A prelude to Neutron Stars: The phase diagram of the strong interactions   at finite density
  We consider strong interactions at finite density in mean field theory, through an effective lagrangian that can describe both nuclear matter and quark matter. This lagrangian has three couplings that are all fixed by experiment and no other parameters. With increasing baryon density we then find the following hierarchy. At nuclear density and above we have nuclear matter with chiral spontaneous symmetry breaking (SSB), followed by the pion condensed quark matter, again with chiral SSB, albeit with a different realization and finally a transition to the diquark CFL state which also has chiral SSB (and colour SSB), with yet another realization. To one's surprise at zero temperature (in mean field theory), at any finite density chiral symmetry is never restored!   We find another remarkable feature and this is that the tree level mass of the sigma particle, that is set by experiment to about 800 MeV, has a crucial and unexpected influence on the physics. Strange quark matter and strange stars are ruled out for a sigma mass above 700 MeV and neutron stars with magnetic pion condensed cores, that could provide magnetic fields of neutron stars, exist only for a small interval, between 750-850 MeV, for the sigma mass. 
Vikram Soni and Dipankar Bhattacharya