# Net-proton number fluctuations in the presence of the QCD critical point

## TL;DR

This paper models net-proton fluctuations near the QCD critical point, reproducing some experimental fluctuation patterns and suggesting the critical point's influence on observed heavy-ion collision data.

## Contribution

It introduces a phenomenological model coupling the critical mode to protons, providing insights into net-proton fluctuations and their relation to the QCD critical point.

## Key findings

- Reproduces the non-monotonic kurtosis observed in experiments
- Shows the variance-to-mean ratio changes smoothly with beam energy
- Highlights discrepancies in skewness behavior compared to critical expectations

## Abstract

Event-by-event fluctuations of the net-proton number studied in heavy-ion collisions provide an important means in the search for the conjectured critical end point (CP) in the QCD phase diagram. We propose a phenomenological model in which the fluctuations of the chiral critical mode couple to protons and anti-protons. This allows us to study the behavior of the net-proton number fluctuations in the presence of the CP. Calculating the net-proton number cumulants, $C_n$ with n=1,2,3,4, along the phenomenological freeze-out line we show that the ratio of variance and mean $C_2/C_1$, as well as kurtosis $C_4/C_2$ resemble qualitative properties observed in data in heavy-ion collisions as a function of beam energy obtained by the STAR Collaboration at RHIC. In particular, the non-monotonic structure of the kurtosis and smooth change of the $C_2/C_1$ ratio with beam energy could be due to the CP located near the freeze-out line. The skewness, however, exhibits properties that are in contrast to the criticality expected due to the CP. The dependence of our results on the model parameters and the proximity of the chemical freeze-out to the critical point are also discussed.