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

Properties of Infinite Nuclear Medium from QCD Sum Rules and the Neutron Star-Black Hole Mass Gap