Analysis of nonperturbative flavor violation at chiral crossover criticality in QCD

We discuss the violation of quark-flavor symmetry at high temperatures, induced from nonperturbative thermal loop corrections and axial anomaly, based on a three-flavor linear-sigma model including an SU(3) flavor violation induced by U(1)(A) anomaly which we call an axial-anomaly induced-flavor breaking term. We employ a nonperturbative analysis following the Cornwall-Jackiw-Tomboulis formalism, and show that the model undergoes a chiral crossover with a pseudocritical temperature, consistently with lattice observations. We find following features regarding the flavor breaking eminent around and above the pseudocritical temperature: (i) up-and down-quark condensates drop faster than the strange quark's toward the criticality, but still keep nonzero value even going far above the critical temperature; (ii) the introduced anomaly-related flavor-breaking effect acts as a catalyzer toward the chiral restoration, and reduces the amount of flavor breaking in the up, down and strange quark condensates; (iii) a dramatic deformation for the meson flavor mixing structure is observed, in which the anomaly-induced favor breaking is found to be almost irrelevant; (iv) the meson spectroscopy gets corrected by the net nonperturbative flavor breaking effects, where the scalar meson mass hierarchy (inverse mass hierarchy) is significantly altered by the presence of the anomaly-related flavor breaking; (v) the topological susceptibility significantly gets the contribution from the surviving strange quark condensate, which cannot be dictated by the chiral perturbation theory, and deviates from the dilute instanton gas prediction. There the anomaly-induced flavor breaking plays a role of the destructive interference for the net flavor violation, as in the flavor breaking in the quark condensates; (vi) the U(1)(A) breaking signaled by nonzero topological susceptibility is enhanced by the nonperturbative strange quark condensate, which may account for the tension in the effective restoration of the U(1)(A) symmetry currently observed on lattices with two flavors and 2 + 1 flavors near the chiral limit. Our founding critical natures can be checked in the future lattice simulations, and will give some implications to the thermal history of QCD axion.