Mixing of Pseudoscalar Mesons

Abstract

η-η' mixing is discussed in the quark-flavor basis with the hypothesis that the decay constants follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents – which embody the axial vector anomaly – all mixing parameters are fixed to first order of flavor symmetry breaking. An alternative set of parameters is obtained from a phenomenological analysis. We also discuss mixing in the octet-singlet basis and show how the relevant mixing parameters are related to those in the quark-flavor basis. The dependence of the mixing parameters on the strength of the anomaly and the amount of flavor symmetry breaking is investigated. Finally, we present a few applications of the quark-flavor mixing scheme, such as radiative decays of vector mesons, the photon-pseudoscalar meson transition form factors, the coupling constants of η and η' to nucleons, and the isospin-singlet admixtures to the π0 meson.