COUPLED-CHANNEL DYNAMICS IN THE NAMBU-JONA-LASINIO MODEL

We study the scalar-isoscalar sector of the Nambu-Jona-Lasinio (NJL) m odel and extend the model to include a description of the coupling of the quark-antiquark states to the two-pion continuum. The qqBAR intera ction gives rise to a sigma meson, which takes on a width and energy s hift that depends upon the strength of the coupling for q+qBAR-->pi+pi . (For weak channel coupling, the resonance is located at the mass of the sigma, m(sigma) congruent-to 2m(q)cons, where m(q)cons is the cons tituent quark mass of the NJL model.) We consider two models for the q qBAR-->pipi coupling. In the first model, we find a low-energy resonan ce, with the resonance energy E(R) less-than-or-equal-to 2m(q)cons. We then see that the values, obtained from the analysis of experimental data, of the scalar-isoscalar phase shift describing pipi scattering d elta0(0), are not compatible with the existence of a low-mass sigma. I n the second model, the resonance is pushed upward into the region of the two-quark continuum, E(R) > 2m(q)cons. This second model provides an example of a phenomenon where the behavior of the qqBAR T matrix is parametrized for q2 less-than-or-equal-to 0 by a mass that is smaller than the physical mass that characterizes the pole in the T matrix. T he behavior of the second model suggests how the absence of experiment al evidence for a low-mass sigma may be reconciled with the importance of such a meson in nuclear structure studies.