ar X iv : h ep - p h / 02 07 25 5 v 1 2 2 Ju l 2 00 2 1 Chiral and Color - superconducting Phase Transitions with Vector Interaction in a Simple Model

We investigate effects of the vector interaction on chiral and color superconducting (CSC) phase transitions at finite density and temperature in a simple Nambu-Jona-Lasinio model. It is shown that the repulsive density-density interaction comming from the vector term, which is present in the effective chiral models but has been omitted, enhances the competition between the chiral symmerty breaking (χSB) 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 χSB 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 χSB 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. It is one of the central issues in hadron physics to determine the phase diagram of strongly interacting matter in the temperature(T)-chemical potential (µ) or T-ρ B plane with ρ B being the baryonic density. In extremely hot and dense matter, the non-Abelian nature of QCD ensures that the colored quarks and gluons are not confined and the chiral symmetry is restored. The lattice simulations of QCD 1), 2) show that the QCD vacuum undergoes the chiral and deconfinement transition at a temperature T c around 150 ∼ 175 MeV at vanishing chemical potential, with the order and the critical temperature being dependent on the number of the active flavors. Although there are several promising attempts 3)–9) to make simulations of the lattice QCD with finite µ possible, they are still not matured enough to predict a definite thing about the phase transition at finite ρ B or µ. It is widely believed on the basis of effective theories 10)–12) and chiral random matrix theory 13) that the chiral phase transition from the chiral-symmetry broken to restored phase is a first order