η′ and η mesons at high T when the

Abstract

The approach to the η 0-η 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 ð1Þ 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 ð1Þ transition with a smooth and gradual melting of anomalous mass contributions. In this way, we obtain a substantial decrease in the η 0 mass around the chiral transition temperature, but no decrease in the η mass. This is consistent with current empirical evidence.

Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the UA(1) Symmetry

“…[48], where the condensate of massless quarks ⟨qq⟩ 0 (T) was used, in Ref. [17] and here we follow Shore [69] masses. The smooth, crossover behavior around the pseudocritical temperature T c for the chiral transition (now confirmed at vanishing baryon density by lattice studies such as [44,67,68,70,71]), is obtained thanks to the DChSB condensates of realistically massive light quarks -i.e., the quarks with realistic explicit chiral symmetry breaking [17].…”

“…[17] and here we follow Shore [69] masses. The smooth, crossover behavior around the pseudocritical temperature T c for the chiral transition (now confirmed at vanishing baryon density by lattice studies such as [44,67,68,70,71]), is obtained thanks to the DChSB condensates of realistically massive light quarks -i.e., the quarks with realistic explicit chiral symmetry breaking [17]. In contrast, using in Equation (9) the massless-quark condensate ⟨qq⟩ 0 (which drops sharply to zero at T c ) instead of the "massive" ones, would dictate a sharp transition of the second order at T c [17,48] also for χ(T), illustrated in Figure 5 by the dotted curve.…”

“…Light pseudoscalar mesons can be studied by various methods. We have preferred using [17,[21][22][23][24][25][26][27][28][29][30][31][32] the relativistic bound-state approach to modeling nonperturbative QCD through Dyson-Schwinger equations (DSE), where, if approximations are consistently formulated, model DSE calculations also reproduce the correct chiral behavior of QCD. This is of paramount importance for descriptions of the light pseudoscalar mesons, which are quark-antiquark bound states but simultaneously also the (almost-)Goldstone bosons of DChSB of QCD.…”

“…Again, C ′ m is a very small correction term of higher orders in the small current quark masses m q (q = u, d, s), and we can neglect it in the present context, where we actually have a simpler task than finding T-dependence of the η and η ′ masses in Ref. [17]. Since it turns out that for determining the T-dependence of the mass of the QCD axion we do not need to find A, we set C ′ m = 0 in this paper throughout.…”

“…All values are in MeV (or the indicated 3rd or 4th powers of MeV). [17] 5. 49 The T-dependence of the resulting χ(T) 1 4 is given by the short-dashed black curve in Figure 6.…”