Isospin properties of quark matter from a 3-flavor NJL model
  We have studied the properties of hot and dense quark matter based on the 3-flavor Nambu-Jona-Lasinio (NJL) model as well as its Polyakov-loop extension (pNJL) with scalar-isovector and vector-isovector couplings. Provided a considerable large isospin asymmetry or isospin chemical potential, isospin splittings of constituent mass, chiral phase transition boundary, and critical point for $u$ and $d$ quarks can be observed for positive isovector coupling constants but are suppressed for negative ones. The quark matter symmetry energy decreases with the increasing isovector coupling constant, and is mostly enhanced in the pNJL model than in the NJL model. A positive scalar-isovector coupling constant is more likely to lead to an unstable isospin asymmetric quark matter. The isovector coupling has been further found to affect particle fractions as well as the equation of state in hybrid stars. Possible effects on the isospin properties of quark matter have also been discussed if the strangeness sector is further broken among the flavor symmetry. 
He Liu, Jun Xu, Lie-Wen Chen, and Kai-Jia Sun
nucl-th hep-ph