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The quark antiquark components of the U(3) lightest scalar meson nonet areinvestigated by considering the Nambu-Jona-Lasinio model with flavor-dependentcoupling constants that were derived by considering (non-perturbative) gluonexchange.The strange quark effective mass ($M_s^*$) is varied such that thestrangeness content of these scalar mesons can be analyzed further. The neutralstates $S_0$, $S_8$ and $S_3$, are adopted as the most relevant quark-antiquarkcomponents 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 forquite low values of the strange quark constituent mass. Besides that, for someparticular values of $M_s^*$, the masses of $\sigma(500)$ and $f_0(980)$ canalso be obtained by considering the mixing coupling constant $G_{08}$. However,the masses of all the nine mesons are not described simultaneously in aself-consistent procedure and this goes along with the need ofnon-quark-antiquark states to completely describe their masses. A neutral-mesonmixing matrix is defined and the leading mixing angle is found by fitting acorrect value of the $\sigma(500)$-$f_0(980)$ mass difference. Two differentestimates 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 assumingleading transitions to intermediary flavor eigenstates and secondly byconsidering a dynamical evolution. Results may be in good agreement withexperimental values from BESS-III depending on the value of the strange quarkeffective mass.

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