$\pi^0$-$\eta$ -$\eta'$ mixing in the theory with four-quark interactions

Mass formulas, mixing angles, and decay constants of the pseudoscalar$\pi^0$, $\eta$ and $\eta'$ mesons have been obtained in the theory with four-quark interactions with an accuracy to $\mathcal O(1/N_c^2)$ terms inclusively. Unlike the standard Nambu–Jona-Lasinio model, the meson Lagrangian has been obtained using the Volterra series, which allows a more detailed description of effects caused by the inequality of quark masses. The results have been compared to similar calculations in the $1/N_c$ chiral perturbation theory. The first corrections to the interaction violating the Zweig formulas have been calculated, and it has been shown that they are important for the description of the mass spectrum of the $\eta$-$\eta'$ mesons.