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The Witten-Veneziano relation, or, alternatively, its generalization proposedby Shore, facilitates understanding and describing the complex of eta and eta'mesons. We present an analytic, closed-form solution to Shore's equations whichgives results on the eta-eta' complex in full agreement with results previouslyobtained numerically. Although the Witten-Veneziano relation and Shore'sequations are related, the ways they were previously used in the context ofdynamical models to calculate eta and eta' properties, were rather different.However, with the analytic solution, the calculation can be formulatedsimilarly to the approach through the Witten-Veneziano relation, and with someconceptual improvements. In the process, one strengthens the arguments in favorof a possible relation between the U_A(1) and SU_A(3) chiral symmetry breakingand 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 tothe finite-density parts of the QCD phase diagram, should pay particularattention to the signatures from the eta'-eta complex indicating the symmetryrestoration.

A $U_A(1)$ symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution