Light quark mass differences in the $\pi^0 - \eta - \eta'$ system

TL;DR

This paper uses a generalized Nambu-Jona-Lasinio model to analyze light quark mass differences and mixing angles in the pseudoscalar meson system, achieving results consistent with phenomenology.

Contribution

It introduces explicit chiral symmetry breaking interactions at the same order as the U_A(1) anomaly in a 3-flavor NJL model to determine meson mixing angles and quark mass ratios.

Findings

Accurate meson mixing angles obtained

Quark mass ratios closely match phenomenological values

Correct ordering and splitting of pseudoscalar states

Abstract

A generalized 3 flavor Nambu-Jona--Lasinio Lagrangian including the explicit chiral symmetry breaking interactions which contribute at the same order in the large $1/N_c$ counting as the $U_A(1)$ 't Hooft flavor determinant is considered to obtain the mixing angles in the $\pi^0-\eta-\eta'$ system and related current quark mass ratios in close agreement with phenomenological values. At the same time an accurate ordering and magnitude of the splitting of states in the low lying pseudoscalar nonet is obtained.