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Effects of Initial Density Fluctuations and

Centrality Determination in Heavy-ion Collisions

Xiaoqing Yue · IWND 2026

Supervisors: Pengcheng Li, Yongjia Wang, Qingfeng Li, Fuhu Liu

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1) Background

2) Transport model

3) Initial Density Fluctuations

4) Centrality Determination

5) Reconstructing impact parameter using machine learning

6) Summary

outline

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Intermediate-energy Heavy-ion Collisions

heavy-ion collisions at intermediate energies
nuclear equation of state (EoS), QCD phase structure, neutron stars and neutron-star mergers ...
Exp: RHIC-BES/FXT, FAIR-CBM, NICA-MPD, HADES and HIAF-CEE

L. Du, A. Sorensen, and M. Stephanov, arXiv:2402.10183

Zhang Y, Zhang D W, Luo X F. Nuclear Techniques, 2023, 46(4): 040001

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Fluctuations and Initial Density Fluctuations

STAR Collaboration. Phys.Rev.Lett. 135 (2025) 14, 142301

Event-by-event fluctuations —— cumulants

→ critical point, initial-state fluctuations,

dynamical evolution, acceptance, and

centrality definition ...

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Centrality Determination and Impact-parameter Reconstruction

HADES Collaboration. Eur. Phys. J. A (2018) 54: 85

How do centrality determination methods affect observables?
Can machine-learning methods provide a more robust reconstruction of b across different transport models?

The impact parameter b is a key quantity characterizing the collision geometry, but it cannot be measured directly .

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1) Background

2) Transport model

3) Initial Density Fluctuations

4) Centrality Determination

5) Reconstructing impact parameter using machine learning

6) Summary

outline

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Ultrarelativistic Quantum Molecular Dynamics (UrQMD) Model

Initialization

Propagation

Collision term

Cluster recognition

Each nucleon is represented by a Gaussian wave packet

|The centers of the Gaussian wave packets are randomly distributed within a sphere of radius

|Nuclear density distribution (Woods-Saxon / Hard sphere) |Minimum nucleon distance d_min

The evolution of nucleon coordinates and momenta satisfies Hamilton's equations

|Mean-field (MF) potential |Soft / Hard EoS |With / without momentum-dependent potential

Two-body collisions and resonance decays

|In-medium cross sections |Pauli blocking

Isospin-dependent Minimum Spanning Tree

https://itp.uni-frankfurt.de/~bleicher/index.html?content=urqmd

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1) Background

2) Transport model

3) Initial Density Fluctuations

4) Centrality Determination

5) Reconstructing impact parameter using machine learning

6) Summary

outline

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Initial Density Distribution and Evolution

In coordinate space, density distribution fluctuations increase as the d_min value decreases.

t ≤ 3 fm/c, the density influences are sensitive to d_min ; with a larger σ_ρ for d_min = 1.0 fm
t > 3 fm/c, the difference caused by d_min is largely washed out during the fireball expansion stage; effect in UrQMD/c was larger than in UrQMD/m

Xiaoqing Yue, Yongjia Wang, Qingfeng Li, and Fuhu Liu. Universe 2022, 8, 491.

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Cumulant Ratios at b=0 and 5 fm

(a)

(b)

(c)

(d)

∆η ≤ 4, the effect of the MF dominant
∆η ≥ 4, the influence of MF is suppressed; the sensitivity to d_min = 1.0 fm becomes visible
∆η = 4–6 and b = 5 fm, the cumulant ratios all increase

The initial density fluctuations increased with the decrease of d_min from 1.6 fm to 1.0 fm

Xiaoqing Yue, Yongjia Wang, Qingfeng Li, and Fuhu Liu. Universe 2022, 8, 491.

