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We discuss the violation of quark-flavor symmetry at high temperatures,induced from nonperturbative thermal loop corrections and axial anomaly, basedon a three-flavor linear-sigma model including an axial-anomaly induced-flavorbreaking term. We employ a nonperturbative analysis following theCornwall-Jackiw-Tomboulis formalism, and show that the model undergoes a chiralcrossover with a pseudo-critical temperature, consistently with latticeobservations. We find following features regarding the flavor breaking eminentaround and above the pseudo-critical temperature: i) up-and down-quarkcondensates drop faster than the strange quark's toward the criticality, butstill keep nonzero value even going far above the critical temperature; ii) theintroduced anomaly-related flavor-breaking effect acts as a catalyzer towardthe chiral restoration, and reduces the amount of flavor breaking in the up,down and strange quark condensates; iii) a dramatic deformation for the mesonflavor mixing structure is observed, in which the anomaly-induced favorbreaking is found to be almost irrelevant; iv) the meson spectroscopy getscorrected by the net nonperturbative flavor breaking effects, where the scalarmeson mass hierarchy (inverse mass hierarchy) is significantly altered by thepresence of the anomaly-related flavor breaking; v) the topologicalsusceptibility significantly gets the contribution from the surviving strangequark condensate, which cannot be dictated by the chiral perturbation theory,and deviates from the dilute instanton gas prediction. There theanomaly-induced flavor breaking plays a role of the destructive interferencefor the net flavor violation; vi) the U(1)_A breaking is enhanced by thestrange quark condensate, which may account for the tension in the effectiveU(1)_A restoration observed on lattices with two flavors and 2+1 flavors nearthe chiral limit.

Analysis on nonperturbative flavor violation at chiral crossover criticality in QCD