Mixing interactions and effects in the NJL-model

TL;DR

This paper explores how flavor-dependent contact interactions and mixing effects in the NJL model influence meson mixing and quark interactions, including contributions from higher-order interactions and symmetry breaking.

Contribution

It introduces explicit flavor mixing interactions in the NJL model and analyzes their effects on meson mixing and quark gap equations, including sixth order interactions breaking $U_A(1)$ symmetry.

Findings

Mixing interactions affect meson mixing without 't Hooft interactions.

Scalar channel mixing can induce quark mixing in gap equations.

Higher-order interactions contribute to $U_A(1)$ symmetry breaking.

Abstract

The flavor-dependent quark-antiquark contact interactions, induced by vacuum polarization and recently derived for flavor U(3) Nambu-Jona-Lasinio model, are articulated with the resulting mixing effects emerging from flavor symmetry breaking in view. The formal effects of the explicit mixing interactions, $G_{i\neq j}$, are detailed firstly for the meson mixing problem without the inclusion of 't Hooft interactions induced by instantons. Secondly, it is shown that these mixings, in the scalar channel of quark-antiquark interactions, might give rise to quark mixing in the gap equations. Sixth order quark-antiquark interactions from vacuum polarization, that break $U_A(1)$ symmetry, also contribute.