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

Abstract

We reinvestigate the conditions for stable matter solutions in the Nambu-JonaLasinio (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 NJL 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.

The stability of nuclear matter in the Nambu–Jona-Lasinio model

“…Since the first applications of models based on the linear realization of chiral symmetry to the description of nuclear many-body systems systems [1], the problem of the saturation of the nuclear matter ground state in σ [2] or Nambu-Jona-Lasinio [3] (NJL) type models has been extensively discussed [4]- [9]. The common feature of these models is a vacuum effective potential, which has a "Mexican hat" shape as a function of the classical scalar field.…”

“…For this purpose, however, one needs the equation of state, and one first has to solve the problem of the stability of nuclear matter. A natural question in this respect is of course whether or not the quark substructure of 1 Recently it has been argued [9] that the stable abnormal state of quark matter, which can be described in the NJL model, should be interpreted as a droplet of massless quarks surrounded by the vacuum, i.e., as the nucleon. While this viewpoint is interesting, it seems very difficult to proceed to the description of nuclear matter along these lines.…”

The nuclear matter stability in a non-local chiral quark model

“…As the nuclear matter density increases the scalar and the axial diquark masses decrease, consequently the diquark interaction couplings g s and g a grow. This effect can be realized from It is well known that in the chiral models the stability of the nuclear matter depends very much on the dynamical chiral restoration [2,4,5,45]. The necessary condition for saturation of nuclear matter in any relativistic mean field theory is that nucleon attraction 8 Notice that here we have only one free parameter g v in medium and it is not straightforward to fix two values via it.…”

“…mediated from the σ-meson exchange should decrease at high density. Therefore, if σ-meson mass decreases too rapidly with density due to chiral restoration, it may work against the stabilization of the system [2,4,5,45]. However, as we have numerically proven, it is in principle possible to obtain a saturating nuclear matter equation of state, if the scalar field couples with the quarks instead of directly with the nucleons (see also [5]).…”

“…Application of the model to low density, however, has posed serious problems like the absence of saturation [2,3,4,5]. This is in contrast to nonchiral models like the Walecka model [6] which has been phenomenologically successful in describing the nuclear matter ground state in the mean field approximation.…”