Chiral and Color-Superconducting Phase Transitions with Vector Interaction in a Simple Model

We investigate effects of the vector interaction on chiral and colorsuperconducting (CSC) phase transitions at finite density and temperature in a simple Nambu-Jona-Lasinio model. It is shown that the repulsive density-density interaction coming from the vector term, which is present in the effective chiral models but has been omitted, enhances the competition between the chiral symmerty breaking (chi-SB) and CSC phase transition, thereby makes the thermodynamic potential have a shallow minimum in a wide range of the correlated chiral and CSC order parameters. We find that when the vector coupling is increased, the first order transition between the chi-SB and CSC phases becomes weaker and the coexisting phase in which both the chiral and color-gauge symmetry are dynamically broken gets to exisit in a wider range of the density and temperature. We shall also show that there can exist two end points, which are tricritical points in the chiral limit, in the critical line of the first order transition in some range of the vector coupling. Although our analysis is based on a simple model, the nontrivial interplay between the chi-SB and CSC phases induced by the vector interaction is expected to be a universal phenomenon and might give a clue to understand results obtained by the two-color QCD on the lattice