Chiral symmetry breaking, color superconductivity, and color neutral quark matter: A variational approach

We investigate the vacuum realignment for chiral symmetry breaking and color superconductivity at finite density in the Nambu-Jona-Lasinio model in a variational method. The treatment allows us to investigate the simultaneous formation of condensates in quark-antiquark as well as in diquark channels. The methodology involves an explicit construction of a variational ground state and minimization of the thermodynamic potential. Color and electric charge neutrality conditions are imposed through introduction of appropriate chemical potentials. Color and flavor dependent condensate functions are determined through minimization of the thermodynamic potential. The equation of state is calculated. Simultaneous existence of a mass gap and superconducting gap is seen in a small window of the quark chemical potential within the model when charge neutrality conditions are not imposed. Enforcing color and electric charge neutrality conditions gives rise to the existence of gapless superconducting modes depending upon the magnitude of the gap and the difference of the chemical potentials of the condensing quarks.