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

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.

elsarticle style, 6 pages

References in corpus (27)

• Mixing and Decay Constants of Pseudoscalar Mesons
• Quark structure of pseudoscalar mesons
• Mixing and Decay Constants of Pseudoscalar Mesons: The Sequel
• Pion interferometry in Au+Au collisions at $\sqrt{{\mathrm{s}}_{{}_{\mathrm{NN}}}}$ = 200 GeV
• On the 1/N expansion in chiral perturbation theory
• Bose-Einstein Correlations of Charged Pion Pairs in Au+Au Collisions at sqrt(s_NN)=200_ GeV
• Topological susceptibility in the SU(3) gauge theory
• Effective Hadron Dynamics: From Meson Masses to the Proton Spin Puzzle
• The Return of The Prodigal Goldstone Boson
• Precision study of the SU(3) topological susceptibility in the continuum
• Topology of SU(N) gauge theories at T=0 and T=Tc
• Fluctuations and the axial anomaly with three quark flavors
• Indirect observation of an in-medium eta' mass reduction in sqrt(s_{NN})=200 GeV Au+Au collisions
• In medium eta' mass and eta' N interaction based on chiral effective theory
• Significant in-medium eta' mass reduction in sqrt(s(NN))=200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider
• Topological susceptibility on the lattice and the three-flavour quark condensate
• eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach
• Pseudoscalar Meson Decay Constants and Couplings, the Witten-Veneziano Formula beyond large N_c, and the Topological Susceptibility
• Functional Renormalization for Chiral and U_A(1) Symmetries at Finite Temperature
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach at finite temperature
• Revisiting the U_A(1) problems
• eta and eta' mesons and dimension 2 gluon condensate <A^2>
• η' Multiplicity and the Witten-Veneziano relation at finite temperature
• Analyticity in theta on the lattice and the large volume limit of the topological susceptibility
• A renewed look at eta' in medium
• Chiral and U_A(1) symmetry in correlation functions in medium
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation

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• ${\gamma }^{\ast }\gamma \to \eta ,{\eta }^{\prime }$ transition form factors
• Topological Susceptibility in Three-Flavor Quark Meson Model at Finite Temperature
• ${\eta }^{\prime }$ and $\eta$ mesons at high T when the U_A(1) and chiral symmetry breaking are tied
• Pion and $\eta$-meson mass splitting at the two-flavour chiral crossover
• Exploring axial $U(1)$ restoration in a modified 2+1 flavor Polyakov quark meson model
• New Insight about the Effective Restoration of U_A(1) Symmetry
• A Dyson-Schwinger model beyond isospin limit prepared for investigating U_A(1)-breaking temperature dependence
• Aspects of model dependence of eta'-eta complex treated by going beyond the isospin limit
• QCD topological susceptibility from the nonlocal chiral quark model