Gluonic contributions in a four-fermion interaction model

The gap equation for the fermion in nuclear medium is obtained in a two-flavor gauged Nambu-Jona-Lasino (NJL) model using the Schwinger-Dyson (SD) equations. The gap equation is solved with a quenched truncation. Compared to the four-fermion interaction, the one-gluon-exchange interaction accounts for considerable contributions (about 15-50%) to dynamically generated fermion mass. With incorporation of gluonic contributions into a scheme where there is only four-fermion interaction, the four-fermion coupling constant is made density dependent. Impacts of the density-dependent four-fermion (DDFF) coupling constants on quantities,, such as the fermion mass and the chiral order parameter as well as masses of mesons (sigma, pi), are estimated, The DDFF coupling constants lead to less density dependence of hadron masses and the larger critical density of chiral symmetry restoration than those from the pure four-fermion interaction, The calculated quantities are somehow dependent on the confinement scale Lambda(QCD). However, the range of Lambda(QCD) in the present parametrization can be determined by the saturation property of the gluonic contribution in the medium and it turns out quite small.