Neutral quark matter in a Nambu-Jona Lasinio model with vector interaction

We investigate the three flavor Nambu-Jona Lasinio model of neutral quark matter at zero temperature and finite density, keeping into account the scalar, the pseudoscalar and the Kobayashi-Maskawa-'t Hooft interactions as well as the repulsive vector plus axial-vector interaction terms (vector extended NJL, VENJL in the following). We focus on the effect of the vector interaction on the chiral restoration at finite density in neutral matter. We also study the evolution of the charged pseudoscalar meson energies as a function of the quark chemical potential.