Color superconductivity at moderate baryon density

This article focuses on the two-flavor color superconducting phase at moderate baryon density. In order to simultaneously investigate the chiral phase transition and the color superconducting phase transition, the Nambu-Gorkov formalism is extended to treat the quark-antiquark and diquark condensates on an equal footing. The competition between the chiral condensate and the diquark condensate is analyzed. The cold dense charge neutral two-flavor quark system is investigated in detail. Under the local charge neutrality condition, the ground state of two-flavor quark matter is sensitive to the coupling strength in the diquark channel. When the diquark coupling strength is around the value obtained from the Fierz transformation or from fitting the vacuum bayron mass, the ground state of charge neutral two-flavor quark matter is in a thermal stable gapless 2SC (g2SC) phase. The unusual properties at zero as well as nonzero temperatures and the chromomagnetic properties of the g2SC phase are reviewed. Under the global charge neutrality condition, assuming the surface tension is negligible, the mixed phase composed of the regular 2SC phase and normal quark matter is more favorable than the g2SC phase. A hybrid nonstrange neutron star is constructed.