On the scalar nonet in the extended Nambu Jona-Lasinio model

TL;DR

This paper examines the lightest scalar mesons within the extended Nambu Jona-Lasinio model, highlighting challenges in parameter tuning and issues with the K matrix unitarization method.

Contribution

It analyzes scalar mesons in the extended NJL model and discusses limitations of parameter tuning and unitarization techniques.

Findings

Model parameters can be tuned, but unnaturally, to fit scalar mesons.

Difficulty in accommodating the $f_0(980)$ scalar.

Problems with the K matrix unitarization approximation.

Abstract

We discuss the lightest scalar resonances, $f_0(600)$, $\kappa(800)$, $a_0(980)$ and $f_0(980)$ in the extended Nambu Jona-Lasinio model. We find that the model parameters can be tuned, but unnaturally, to accommodate for those scalars except the $f_0(980)$. We also discuss problems encountered in the K Matrix unitarization approximation by using $N_c$ counting technique.