Mamiya Kawaguchi, Shinya Matsuzaki, Akio Tomiya
Physical Review D, 103(5), Mar 25, 2021
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 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 pseudo-critical temperature, consistently with lattice
observations. We find following features regarding the flavor breaking eminent
around and above the pseudo-critical 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; vi) the U(1)_A breaking is enhanced by the
strange quark condensate, which may account for the tension in the effective
U(1)_A restoration observed on lattices with two flavors and 2+1 flavors near
the chiral limit.