$\eta$-$\eta'$ mixing in large-$N_c$ chiral perturbation theory: discussion, phenomenology, and prospects

TL;DR

This paper systematically analyzes $ ext{η}$-$ ext{η'}$ mixing using large-$N_c$ chiral perturbation theory, emphasizing higher-order contributions, loop corrections, and OZI-rule violations, and compares results with phenomenological models.

Contribution

It introduces a comprehensive framework incorporating next-to-next-to-leading-order effects in $ ext{η}$-$ ext{η'}$ mixing within large-$N_c$ chiral perturbation theory, including loop and OZI-rule-violating terms.

Findings

Mixing angles and decay constants are calculated within the framework.

Results show consistency with recent phenomenological approaches.

Higher-order contributions significantly impact the mixing parameters.

Abstract

A systematic study of the $\eta$-$\eta'$ mixing in Large-$N_c$ chiral perturbation theory is presented with special emphasis on the role of the next-to-next-to-leading-order contributions in the combined momentum, quark-mass, and $1/N_c$ expansions. At this order, loop corrections as well as OZI-rule-violating pieces need to be included. Mixing angles as well as pseudoscalar decay constants are discussed within this framework. The results are compared with recent phenomenological approaches.