  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 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 (chiSB) and CSC phase transition, and thereby makes the
thermodynamic potential have a shallow minimum over a wide range of values of
the correlated chiral and CSC order parameters. We find that when the vector
coupling is increased, the first order transition between the chiSB and CSC
phases becomes weaker, and the coexisting phase in which both the chiral and
color-gauge symmetry are dynamically broken comes to exisit over a wider range
of the density and temperature. We also show that there can exist two
endpoints, which are tricritical points in the chiral limit, along the critical
line of the first order transition in some range of values of the vector
coupling. Although our analysis is based on a simple model, the nontrivial
interplay between the chiSB and CSC phases induced by the vector interaction is
expected to be a universal phenomenon and might give a clue to understanding
results obtained with two-color QCD on the lattice.
