$\eta$-$\eta'$ Mixing in Large-$N_c$ Chiral Perturbation Theory

TL;DR

This paper calculates the $ ext{eta}$-$ ext{eta'}$ mixing using large-$N_c$ chiral perturbation theory, deriving expressions up to NNLO and analyzing the effects of higher-order corrections and parameters.

Contribution

It provides the first comprehensive NNLO calculation of $ ext{eta}$-$ ext{eta'}$ mixing including higher-derivative terms and decay constants within large-$N_c$ chiral perturbation theory.

Findings

NNLO expressions for $ ext{eta}$-$ ext{eta'}$ mixing derived

One-loop corrections and OZI-rule violations analyzed

Numerical results show impact of higher-order terms

Abstract

We present a calculation of the $\eta$-$\eta'$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $\eta$-$\eta'$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the $\eta$-$\eta'$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and $\mathcal{O}(N_c p^6)$ contact terms.