Interaction fingerprints in temperature-fluctuation cumulants from the QCD crossover to nuclear liquid-gas criticality

Abstract

Temperature fluctuations of the matter produced in relativistic heavy-ion collisions are related to event-by-event fluctuations of the mean transverse momentum and, through the specific heat, to the QCD equation of state. We calculate the temperature-fluctuation cumulants $c_2$, $c_3$, and $c_4$ in the ideal hadron resonance gas (HRG), in an excluded-volume HRG consistent with lattice QCD constraints on baryon repulsion, and in a van der Waals HRG that reproduces the nuclear ground state. At zero baryon density all three models agree with lattice QCD thermodynamics up to the chiral crossover and separate above it. Along the chemical freeze-out curve the models remain close for $\sqrt{s_{NN}} \gtrsim 20$ GeV and separate strongly at lower energies, where baryonic interactions dominate the thermal response. In the van der Waals model the variance $c_2$ develops a minimum along the Widom line of the nuclear liquid-gas transition and $c_3$ changes sign across it. Temperature cumulants thus connect mean-transverse-momentum fluctuations to thermodynamic structures in two regions of the QCD phase diagram.