Theoretical study of the mixing of the π0-η-η′-axion system

Abstract

The mass term of the Chiral Lagrangian at leading order mixes the strangeness-zero states. In order to perform calculations of physical quantities such as decay rates and scattering amplitudes involving the neutral π0, η and η′ mesons, the mass matrix of the Lagrangian needs to be diagonalized. In this work, we find the relation between the Lagrangian and physical states in terms of mixing angles as well as the expressions for the corresponding physical meson masses. We also incorporate mixing with the axion, thus preparing the Lagrangian for applications in axion phenomenology.