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

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.