# Conserved Charge Fluctuations from RHIC BES and FXT

## Abstract

**:**

## 1. Introduction

## 2. Conserved Charge Fluctuations

#### 2.1. Cumulants

#### 2.2. Analysis Techniques

#### 2.3. Baselines

## 3. Net-Proton Fluctuations

#### 3.1. ${C}_{4}/{C}_{2}$ for the Critical Point Search

#### 3.2. ${C}_{6}/{C}_{2}$ for the Crossover Search

## 4. Challenge for Baryon–Strangeness Correlations

#### 4.1. Previous Measurement

#### 4.2. New Method: Purity Correction

#### 4.3. Measurement of $\Lambda $ and ${\Xi}^{-}$ Hyperons

#### 4.4. Results

## 5. Summary

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | The ratio of the signal to the background yields. |

2 | The ratio of the signal yield to the square-root of signal candidates, which is a proxy for the product of purity and reconstruction efficiency. |

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**Figure 1.**The conjectured QCD phase diagram with respect to the baryon chemical potential and temperature [1]. The energies and ranges represent collision energies from the experimental programs at RHIC and LHC.

**Figure 2.**Event−by−event raw net-proton multiplicity distributions for Au+Au collisions at BES-I energies [5].

**Figure 3.**Collision energy dependence of (net−)proton ${C}_{4}/{C}_{2}$ for Au+Au most central collisions from the BES-I and FXT [32]. The golden band and cross represent the UrQMD calculations. The green band shows the projection of statistical uncertainties for BES-II energies in the collider mode.

**Figure 4.**(

**Left**) Centrality dependence of net-proton ${C}_{6}/{C}_{2}$ at 27, 54.4, and 200 GeV Au+Au collisions [38]. The lattice QCD calculations are from Ref. [39]. (

**Right**) Collision energy dependence of (net-)proton ${C}_{6}/{C}_{2}$ for Au+Au collisions at 0–40% and 50–60% centralities [41]. The ${C}_{6}/{C}_{2}$ values for lattice QCD and FRG calculations are from Refs. [39,40].

**Figure 5.**Example of the invariant mass distribution for $\Lambda $ [48]. The red shaded area corresponds to the signal particles, and the blue one corresponds to the background particles. The dotted blue lines are the boundaries for the sideband windows.

**Figure 6.**Invariant mass distribution of $\Lambda $ (

**left**) and ${\Xi}^{-}$ (

**right**) hyperons. The cyan solid lines represent the rotation backgrounds, and the magenta dotted lines are the sideband boundaries for the purity corrections.

**Figure 7.**The 1st- and 2nd-order cumulants of sideband particles, ${\langle {\Lambda}_{R}\rangle}_{\mathrm{c}}$ and ${\langle {\Lambda}_{R}^{2}\rangle}_{\mathrm{c}}$ (the subscript R represents the rotational backgrounds), and the 2nd-order mix-cumulants between signal candidates and sideband particles, ${\langle {\Lambda}_{SN}{\Lambda}_{R}\rangle}_{\mathrm{c}}$, for $\Lambda $ (

**left**) and ${\Xi}^{-}$ (

**right**).

**Figure 8.**The 2nd-order $\Lambda $ cumulant as a function of $\Lambda $ purity from Au+Au most central collisions at 200 GeV. Purity-uncorrected results are shown by black squares, and purity-corrected results are shown by red circles. All results are corrected for reconstruction efficiencies. The branching ratio is not taken into account.

**Figure 9.**Centrality dependence of ${C}_{BS}$ from Au+Au 200 GeV collisions. The results are corrected for purity and reconstruction efficiencies for hyperons, while their branching ratios are not taken into account. The purple band represents the results from the lattice QCD calculations [49]. The UrQMD calculations are shown by red and blue shaded bands.

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**MDPI and ACS Style**

Nonaka, T., on behalf of STAR Collaboration.
Conserved Charge Fluctuations from RHIC BES and FXT. *Universe* **2024**, *10*, 49.
https://doi.org/10.3390/universe10010049

**AMA Style**

Nonaka T on behalf of STAR Collaboration.
Conserved Charge Fluctuations from RHIC BES and FXT. *Universe*. 2024; 10(1):49.
https://doi.org/10.3390/universe10010049

**Chicago/Turabian Style**

Nonaka, Toshihiro on behalf of STAR Collaboration.
2024. "Conserved Charge Fluctuations from RHIC BES and FXT" *Universe* 10, no. 1: 49.
https://doi.org/10.3390/universe10010049