Flavor-dependent U(3) Nambu Jona Lasinio coupling constant

TL;DR

This paper derives flavor-dependent coupling constants in a NJL model from a one-gluon exchange interaction, analyzing their impact on meson masses and properties, highlighting significant flavor effects in light meson phenomenology.

Contribution

It introduces a method to compute flavor-dependent NJL coupling constants from a one-loop polarization process considering non-degenerate quark masses, extending previous flavor-symmetric models.

Findings

Flavor-dependent couplings deviate from symmetric values by mass difference ratios.

Scalar channel couplings can be significantly smaller than pseudoscalar ones.

Flavor dependence impacts pion and kaon masses similarly to quark mass non-degeneracy.

Abstract

A non-perturbative one gluon exchange quark-antiquark interaction is considered to compute flavor dependent U(3) Nambu-Jona-Lasinio (NJL)-type interaction of the form $G_{ij, \Gamma} (\bar{\psi} \lambda_i \Gamma \psi ) ( \bar{\psi} \lambda_j \Gamma \psi)$ for $i,j=0...8$ and $\Gamma=I, i \gamma_5$ from one loop polarization process with non degenerate u-d-s quark effective masses. The resulting NJL-type coupling constants in all channels are resolved in the long-wavelength limit and numerical results are presented for different choices of an effective gluon propagator. Leading deviations with respect to a flavor symmetric coupling constant are found to be of the order of $(M_{f_2}^*-M_{f_1}^*)^n/(M_{f_2}^*+M_{f_1}^*)^n$, for $n=1,2$, where $M_{f_i}^*$ are the effective masses of quarks $f_1,f_2=u, d$ and $s$. The scalar channel coupling constants $G_{ij, s}$ can be considerably smaller than pseudoscalar ones. The effect of the flavor-dependence of coupling constants for the masses of pions and kaons may be nearly of the same order of magnitude as the effect of the u,d and s quark mass non-degeneracy. The effect of these coupling constants is also verified for some of the light scalar mesons masses, usually described by quark-antiquark states, and for some observables of the pseudoscalar mesons.