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Mean- $p_T$ fluctuations in Au+Au collisions at $\sqrt{s_{\rm NN}}=3.0$ --$19.6$ GeV within JAM2

Using the JAM2 transport model with RQMDv mean-field dynamics, this study investigates event-by-event mean- $p_T$ fluctuations in Au+Au collisions at 3.0–19.6 GeV, finding that while the model qualitatively reproduces spectra and scaled fluctuations at higher energies, it exhibits stronger centrality dependence than data at lower energies and reveals species-dependent correlator behaviors that evolve similarly to elliptic flow without establishing a common microscopic origin.

Original authors: Yaqi Liu, Liuyao Zhang, Chunjian Zhang, Jinhui Chen, Chunwang Ma

Published 2026-09-24

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CC BY 4.0

Original authors: Yaqi Liu, Liuyao Zhang, Chunjian Zhang, Jinhui Chen, Chunwang Ma

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the heart of heavy-ion physics, scientists smash gold nuclei together at nearly the speed of light to recreate the extreme conditions that existed microseconds after the Big Bang. When these massive atomic cores collide, they create a fleeting, super-hot soup of particles known as quark-gluon plasma, which then cools and expands into a shower of ordinary matter. To understand how this transformation happens, researchers do not just look at the final pile of debris; they watch how the particles move and how their speeds fluctuate from one collision to the next. Specifically, they measure the average sideways push, or transverse momentum, of the particles produced. If the initial collision is slightly lopsided or if the energy is deposited unevenly, the resulting flow of matter changes in a predictable way. By studying these tiny variations in speed, physicists can probe the hidden properties of the nuclear matter, such as how stiff or compressible it is, and whether the matter behaves like a fluid or a gas during its brief existence.

A team of researchers has now used a sophisticated computer simulation to explore these speed fluctuations in gold-gold collisions across a wide range of energies, specifically between 3.0 and 19.6 billion electron volts. This energy range is particularly interesting because it sits in a transition zone where the behavior of the colliding matter is not yet fully understood. The scientists employed a model called JAM2, which simulates the collision by tracking individual particles as they bounce off one another, decay, and interact with invisible pressure fields generated by the dense nuclear matter. Unlike some other models that assume the matter instantly turns into a soup of free-floating quarks, this simulation keeps the particles as distinct hadrons, interacting through well-defined forces and mean fields, which act like a collective pressure pushing the particles apart. The goal was to see if this purely hadronic approach, without an explicit stage of free quarks, could reproduce the patterns of speed fluctuations observed in real experiments.

The researchers first checked if their simulation could accurately describe the basic behavior of the particles. They compared the simulated speeds of pions, kaons, and protons against actual measurements taken by the STAR collaboration at similar energies. The simulation successfully matched the general shapes of the speed distributions and the way these distributions changed as the collisions became more central, or head-on. This validation gave the team confidence to proceed with analyzing the fluctuations. They then looked at how the average speed of particles varied from event to event, calculating a specific value that represents the strength of these fluctuations. As the collisions became more central, involving more participating particles, the strength of these fluctuations naturally decreased. This trend, where the signal gets diluted as the number of sources increases, matched the experimental data well at higher energies between 7.7 and 19.6 billion electron volts.

However, a notable difference emerged at the lower end of the energy spectrum, between 3.0 and 4.5 billion electron volts. In this region, the simulation predicted that the fluctuations would change much more sharply as the collisions became more central than what the actual data showed. This discrepancy suggests that while the model captures the general physics, it may be missing some subtle dynamical effects that become important at these lower energies, such as specific ways the nuclear matter stops or how the surrounding "spectator" particles influence the core collision. The study also examined how these fluctuations differed between types of particles. When looking at protons and antiprotons together, the simulation showed a positive correlation in their speed variations, meaning they tended to fluctuate in the same direction. This effect was much stronger for protons than for charged pions. In contrast, the fluctuations for pions were negative or near zero at the lowest energies, indicating an anti-correlation, before turning slightly positive at higher energies.

Interestingly, the way the pion fluctuations changed with energy bore a resemblance to the evolution of elliptic flow, a measure of how the particles spread out in an oval shape rather than a circle. While the two trends moved in a similar direction as the energy increased, the researchers caution that this similarity does not prove they share the same microscopic origin. The elliptic flow measures the direction of the spread, while the speed fluctuations measure the magnitude of the push; they are distinct physical quantities. The simulation demonstrated that these complex patterns, including the sign change in pion fluctuations, can arise in a model that does not include a stage of free quarks. This finding provides a crucial baseline, showing that certain features of the data do not necessarily require the presence of a quark-gluon plasma to be explained. The work highlights the need for further controlled variations in the simulation to isolate the specific contributions of nuclear mean fields, particle rescattering, and spectator interactions, ensuring that future interpretations of these fluctuations are built on a solid, verified foundation.

