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

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 () 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 σ(500), f 0(980) and mesons. As a result, the mass hierarchy between states S 0 and S 8, and mesons, can be, respectively, inverted and corrected for quite low values of the strange quark constituent mass. In addition, for some particular values of , the masses of σ(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 σ(500) − f 0(980) mass difference. Two different estimates for the strengths of the mixings and are proposed, leading to somewhat different behaviors. First by assuming leading transitions to intermediary flavor eigenstates and second by considering a dynamical evolution. The results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass.