Pion Condensation in a two-flavor NJL model: the role of charge neutrality

Abstract

We study pion condensation and the phase structure in a two-flavor 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 ${\mu }_I^c$ 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. 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.

Comments: 16 pages. 13 figs. Second version expanded significantly: Discussion and results now include finite quark masses as well as comparison with other approaches. More appropriate title. Third version matches published paper