Electrical neutrality and pion modes in the two flavor PNJL model

We study the phase diagram and the pion modes in the electrically neutral two flavor PNJL model. One of the main result of this paper is that 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 NJL model. We close this paper by studying the intriguing possibility that a bound state with the quantum numbers of the pions can be formed above the chiral phase transition.