Possible scenario of dynamical chiral symmetry breaking in the instanton liquid

Abstract

Based on simulations of the interacting instanton liquid model (IILM) with three-flavor quarks, we compute the free energy density of the QCD vacuum as a function of the quark condensate. We then evaluate the second derivative of the free energy density with respect to the quark condensate at the origin. This evaluation allows us to investigate whether chiral symmetry breaking in the IILM occurs in an anomaly-driven way. Such a breaking pattern of chiral symmetry has been proposed in a previous study to connect the QCD vacuum structure with meson properties, such as the mass of the sigma meson. We also perform the quenched simulations, in which no dynamical quarks interact with instantons. Comparing these results with the full calculations provides a better understanding of the pattern of chiral symmetry breaking in the IILM. We find that in the full IILM, chiral symmetry is dynamically broken in anomaly-driven way, whereas in the quenched IILM, it is broken through the ordinary mechanism. Based on these results, we suggest that chiral symmetry breaking in real QCD could also occur in an anomaly-driven way. Consequently, in phenomena where chiral symmetry breaking plays a crucial role, the anomaly effect may also have significant influence.