$\eta$ and $\eta'$ mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation

TL;DR

This paper investigates the impact of using Shore's generalized Witten-Veneziano relation versus the standard relation within the Dyson-Schwinger framework for describing $ta$ and $ta'$ mesons, finding the standard relation more phenomenologically successful.

Contribution

It compares the effects of the standard and generalized Witten-Veneziano relations in Dyson-Schwinger models for $ta$ and $ta'$ mesons, showing the standard relation's superior phenomenological performance.

Findings

Standard Witten-Veneziano relation yields better phenomenological results.

Generalized relation does not improve model predictions across different interactions.

Dyson-Schwinger approach favors the standard relation for meson description.

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.