Phase Structure of Color Superconductivity and Chiral Restoration

In the ideal case at asymptotically high baryon density, the color superconductivity with two massless flavors and the color-flavor-locking (CFL) phase with three degenerated massless quarks have been widely discussed from first principle QCD calculations1. For physical applications we are more interested in the moderate baryon density region which may be related to the neutron stars and, in very optimistic cases, even to heavy-ion collisions. Usually, four-fermion interaction models such as the instanton, as well as the Nambu–Jona-Lasinio (NJL) model, are used in the study of color superconductivity phase transition. It was found that the color superconductivity gap can be of the order of 100 MeV2, which is two orders larger than early perturbative QCD estimation3. The electric and color charge neutrality condition4,5 leads to a new phase of color superconductivity, the gapless color superconductivity6 or the breached pairing phase7. The most probable temperature for this new phase is finite but not zero8. It is generally accepted that the NJL model9 applied to quarks10 offers a simple but effective scheme to study spontaneous chiral symmetry breaking in the vacuum, chiral restoration at finite temperature and density, and spontaneous color symmetry breaking at high density5,6,8,11. From the study of chiral phase transition without considering color superconductivity, it is well-known that10 the mean field approximation to quarks and random phase approximation (RPA) to mesons can describe well the thermodynamics of the system, especially the massless Goldstone mode in the spontaneous symmetry breaking phase. In this letter I will determine