Singlet-octet mixing of scalar mesons in a generalized Nambu-Jona-Lasinio model

We study the nonstrange scalar-isoscalar states of a generalized Nambu-Jona-Lasinio model that includes the 't Hooft interaction and a model of confinement. We also include coupling of the q (q) over bar states to the two-pion continuum in our analysis. (Our study is limited to energies q(2) less than or equal to 1.8 GeV2, since to go beyond q(2) = 2.0 GeV2 we need to change our method of calculation.) After introducing octet-singlet mixing we find two states, sigma(1) and sigma(2), at energies of 1.00 and 1.28 GeV, respectively. The first of these is predominantly a SU(3) singlet, while the second state is rather strongly mixed. Of particular interest for nuclear physics is the behavior of the quark-quark T matrix for small spacelike values of q(2). Because of a strong q(2) dependence of the T matrix at the opening of the two-pion continuum at q(2)=4m(pi)(2), the effective mass that parametrizes scalar-isoscalar exchange in the T matrix is about 520 MeV. Thus, in a model of the nucleon-nucleon interaction, whose ingredients are a T matrix for the interaction of off-mass-shell quarks and valence-quark nucleon form factors, we can provide a basis for the use of a low-mass effective a meson in nuclear physics.