Scalar field in nuclear matter: the roles of spontaneous chiral symmetry breaking and nucleon structure

Chiral theories with spontaneous symmetry breaking such as the Nambu-Jona-Lasinio (NJL) model lead to the existence of a scalar mode. We present in a detailed manner how the corresponding low momentum effective lagrangian involving the scalar field can be constructed starting from the NJL model. We discuss the relevance of the scalar mode for the problem of the nuclear binding and saturation. We show that it depends on the nucleon mass origin with two extreme cases. If this origin is entirely due to confinement the coupling of this mode to the nucleons vanishes, making it irrelevant for the nuclear binding problem. If instead it is entirely due to spontaneous symmetry breaking it couples to the nucleons but nuclear matter collapses. It is only in the case of a mixed origin with spontaneous breaking that nuclear matter can be stable and reach saturation. We describe models of nucleon structure where this balance is achieved. We also show how chiral constraints and confinement modify the QCD sum rules for the mass evolution in nuclear matter.