0 and sigma0, in the linear sigma model to be satisfied for the anomaly driven symmetry breaking in the chiral limit, and find that it is also supported in the NJL model. With the explicit breaking of chiral symmetry, we find that the chiral effective models reproducing the observed physical quantities suggest that the sigma0 meson regarded as the quantum fluctuation of the chiral condensate should have a mass smaller than an order of 800 MeV when the anomaly driven symmetry breaking takes place.