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

Abstract

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 σ(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. In addition, for some particular values of M s * , 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 A 0 0 → f 0 and f 0 → A 0 0 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.