Scrutinizing the eta-eta' mixing, masses and pseudoscalar decay constants in the framework of U(3) chiral effective field theory

Understand

We study the $\eta$-$\eta'$ mixing up to next-to-next-to-leading-order in $U(3)$ chiral perturbation theory in the light of recent lattice simulations and phenomenological inputs.

• A general treatment for the $\eta$-$\eta'$ mixing at higher orders, with the higher-derivative, kinematic and mass mixing terms, is addressed.
• The connections between the four mixing parameters in the two-mixing-angle scheme and the low energy constants in the $U(3)$ chiral effective theory are provided both for the singlet-octet and the quark-flavor bases.
• The axial-vector decay constants of pion and kaon are studied in the same order and confronted with the lattice simulation data as well.