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

Abstract

We study the nonstrange scalar-isoscalar states of a generalized Nambu{endash}Jona-Lasinio model that includes the {close_quote}t Hooft interaction and a model of confinement. We also include coupling of the q{bar q} states to the two-pion continuum in our analysis. (Our study is limited to energies q{sup 2}{le}1.8GeV{sup 2}, since to go beyond q{sup 2}=2.0GeV{sup 2} we need to change our method of calculation.) After introducing octet-singlet mixing we find two states, {sigma}{sub 1} and {sigma}{sub 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{sup 2}. Because of a strong q{sup 2} dependence of the T matrix at the opening of the two-pion continuum at q{sup 2}=4m{sub {pi}}{sup 2}, the {ital 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 {ital effective} {sigma} mesonmore » in nuclear physics. {copyright} {ital 1997} {ital The American Physical Society}« less