Axion-meson mixing in light of recent lattice η–η′ simulations and their two-photon couplings within U(3) chiral theory

Abstract

We study the mixing of the QCD/QCD-like axion and light-flavor mesons π0, η, η′ within the framework of U(3) chiral perturbation theory up to next-to-leading order in this work. The axion-meson mixing formulas are calculated order by order in the U(3) δ-expansion scheme, namely the joint expansions of the momentum, light-quark masses and 1/NC. We provide axion-meson mixing relations in terms of the π0–η–η′ mixing parameters and their masses. The recent lattice simulations on the η–η′ systems turn out to be able to offer valuable inputs to constrain the unknown low-energy constants. The relation of the mass and decay constant of the axion is then further explored based on our updated calculations. The two-photon couplings of the light-flavor mesons, together with the axion, are also investigated in the U(3) chiral theory up to next-to-leading order in the δ-counting scheme.