Equilibrium expectations for non-Gaussian fluctuations near a QCD critical point

TL;DR

This paper estimates equilibrium particle-number fluctuations near a QCD critical point using a 3D Ising Model-based equation of state, aiding interpretation of experimental fluctuation measurements in heavy-ion collisions.

Contribution

It provides a systematic calculation of equilibrium proton factorial cumulants and correlation length near a QCD critical point using the BEST EoS, incorporating critical features from the 3D Ising Model.

Findings

Proton factorial cumulants depend on non-universal mapping parameters.

Correlation length is calculated consistently with the scaling EoS.

Results serve as baseline for out-of-equilibrium fluctuation estimates.

Abstract

With the highly anticipated results from the Beam Energy Scan II program at RHIC being recently revealed, an understanding of particle-number fluctuations and their significance as a potential signature of a possible QCD critical point is crucial. Early works that embarked on this endeavor sought to estimate the fluctuations due to the presence of a critical point assuming they stay in equilibrium. From these results came the proposal to focus efforts on higher, non-Gaussian, moments of the event-by-event distributions, in particular of the number of protons. These non-Gaussian moments are especially sensitive to critical fluctuations, as their magnitudes are proportional to high powers of the critical correlation length. As the equation of state provides key input for hydrodynamical simulations of heavy-ion collisions, we estimate equilibrium fluctuations from the BEST equation of state (EoS) that includes critical features from the 3D Ising Model. In particular, the proton factorial cumulants and their dependence on non-universal mapping parameters is investigated within the BEST EoS. Furthermore, the correlation length, as a central quantity for the assessment of fluctuations in the vicinity of a critical point, is also calculated in a consistent manner with the scaling equation of state. An understanding of the equilibrium estimates of proton factorial cumulants will be useful for further comparison to estimates of out-of-equilibrium fluctuations in order to determine the magnitude of the observable fluctuations to be expected in heavy-ion collision experiments, in which the time spent near a critical point is short.