The role of the UA(1) breaking term in dynamical chiral symmetry breaking of chiral effective theories

Abstract

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. We discuss the properties of the sigma meson regarded as the quantum fluctuation of the chiral condensate when the chiral symmetry is spontaneously broken, mainly by the U$_{A}$(1) anomaly. We derive a mass relation among the SU(3) flavor singlet mesons, $\eta_{0}$ and $\sigma_{0}$, 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 show that both of the chiral effective models reproducing the observed physical quantities suggest that the $\sigma_{0}$ meson should have a mass smaller than $\sim$800 MeV when anomaly-driven symmetry breaking takes place.