The $\pi^0-\eta-\eta'$ mixing in a generalized multi-quark interaction scheme

TL;DR

This paper models isospin symmetry breaking in mesons using an advanced NJL framework, achieving accurate meson properties, quark masses, and a significant reduction in mixing angle ratios, surpassing traditional models.

Contribution

It introduces a generalized multi-quark interaction scheme including next-to-leading order terms, improving the description of meson mixing and quark masses over conventional NJL models.

Findings

Accurate fit of pseudoscalar meson properties.

Quark masses align with PDG values.

Reduces the $rac{ ext{epsilon}}{ ext{epsilon}'}$ ratio by 40%.

Abstract

We investigate the isospin symmetry breaking effects within a recently derived Nambu-Jona-Lasinio related model by fitting the measured pseudoscalar meson masses and weak decay couplings $f_\pi$, $f_K$. Our model contains the next to leading order terms in the $1/N_c$ expansion of the effective multi-quark Lagrangian, including the ones that break the chiral symmetry explicitly. We show the important phenomenological role of these interactions: (1) they lead to an accurate fit of the low-lying pseudoscalar nonet characteristics; (2) they account for a very good agreement of the current quark masses with the present PDG values; (3) they reduce by $40\%$ the ratio $\epsilon/\epsilon'$ of the $\pi_0-\eta$ and $\pi_0-\eta'$ mixing angles, as compared to the case that contemplates explicit breaking only in the leading order, bringing it in consonance with the quoted values in the literature. The conventional NJL-type models fail in the joint description of these parameters.