An extension of the ideal hadron resonance gas (HRG) model which includes attractive and repulsive van der Waals (VDW) interactions between hadrons is constructed. It employs a multi-component VDW equation, generalized to include quantum statistical effects. The VDW parameters a and b of baryon-baryon interaction are fixed by the ground state properties of nuclear matter, and this VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryonic densities.
First, the VDW equation for nucleons is used to calculate the scaled variance, skewness, and kurtosis of nucleon number fluctuations in nuclear matter, and these quantities show singular behavior with rich structures around the critical point. The strongly intensive measures Delta and Sigma of the particle number and excitation energy fluctuations are also considered, and, similarly, show singular behavior near the CP.
The predictions of the full VDW-HRG model are then confronted with the lattice QCD calculations at zero chemical potential. The inclusion of baryonic interactions leads to a qualitatively different behavior of the fluctuations of conserved charges in the crossover region. In many cases it resembles the lattice data. For instance, the VDW-HRG model predicts the drop of the \chi_4/\chi_2 cumulant ratio for the net baryon number fluctuations in the crossover region, which is also seen on the lattice. The behavior of lattice QCD observables is found to correlate strongly with nuclear ground state properties.
Calculations are also performed at finite chemical potentials.
The VDW-HRG model predicts a non-monotonic behavior of the net baryon \chi_4/\chi_2 ratio with respect to the collision energy, in stark contrast to the ideal HRG. This implies that non-trivial fluctuations of net-baryon number in heavy-ion collisions manifest traces of the nuclear liquid-gas phase transition.
We also analyze the preliminary lattice data at imaginary chemical potential with the VDW-HRG model. The lattice behavior of the Fourier coefficients in the Fourier expansion of baryon density at imaginary baryochemical potential is shown to be consistent with presence of eigenvolume-type repulsive baryonic interactions. Similar conclusion is obtained from the phase shifts of nucleon-nucleon scattering.
This presentation is mainly based on
 V. Vovchenko, M.I. Gorenstein, H. Stoecker, Phys. Rev. Lett. 118, 182301 (2017)
as well as on
 V. Vovchenko, D.V. Anchishkin, M.I. Gorenstein, Phys. Rev. C 91, 064314 (2015)
 V. Vovchenko, D.V. Anchishkin, M.I. Gorenstein, R.V. Poberezhnyuk, Phys. Rev. C 92, 054901 (2015)
 V. Vovchenko, arXiv:1701.06524 [nucl-th].