Abstract
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.
Highlights
The QCD phase transition, involving the chiral symmetry restoration, is the major subject to understand the QCD vacuum structure present in the early Universe, and would provide hints for astrophysical consequences related to the QCD thermal history, such as the QCD axion
Of interest is that the meson spectroscopy gets corrected by the net nonperturbative flavor breaking effects around and above the critical temperature, where the scalar meson mass hierarchy is significantly altered by the presence of the anomaly-related flavor breaking
We find that around and above the chiral crossover, the topological susceptibility gets a nonperturbative flavor breaking via the surviving strange quark condensate, which cannot be detected by the chiral perturbation theory (ChPT), and significantly deviates from the dilute instanton gas prediction
Summary
The QCD phase transition, involving the chiral symmetry restoration, is the major subject to understand the QCD vacuum structure present in the early Universe, and would provide hints for astrophysical consequences related to the QCD thermal history, such as the QCD axion. Thereby, the topological susceptibility at high temperatures would be a crucial quantity to explore some (effective or partial) Uð1ÞA restoration in the presence of nonzero current quark masses, in relation to the hot-QCD θ vacuum structure, and the chiral symmetry restoration via quark condensates. As has been observed in several analyses on lattice simulations for finite tempeture QCD [8,9], thermal loop effects would cause a partial restoration of the chiral symmetry (or chiral crossover) at the (pseudo) critical temperature, where only the lightest l quark condensate hlli drops more quickly than the strange quark hssi does This implies a nonperturbative flavor breaking generated in hot-QCD. The Uð1ÞA breaking dictated by nonzero topological susceptibility is catalyzed by the nonperturbative strange quark condensate at around the chiral crossover criticality, which may account for the tension in the effective restoration of the Uð1ÞA symmetry currently observed on lattices near the chiral limit with two flavors [13,14,15,16] and 2 þ 1 flavors [17,18,19]
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