Chemical freeze-out curve in heavy-ion collisions and the QCD critical point

The chemical freeze-out curve in heavy-ion collisions is investigated in the context of a quantum chromodynamics (QCD) critical point (CP) search at finite baryon densities. Taking the hadron resonance gas picture at face value, chemical freeze-out points at a given baryochemical potential provide a lower bound on the possible temperature of the QCD CP. We first verify that the freeze-out data in heavy-ion collisions are well described by a constant energy per particle curve, $E/N = \rm const$, under strangeness neutrality conditions ($\mu_S \neq 0$, $\mu_Q \neq 0$). We then evaluate the hypothetical lower bound on the freeze-out curve based on this criterion in the absence of strangeness neutrality ($\mu_S = 0$, $\mu_Q = 0$) and confront it with recent predictions on the CP location. We find that recent estimates based on Yang-Lee edge singularities from lattice QCD data on coarse lattices ($N_{\tau} = 6$) place the CP significantly below the freeze-out curve, hinting at the importance of performing continuum extrapolation within this method. Predictions based on functional methods and holography place the CP slightly above the freeze-out curve, indicating that the QCD CP may be located very close to the chemical freeze-out in $A$+$A$ collisions at $\sqrt{s_{NN}} = 3.5$-$6$ GeV.