Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants

TL;DR

This paper investigates the quark-antiquark structure of the lightest scalar mesons using an extended Nambu-Jona-Lasinio model with flavor-dependent couplings, analyzing mass hierarchies, mixing, and experimental consistency.

Contribution

It introduces a flavor-dependent coupling approach within the NJL model to better understand scalar meson structures and their mixing behaviors.

Findings

Mass hierarchy corrections for scalar mesons are achieved at low strange quark masses.

Mixing angles are estimated by fitting the sigma-f0 mass difference.

Results align with experimental data depending on strange quark mass values.

Abstract

The quark antiquark components of the U(3) lightest scalar meson nonet are investigated by considering the Nambu-Jona-Lasinio model with flavor-dependent coupling constants that were derived by considering (non-perturbative) gluon exchange.The strange quark effective mass ($M_s^*$) is varied such that the strangeness content of these scalar mesons can be analyzed further. The neutral states $S_0$, $S_8$ and $S_3$, are adopted as the most relevant quark-antiquark components respectively of the $\sigma(500)$, $f_0(980)$ and $A_0^0(980)$ mesons. As a result, the mass hierarchy between states $S_0$ and $S_8$, and $K^*_0(700) - A_0(980)$ mesons, can be respectively inverted and corrected for quite low values of the strange quark constituent mass. Besides that, for some particular values of $M_s^*$, the masses of $\sigma(500)$ and $f_0(980)$ can also be obtained by considering the mixing coupling constant $G_{08}$. However, the masses of all the nine mesons are not described simultaneously in a self-consistent procedure and this goes along with the need of non-quark-antiquark states to completely describe their masses. A neutral-meson mixing matrix is defined and the leading mixing angle is found by fitting a correct value of the $\sigma(500)$-$f_0(980)$ mass difference. Two different estimates for the strengths of the mixings $A_0^0 \to f_0$ and $f_0 \to A_0^0$ are proposed, leading to somewhat different behaviors. Firstly, by assuming leading transitions to intermediary flavor eigenstates and secondly by considering a dynamical evolution. Results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass.