$\eta$-$\eta'$ Mixing in Large-$N_c$ Chiral Perturbation Theory

Understand

We present a calculation of the $\eta$-$\eta'$ mixing in the framework of large-$N_c$ chiral perturbation theory.

• A general expression for the $\eta$-$\eta'$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms.
• In addition, the axial-vector decay constants of the $\eta$-$\eta'$ system are determined at NNLO.
• The numerical analysis of the results is performed successively at LO, NLO, and NNLO.