Electrical neutrality and pion modes in the two flavor Polyakov-Nambu-Jona-Lasinio model

We study the phase diagram and the pion modes in the electrically neutral two flavor Polyakov-Nambu-Jona-Lasinio model. One of the main results of this paper is that in the model with massive quarks, when electrical neutrality is required, pions do not condense in the ground state of the model: the isospin chemical potential mu(I) = -mu(e)/2 is always smaller than the value required for pion condensation to occur. Moreover we investigate on the pions and sigma mass spectra. We find that the qualitative behavior of the masses resembles that obtained in the Nambu-Jona-Lasinio model. We close this paper by studying the intriguing possibility that bound states with the quantum numbers of the pions can be formed above the chiral phase transition.