  A non-perturbative framework is provided to connect QCD with nuclear
phenomenology in the intermediate and high density regime. Using QCD Sum Rules,
in-medium scalar and vector self-energies of nucleons are calculated as
functions of the density of an infinite nuclear medium. The self-energies are
used in the relativistic mean field theory lagrangian of a high-density nuclear
medium to find the binding energy of in-medium nucleons and the value of light
quark condensate, $\langle \bar{q} q \rangle_{\rm{vac}} = -~(0.288
~\rm{GeV})^3$, in the Borel-improved resummation scheme. The critical mass of
an ideal neutron star is obtained by coupling a uniform saturation energy
density of cold, dense nuclear matter to Einstein equation in hydrostatic
equilibrium. Since it is less likely for a neutron star core to avoid
deconfinement and enter the rigid vector repulsion phase where the speed of
sound can smoothly approach from conformal to causal limit, a gap should exist
in the stellar mass spectrum, $[3.48M_\odot, 5.47M_\odot]$, where it would be
rare to find any isolated, cold, non-rotating neutron star or a black hole.
