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We study the temperature dependence of the pseudoscalar meson properties in a relativistic boundstate approach exhibiting the chiral behavior mandated by QCD. Concretely, we adopt the DysonSchwinger approach with a rank-2 separable model interaction. After extending the model to the strange sector and fixing its parameters at zero temperature, T = 0, we study the T -dependence of the masses and decay constants of all ground-state mesons in the pseudoscalar nonet. Of chief interest are η and η ′ . The influence of the QCD axial anomaly on them is successfully obtained through the Witten-Veneziano relation at T = 0. The same approach is then extended to T > 0, using lattice QCD results for the topological susceptibility. The most conspicuous finding is an increase of the η ′ mass around the chiral restoration temperature T Ch , which would suggest a suppression of η ′ production in relativistic heavy-ion collisions. The increase of the η ′ mass may also indicate that the extension of the Witten-Veneziano relation to finite temperatures becomes unreliable around and above T Ch . Possibilities of an improved treatment are discussed.

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1=N c expansion scheme. The parameters of the nonlocal model are refitted so that the physical values of the pion mass and the weak pion decay constant are obtained. The size of the 1=N c correction to the quark condensate is carefully studied and compared with the usual local Nambu-Jona-Lasinio model. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cutoff of the local model. The model is also applied to finite temperature. We find that the 1=N c corrections dominate the melting of the chiral condensate at low temperatures, T & 100 MeV, in agreement with chiral perturbation theory. On the other hand, the relative importance of the 1=N c corrections in the crossover regime depends on the parameter T 0 of the Polyakov-loop potential. For T 0 ¼ 270 MeV, corresponding to a fit of lattice data for pure gluodynamics, the correction terms are large and lead to a lowering of the chiral phase-transition temperature in comparison with the mean-field result. Near the phase transition the 1=N c expansion breaks down and a nonperturbative scheme is needed to include mesonic correlations in that regime. Lowering T 0 leads to a more rapid crossover even at the mean-field level and the unstable region for the 1=N c corrections shrinks. For T 0 & 220 MeV the temperatures of deconfinement and chiral restoration are practically synchronized.

The finite temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T_c the pressure is well described by the mean-field approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed.Comment: 11 pages, 4 figures; version accepted for publication in Yad. Fiz., text extended, 1 figure adde