A key question about the QCD phase diagram is whether there is a critical point somewhere on the boundary between the hadronic and quark-gluon plasma phases, and if so where. Heavy-ion collisions offer a unique opportunity to search for signatures of such a critical point by analyzing event-by-event fluctuations in particle multiplicities. To draw meaningful conclusions from experimental data, a theoretical framework is needed to link QCD thermodynamics with the particle spectra and correlations observed in detectors. The equation of state (EoS) of QCD near a critical point can be related to the universal Gibbs free energy of the 3D Ising model using four currently unknown nonuniversal mapping parameters whose values are determined by the microscopic details of QCD. We utilize the maximum entropy approach to freeze-out the fluctuations in order to make estimates for factorial cumulants of proton multiplicities, assuming thermal equilibrium, for a family of EoS with a 3D Ising-like critical point, varying the microscopic inputs that determine the strength and structure of the critical features. We quantify the effect of the nonuniversal mapping parameters, and the distance between the critical point and the freeze-out curve, on the factorial cumulants of proton multiplicities.

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• Entropy
• Equations of state
• Fluctuations & noise
• Particle & resonance production
• Particle correlations & fluctuations
• QCD phase transitions
• Relativistic heavy-ion collisions