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

TL;DR

This paper provides an analytic solution to Shore's generalized Witten-Veneziano equations, supporting the scenario of U_A(1) symmetry restoration and its implications for eta and eta' mesons in high-temperature QCD environments.

Contribution

It introduces a closed-form analytic solution to Shore's equations, linking U_A(1) symmetry restoration with eta-eta' meson properties, enhancing theoretical understanding.

Findings

Analytic solution agrees with previous numerical results.

Supports the connection between U_A(1) symmetry restoration and chiral symmetry.

Suggests experimental signatures at RHIC, NICA, and FAIR for symmetry restoration.

Abstract

The Witten-Veneziano relation, or, alternatively, its generalization proposed by Shore, facilitates understanding and describing the complex of eta and eta' mesons. We present an analytic, closed-form solution to Shore's equations which gives results on the eta-eta' 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 eta and eta' 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 eta'-eta complex indicating the symmetry restoration.