The anomaly-driven breaking of chiral symmetry in the NJL and the instanton liquid models

We investigate an anomaly-driven breaking of chiral symmetry based on the Nambu-Jona-Lasinio(NJL) model and the interacting instanton liquid model(IILM). In the NJL model, an enough strong quark attraction induces the spontaneous breaking of chiral symmetry. Furthermore, if we take into account an axial U(1) breaking term, although the attraction is weaker than its critical strength, the chiral symmetry can be broken spontaneously due to the existence of the axial U(1) anomaly effect – we call such a breaking an anomaly-driven breaking of chiral symmetry. On the other hand, it is also known that the anomaly effect is induced by the instantons. In order to reveal the properties of the anomaly-driven breaking from the viewpoints of the instanton QCD vacuum with the quarks, we reconsidered the chiral symmetry breaking based on the IILM. From the analogy of the NJL model, particularly what we expect is that the anomaly-driven breaking can be characterized by a behavior of the vacuum energy density in the small quark condensate region. Therefore, we calculate the vacuum energy density and the quark condensate as a function of the instanton density by using numerical simulations and analyze the quark condensate dependence of the vacuum energy density. We will show our simulation results and discuss their interpretation. [1]S. Kono, et al., PTEP2021, 093D02 (2021).