Nuclear liquid-gas transition in QCD

We estimate the nuclear saturation density and the binding energy in a nuclear liquid from precision data on the coupling of the four-quark scattering vertex in the vector channel, computed within functional QCD. We show that this coupling is directly related to the density-density potential and the latter is used for the estimates. In a first qualitative computation we find a saturation density of $0.2\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}3}$ and an upper bound for the binding energy of 21.5 MeV, in agreement with the empirical values of $0.16\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}3}$ and 16 MeV, respectively. We also use the scattering vertex for constructing an emergent low-energy effective theory for the liquid gas transition from QCD correlation function, whose coupling parameters can be determined within QCD. As a first consistency check of this construction we estimate the in-medium reduction of the nucleon pole mass.