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1) Background

2) Transport model

3) Initial Density Fluctuations

4) Centrality Determination

5) Reconstructing impact parameter using machine learning

6) Summary

outline

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Centrality Determination Methods

Obtain from HADES Collaboration

Centrality	M_ch	b_f (fm)	b_r (fm)
0-10.11%	≥ 174	≤ 4.26	≤ 4.70(0-10%)
10.12-20.13%	173-142	4.27-6.00	4.71-6.60(10-20%)
20.14-29.87%	141-112	6.01-7.31	6.61-8.10(20-30%)
29.88-39.91%	111-84	7.32-8.45	8.11-9.30(30-40%)
39.92-100%	≤ 83	≥ 8.46	≥ 9.31(40-100%)

1.C. Cavata, et al. Phys. Rev. C 42, 1760; 2.Pengcheng Li, et al., J. Phys. G 47 (2020) 035108; 3.HADES Collaboration., et al. Eur. Phys. J. A 54, 85 (2018)

Method 1: Exp —— M_ch

Method 2: Geometric —— b_f

Method 3: Glauber MC —— b_r

Input model after calculation

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The Result of Free Proton Yield

Xiaoqing Yue, Pengcheng Li, Yongjia Wang, Qingfeng Li, Fuhu Liu. Phys.Rev.C 113 (2026) 2, 024905

In 0–10% central collisions, the SM are closer to the HADES than the HM
The results for M_ch and b_f almost overlap, whereas the difference between M_ch and b_r increases as centrality rises

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M_ch vs. b_f

M_ch vs. b_r

The Result of Transverse Momentum Distribution

Xiaoqing Yue, Pengcheng Li, Yongjia Wang, Qingfeng Li, Fuhu Liu. Phys.Rev.C 113 (2026) 2, 024905

The EoS effect gradually weakens with increasing centrality

M_ch is generally consistent with b_f, whereas the deviation between M_ch and b_r increases with centrality and becomes particularly pronounced in the high-p_T region

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1) Background

2) Transport model

3) Initial Density Fluctuations

4) Centrality Determination

5) Reconstructing impact parameter using machine learning

6) Summary

outline

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Performance of ML Algorithms under Different Models

UrQMD/MH: mean-field & hard-sphere

UrQMD/CH: cascade & hard-sphere

UrQMD/CW: cascade & Woods-Saxon

AMPT: string-melting version

JAM/C: cascade & Woods-Saxon

JAM/M: mean-field & Woods-Saxon

<< These two quantities partly estimate how strong the fluctuation between different events is.

>> It can be seen that the typical values of MAE are around 0.2–0.4 fm even for scenarios when training and test data are generated from different models

Xiaoqing Yue, Guojun Wei, Yongjia Wang, Zhilong Li, Pengcheng Li, Haojie Xu, Xiangrong Zhu, Qingfeng Li, Fuhu Liu and Yasushi Nara.

Phys.Rev.C 114 (2026) 1, 014910

Six features:

the yield of charged pions (N_π− and N_π+ )

the yield of charged pions at midrapidity (n_π−and n_π+ )

the total transverse momentum of charged pions(p_tπ− and p_tπ+ )

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Reconstruct impact parameters using ML / traditional models

⇐ Systematically compare the b distributions

⇑ The results of the cross-validation analysis

ML method

polynomial fitting

Xiaoqing Yue, Guojun Wei, Yongjia Wang, Zhilong Li, Pengcheng Li, Haojie Xu, Xiangrong Zhu, Qingfeng Li, Fuhu Liu and Yasushi Nara. Phys.Rev.C 114 (2026) 1, 014910

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K-means clustering algorithm

Divide events with different impact parameters into six clusters via K-means

Xiaoqing Yue, Guojun Wei, Yongjia Wang, Zhilong Li, Pengcheng Li, Haojie Xu, Xiangrong Zhu, Qingfeng Li, Fuhu Liu and Yasushi Nara. Phys.Rev.C 114 (2026) 1, 014910

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1) Background

2) Transport model

3) Initial Density Fluctuations

4) Centrality Determination

5) Reconstructing impact parameter using machine learning

6) Summary

outline

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Summary

Fingerprint of the initial density fluctuations on the cumulants is visible

Establish a mapping between charged-particle multiplicity and collision geometry

Strong robustness of using an ML algorithm trained on transport-model data for impact-parameter determination

Thank you for your attention!

Xiaoqing Yue · IWND 2026