Number of the QCD critical points with neutral color superconductivity

Understand

We investigate the effect of the electric-charge neutrality in $\beta$ equilibrium on the chiral phase transition by solving the chiral and diquark condensates in the two-flavor Nambu--Jona-Lasinio model.

• We demonstrate that the electric-charge neutrality plays a similar role as the repulsive vector interaction; they both weaken the first-order chiral phase transition in the high-density and low-temperature region.
• The first-order chiral phase transition is not affected, however, at finite temperatures where the diquark condensate melts.
• In this way the chiral phase transition could be second-order at intermediate temperatures if the diquark effects overwhelm the chiral dynamics, while the first-order transition may survive at lower and higher temperatures.