Chiral symmetry breaking, color superconductivity and quark matter phase diagram: a variational approach

We discuss in this note simultaneous existence of chiral symmetry breaking and color superconductivity at finite temperature and density in a Nambu-Jona-Lasinio type model. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. There exists solutions to the gap equations at finite densities with both quark antiquark as well as diquark condensates for the "ground" state. However, such a phase is thermodynamically unstable with the pressure being negative in this region. We also compute the equation of state, and obtain the structure of the phase diagram in the model.