The problem of matter stability in the Nambu-Jona-Lasinio model

We reinvestigate the conditions for stable matter solutions in the Nambu-Jona-Lasinio (NJL) model, In mean field approximation the NJL model can be regarded as an extension of the Walecka mean field model to include negative energy fermion states, While this extension is necessary to allow for a chiral phase transition, it was found some time ago that at the same time it destroys the wanted saturation properties of the Walecka model. We reformulate this problem in terms of the thermodynamic potential and find that there is indeed a connection between these two features. We show that the minimum of the thermodynamic potential which corresponds to stable nuclear matter in the Walecka model is shifted from a finite to zero effective fermion mass in the chiral ML model, This shift is closely related to the chiral phase transition, Under certain conditions the shifted minima may still lead to stable matter solutions but only in the chirally restored phase. We discuss a possible interpretation of these solutions as a schematic bag model description.