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

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.