$\eta$-${\eta }^{\prime }$ Mixing in Large-$N_c$ Chiral Perturbation Theory

Abstract

We present a calculation of the $\eta$-${\eta }^{\prime }$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $\eta$-${\eta }^{\prime }$ 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 $\eta$-${\eta }^{\prime }$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and $\mathcal{O}(N_c{p}^6)$ contact terms.

Comments: 39 pages, 8 figures