$\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation

Abstract

The description of the $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach has relied on the Witten-Veneziano relation. The present paper explores the consequences of using instead its generalization recently proposed by Shore. On the examples of three different model interactions, we find that irrespective of the concrete model dynamics, our Dyson-Schwinger approach is phenomenologically more successful in conjunction with the standard Witten-Veneziano relation than with the proposed generalization valid in all orders in the $1/N_c$ expansion.

8 pages, version accepted for publication in the European Physical Journal A

References in corpus (4)

• Infrared Properties of QCD from Dyson-Schwinger equations
• Flavour symmetry breaking and meson masses
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach at finite temperature
• Pseudoscalar Meson Nonet at Zero and Finite Temperature

Cited by in corpus (3)

• A $U_A(1)$ symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution
• Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the $U_A(1)$ Symmetry
• Aspects of model dependence of eta'-eta complex treated by going beyond the isospin limit