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

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.