Higher order conserved charge fluctuations inside the mixed phase

TL;DR

This paper derives formulas for higher order conserved charge fluctuations in the mixed phase, using the van der Waals model, and analyzes their behavior near the critical point relevant for heavy-ion collision experiments.

Contribution

It introduces general formulas for higher order cumulants of conserved charge fluctuations in the mixed phase, with detailed analysis near the critical point using the van der Waals model.

Findings

Even-order fluctuation measures are positive in the mixed phase and diverge at the critical point.

Odd-order measures change sign near the binodals, indicating different fluctuation behaviors.

Results are relevant for interpreting event-by-event fluctuations in heavy-ion collision experiments.

Abstract

General formulas are presented for higher order cumulants of the conserved charge statistical fluctuations inside the mixed phase. As a particular example the van der Waals model in the grand canonical ensemble is used. The higher order measures of the conserved charge fluctuations up to the hyperkurtosis are calculated in a vicinity of the critical point (CP). The analysis includes both the mixed phase region and the pure phases on the phase diagram. It is shown that even-order fluctuation measures, e.g. scaled variance, kurtosis, and hyperkurtosis, have only positive values in the mixed phase, and go to infinity at the CP. For odd-order measures, such as skewness and hyperskewness, the regions of positive and negative values are found near the left and right binodals, respectively. The obtained results are discussed in a context of the event-by-event fluctuation measurements in heavy-ion collisions.