[en] The Dyson-Schwinger approach to mesons as quark-antiquark bound states produces a very satisfactory description of the whole light pseudoscalar nonet, both at zero and at finite temperatures [1]. Especially interesting is the temperature behavior of the η-η′ complex, where results for masses differ very greatly for various possible relationships between the chiral restoration temperature and the temperature of melting of the topological susceptibility χ. Namely, χ is connected with the quantity β in the η-η′ mass matrix as χ = β (2 +X ²)f²_π/6, where $X=f_{\mathrm{\pi <!--\; ??\; -->}}/f_{s\stackrel{¯<!--\; ??\; -->}{s}}$. For example, in certain regimes, the “mass” of η _NS , namely $M_{{\mathrm{\eta <!--\; ??\; -->}}_{NS}}$, for some temperatures becomes larger than $M_{{\mathrm{\eta <!--\; ??\; -->}}_{NS}}$, the “mass” of η _S [1]; that is, $M_{{\mathrm{\eta <!--\; ??\; -->}}_{NS}}$ and can $M_{{\mathrm{\eta <!--\; ??\; -->}}_{NS}}$ can cross.

[en] The Witten–Veneziano relation, or, alternatively, its generalization proposed by Shore, facilitates understanding and describing the complex of η and η"′ mesons. We present an analytic, closed-form solution to Shore's equations which gives results on the η–η"′ complex in full agreement with results previously obtained numerically. Although the Witten–Veneziano relation and Shore's equations are related, the ways they were previously used in the context of dynamical models to calculate η and η"′ properties, were rather different. However, with the analytic solution, the calculation can be formulated similarly to the approach through the Witten–Veneziano relation, and with some conceptual improvements. In the process, one strengthens the arguments in favor of a possible relation between the U_A(1) and SU_A(3) chiral symmetry breaking and restoration. To test this scenario, the experiments such as those at RHIC, NICA and FAIR, which extend the RHIC (and LHC) high-temperature scans also to the finite-density parts of the QCD phase diagram, should pay particular attention to the signatures from the η"′–η complex indicating the symmetry restoration

[en] Theoretical understanding of experimental results from relativistic heavy-ion collisions requires a microscopic approach to the behavior of QCD n-point functions at finite temperatures, as given by the hierarchy of Dyson-Schwinger equations, properly generalized within the Matsubara formalism. The convergence of sums over Matsubara modes is studied. The technical complexity of finite-temperature calculations mandates modeling. We present a model where the QCD interaction in the infrared, nonperturbative domain is modeled by a separable form. Results: for the mass spectrum of light quark flavors (u, d, s ) and for the pseudoscalar bound-state amplitudes at finite temperature are presented.