  The phase diagram for quark matter is investigated within a simple
Nambu-Jona-Lasinio model without vector correlations. It is found that the
phase structure in the temperature-density plane depends sensitively on the
parametrization of the model. We present two schemes of parametrization of the
model where within the first one a first order phase transition from a phase
with broken chiral symmetry to a color superconducting phase for temperatures
below the triple point at T_t= 55 MeV occurs whereas for the second one a
second order phase transition for temperatures below T_t = 7 MeV is found. In
the latter case, there is also a coexistence phase of broken chiral symmetry
with color superconductivity, which is a new finding within this class of
models. Possible consequences for the phenomenology of the QCD phase transition
at high baryon densities are discussed.
