  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.
