Extending our earlier treatments of π 0 , η c and η b , we study the η-η ′ system and its γγ decays using a model which is a leading version of the consistently coupled Schwinger-Dyson (SD) and Bethe-Salpeter (BS) approach. The electromagnetic interactions are incorporated through a (generalized) impulse approximation consistent with this bound-state approach, so that the Ward-Takahashi identities of QED are preserved when quarks are dynamically dressed. To overcome some of the limitations due to the ladder approximation, we introduce a minimal extension to the bound-state approach employed, so that the U A (1) problem is avoided. Pointing out which of our predictions hold in the coupled SD-BS approach in general, and which are the consequences of the specific, chosen model, we present the results for the axial-current decay constants of η 8 , η 0 , and of their physical combinations η and η ′ , the results for the γγ-decay constants of η 0 and η 8 , for the two-photon decay widths of η and η ′ , and for the mixing-independent R-ratio constructed from them.

We survey various U A (1) problems and attempt to resolve the two puzzles related to the eta mesons that have experimental verification. Specifically, we first explore the Goldstone structure of the η and η ′ mesons in the context of η-η ′ mixing using ideas based on QCD. Then we study the eta decays η → 3π 0 , η ′ → 3π 0 and η ′ → ηππ. Finally we arrive at essentially the same picture in the dynamical scheme based on consistently coupled Schwinger-Dyson and Bethe-Salpeter integral equations. This chirally well-behaved bound-state approach clarifies the distinction between the usual axial-current decay constants and the γγ decay constants in the η-η ′ complex. Allowing for the effects of the SU(3) flavor symmetry breaking in the quark-antiquark annihilation, leads to the improved η-η ′ mass matrix.

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.

We discuss and propose the minimal generalization of the Witten-Veneziano relation to finite temperatures, prompted by STAR and PHENIX experimental results on the multiplicity of 0 mesons. After explaining why these results show that the zero-temperature Witten-Veneziano relation cannot be straightforwardly extended to temperatures T too close to the chiral restoration temperature T Ch and beyond, we find the quantity which should replace, at T > 0, the Yang-Mills topological susceptibility appearing in the T ¼ 0 Witten-Veneziano relation, in order to avoid the conflict with experiment at T > 0. This is illustrated through concrete T-dependences of pseudoscalar meson masses in a chirally well-behaved, Dyson-Schwinger approach, but our results and conclusions are of a more general nature and, essentially, model-independent.