  The aim of our contribution is to shed some light on open questions facing
the high density nuclear many-body problem. We focus our attention on the
conceptual issue of naturalness and its role for the baryon-meson coupling for
nuclear matter at high densities. As a guideline for the strengths of the
various couplings the concept of naturalness has been adopted. In order to
encourage possible new directions of research, we discuss relevant aspects of a
relativistic effective theory for nuclear matter with natural parametric
couplings and genuine many-body forces. Among other topics, we discuss in this
work the connection of this theory with other known effective Quantum
Hadrodynamics (QHD) models found in literature and how we can potentially use
our approach to describe new physics for neutron stars. We also show some
preliminary results for the equation of state, population profiles and
mass-radius relation for neutron stars assuming local charge neutrality and
beta equilibrium.
