$\eta'$ and $\eta$ mesons at high T when the U_A(1) and chiral symmetry breaking are tied

TL;DR

This paper investigates the behavior of eta and eta' mesons at high temperatures, showing a crossover U_A(1) symmetry restoration and a significant eta' mass reduction near the chiral transition, aligning with lattice QCD data.

Contribution

It extends the eta'-eta complex approach to finite temperatures, incorporating the axial anomaly and realistic quark effects, revealing a smooth U_A(1) symmetry restoration and eta' mass decrease.

Findings

Crossover U_A(1) transition with gradual anomalous mass melting

Significant eta' mass drop near the chiral transition

No eta mass drop observed

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.