Charge neutrality effects on two-flavor color superconductivity

Four different phases of the two-flavor quark system, i.e., the normal quark matter and color superconducting phases with and without the charge neutrality condition, are investigated in the framework of the SU(2) Nambu–Jona-Lasinio model. It is found that the color superconducting phase without charge neutrality has the lowest thermodynamic potential, and the charge neutral systems have higher thermodynamic potentials. However, the BCS pairing always lowers the system’s thermodynamic potential, i.e., for both the charged and charge neutral systems, the superconducting phases always have lower thermodynamic potentials. Compared with the BCS gap Δ₀ for the color superconducting phase without charge neutrality, the BCS gap Δ in the charge neutral color superconducting phase has been largely reduced. When the thermodynamic potential for the charge neutral color superconducting phase equals that in the neutral normal quark matter, the diquark condensate disappears.