# Locating the QCD critical end point through the peaked baryon number susceptibilities along the freeze-out line

## TL;DR

This paper proposes that peaked baryon number susceptibilities along the freeze-out line serve as a universal signature to locate the QCD critical end point, supported by holographic QCD model analysis and experimental data.

## Contribution

It introduces a model-independent, universal feature of baryon susceptibilities near the CEP and links it to experimental signatures in heavy-ion collisions.

## Key findings

- Peaked baryon susceptibilities form a ridge along the phase boundary.
- A sword-shaped mountain appears around the CEP in susceptibility ratios.
- Experimental data suggests the CEP is near collision energy 3-5 GeV.

## Abstract

We investigate the baryon number susceptibilities up to fourth order along different freeze-out lines in a holographic QCD model with the critical end point (CEP), and we propose that the peaked baryon number susceptibilities along the freeze-out line can be used as a clean signature to locate the CEP in the QCD phase diagram. On the temperature and baryon chemical potential plane, the ratio of the baryon number susceptibilities (up to fourth order) forms a ridge along the phase boundary, and develops a sword shape mountain standing upright around the CEP in a narrow and oblate region. This feature is model independent and universal if the CEP exists. The measurement of the baryon number susceptibilities from heavy-ion collision experiment is along the freeze-out line. If the freeze-out line crosses the foot of the CEP mountain, then one can observe the peaked baryon number susceptibilities along the freeze-out line, and the kurtosis of the baryon number distributions has the tallest magnitude. The data from the first phase of beam energy scan program at the Relativistic Heavy Ion Collisions indicates that a peak of the kurtosis of the baryon number distribution would show up at the collision energy around 5 GeV, which suggests that the freeze-out line crosses the foot of the CEP mountain and the summit of the CEP would be located nearby around the collision energy of 3 GeV.