Pion condensation in a two-flavour NJL model: the role of charge neutrality

We study pion condensation and the phase structure in a two-flavour Nambu-Jona- Lasinio model in the presence of baryon chemical potential mu and isospin chemical potential mu(I) at zero and finite temperature. There is a competition between the chiral condensate and a Bose-Einstein condensate of charged pions. In the chiral limit, the chiral condensate vanishes for any finite value of the isospin chemical potential, while there is a charged pion condensate that depends on the chemical potentials and the temperature. At the physical point, the chiral condensate is always nonzero, while the charged pion condensate depends on mu(I) and T. For T = mu = 0, the critical isospin chemical potential mu(C)(I) for the onset of Bose-Einstein condensation is always equal to the pion mass. For mu = 0, we compare our results with chiral perturbation theory, sigma-model calculations and lattice simulations. Finally, we examine the effects of imposing electric charge neutrality and weak equilibrium on the phase structure of the model. In the chiral limit, there is a window of baryon chemical potential and temperature where the charged pions condense. At the physical point, the charged pions do not condense.