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

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