$1/N_c$ Nambu -- Jona-Lasinio model: ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons

Abstract

We continue to study the properties of the light pseudoscalar nonet within the combined framework of Nambu -- Jona-Lasinio model and $1/N_c$ expansion, assuming that current quark masses count of order $\mathcal{O}(1/N_c)$. The masses, mixing angles and decay constants of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ are calculated. The role of the $U(1{)}_A$ anomaly is emphasized. It is shown that the gluon anomaly suppresses the leading order effects that might otherwise be substantial for the $\eta \to 3\pi$ amplitude. A detailed comparison with the known results of $1/N_c$ chiral perturbation theory is made.

Comments: 15 pages, 2 figures, final version to be published in PRD