SCALAR-ISOSCALAR CORRELATOR IN A PHENOMENOLOGICAL COUPLED-CHANNEL QUARK MODEL

Abstract

We calculate the Fourier transform of the scalar-isoscalar correlator[Formula: see text] making use of a generalized coupled-channel Nambu-Jona-Lasinio (NJL) model. The calculation is based upon the assumption that the correlator may be calculated by inserting two-pion continuum states between the operators [Formula: see text] and [Formula: see text]. We introduce a model for confinement such that the various quark-loop integrals only have cuts due to the physical two-pion continuum thus allowing us to construct dispersion relations for the correlator. It is then shown that for spacelike P2(P2<0) and for small timelike P2, a sigma-dominance model provides an excellent representation of the correlator that was calculated here using a dispersion relation. The parameters of the sigma-dominance model are consistent with those that characterize the low-mass (500–600 MeV) sigma meson that is extensively used in studies of the relativistic nuclear many-body problem. We also contrast the dynamics in the scalar-isoscalar channel with that in the vector-isovector channel where a physical particle (the rho meson) is to be found in the timelike region P2>0.