${\eta }^{\prime }$ and $\eta$ mesons at high T when the U_A(1) and chiral symmetry breaking are tied

Abstract

The approach to the eta'-eta complex employing chirally well-behaved quark-antiquark bound states and incorporating the non-Abelian axial anomaly of QCD through the generalization of the Witten-Veneziano relation, is extended to finite temperatures. Employing the chiral condensate has led to a sharp chiral and U_A(1) symmetry restoration, but with the condensates of quarks with realistic explicit chiral symmetry breaking, which exhibit a smooth, crossover chiral symmetry restoration in qualitative agreement with lattice QCD results, we get a crossover U_A(1) transition, with smooth and gradual melting of anomalous mass contributions. This way we obtain a substantial drop of the eta' mass around the chiral transition temperature, but no eta mass drop. This is consistent with the present empirical evidence.

arXiv comment11 pages, 5 figures. Revised version to be published in Phys. Rev. D. New references and some text corresponding to them added, the second section shortened, some typos corrected

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• Bethe-Salpeter kernel and properties of strange-quark mesons
• Fate of the ${\eta }^{\prime }$ in the Quark Gluon Plasma
• One-loop constituent quark contributions to the vector and axial-vector meson curvature mass
• New Insight about the Effective Restoration of U_A(1) Symmetry
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