Combined study of the η and η′ mesons: Phenomenology, chiral extrapolation of lattice QCD and effective field theory

A comprehensive phenomenological study is carried out of the decay processes with the η or η′ in the initial/final states within the effective field theory approach. Two primary types of processes are analyzed: The ones only with lightflavor hadrons and those involving the J/ψ. The couplings from the effective Lagrangian, together with the ηη′ mixing parameters from the two-mixing-angle scheme, are fitted to a large number of experimental data, including the various decay widths and the form factors. With the phenomenological mixing parameters and the lattice simulation data of the masses and decay constants of the light pseudoscalar mesons as inputs, a next-to-next-to-leading order study is performed of the ηη′ mixing system in U(3) chiral perturbation theory. Updated values of the relevant low energy constants are obtained.