Technical Summary: Mean-pT Fluctuations in Au+Au Collisions at $\sqrt{s_{NN}} = 3.0–19.6$ GeV within JAM2

Problem and Motivation
Event-by-event fluctuations of the mean transverse momentum ( $\langle p_T \rangle$ ) serve as a sensitive probe of initial-state energy deposition, transverse size fluctuations, and their conversion into collective dynamics in relativistic heavy-ion collisions. In the context of the RHIC Beam Energy Scan (BES), where systems reach large net-baryon densities, understanding these fluctuations is critical. The evolution of the system in this energy regime is influenced by baryon stopping, hadronic interactions, nuclear mean fields, and the finite-density QCD equation of state (EoS). While hydrodynamic models relate these fluctuations to initial geometry and collective expansion, and other frameworks like HIJING or AMPT provide references, there is a need for a microscopic transport calculation that incorporates baryonic mean fields but lacks an explicit partonic stage. This study addresses how second-order $p_T$ correlations, specifically their particle-species dependence, behave under these conditions to establish a baseline for baryon-rich matter before isolating critical dynamics.

Methodology and Model Setup
The study utilizes the JAM2 microscopic transport model in the RQMDv mean-field mode with the MH2 parameterization. Key methodological features include:

Dynamics: The model simulates non-equilibrium hadronic evolution via binary scattering, resonance excitations/decays, and string fragmentation. At BES energies, it implements Skyrme-type density- and momentum-dependent hadronic mean fields as Lorentz-vector potentials. The scalar potential vanishes ( $S_i=0$ ), but momentum dependence remains in the single-particle dispersion relation.
Parameters: The MH2 parameterization employs a nuclear incompressibility of $K = 380$ MeV at saturation density. The same parameters are applied across all collision energies ( $\sqrt{s_{NN}} = 3.0–19.6$ GeV) and centralities, with evolution tracked up to 50 fm/c.
Observables: The study defines the second-order correlator $\langle c_2 \rangle$ and the dimensionless scaled fluctuation $k_2 = \sqrt{\langle c_2 \rangle}/\langle \langle p_T \rangle \rangle$ . These are calculated for charged particles within $|\eta| < 0.5$ and $0.2 < p_T < 2.0$ GeV/c.
Event Selection: Centrality is defined via the number of participating nucleons ( $\langle N_{part} \rangle$ ) derived directly from the JAM2 event record (truth-level classification), distinguishing it from experimental multiplicity-based selections. Identified-particle spectra for $\pi^\pm$ and $p+\bar{p}$ are analyzed separately.

Key Results

Single-Particle Baseline: The JAM2/RQMDv calculations qualitatively reproduce the measured identified-particle $p_T$ spectra for $\pi^+$ , $K^+$ , and protons at midrapidity for $\sqrt{s_{NN}} = 7.7–19.6$ GeV. The model captures the centrality ordering and spectral shapes, providing a single-particle baseline for the fluctuation analysis, though it does not independently validate the two-particle correlations or spectra below 7.7 GeV.
Scaled Fluctuation ( $k_2$ ): The scaled fluctuation $k_2$ $k_{2}$ decreases with increasing $\langle N_{part} \rangle$ $⟨ N_{p a r t} ⟩$ across all energies, consistent with the dilution of correlated particle pairs as the number of sources increases.
- At $\sqrt{s_{NN}} = 7.7–19.6$ GeV, the calculated magnitude and centrality dependence show broad agreement with available STAR measurements.
- At $\sqrt{s_{NN}} = 3.0–4.5$ GeV, the calculated centrality dependence is stronger than observed in the data, particularly in central collisions. The authors note this discrepancy requires further investigation into centrality selection, acceptance, and particle composition effects.
Particle-Species Dependence ( $\langle c_2 \rangle$ ):
- Protons ( $p+\bar{p}$ ): The unnormalized correlator $\langle c_2 \rangle$ remains positive across all energies and centralities. Its magnitude is substantially larger than that of charged pions, particularly in peripheral collisions. The authors caution that this hierarchy may reflect the larger characteristic transverse-momentum scale of protons rather than stronger relative fluctuations.
- Charged Pions ( $\pi^\pm$ ): The correlator exhibits a distinct energy dependence. It is negative or consistent with zero over most centrality intervals at 3.0 and 3.5 GeV, becomes weakly positive at 4.5 GeV, and remains positive at higher energies (7.7–19.6 GeV).
Comparison with Elliptic Flow: The energy evolution of the charged-pion $\langle c_2 \rangle$ qualitatively resembles the reaction-plane elliptic flow ( $v_2$ ), which transitions from negative (spectator-induced squeeze-out) to positive (in-plane expansion) around 4.5 GeV. However, the paper explicitly states this comparison does not establish a common microscopic origin, as the scalar $p_T$ correlator and azimuthal harmonic probe distinct dynamical aspects.

Significance and Claims
The paper establishes a model reference for mean- $p_T$ fluctuations within a transport framework that includes baryonic mean fields but excludes an explicit partonic stage.

Baseline Establishment: The study provides species-dependent predictions that serve as a baseline for interpreting experimental data in the BES region.
Modest Scope: The authors emphasize that the study does not extract the EoS, separate individual mechanisms (mean fields vs. rescattering vs. spectators), or confirm the onset of dominant partonic interactions. The comparison with $v_2$ trends is descriptive rather than causal.
Future Directions: The authors suggest that isolating specific contributions requires controlled variations of transport dynamics. They propose that future work should include charge-resolved correlators, checks of centrality and decay contributions, and comparisons with alternative mean-field settings. Furthermore, extending calculations to lower energies and matching experimental acceptances are necessary for quantitative predictions relevant to the CEE program at HIRFL-CSR and the HIAF program.

In summary, the work demonstrates that qualitative trends observed in experimental data, such as the sign change in pion correlations and the energy dependence of fluctuations, can emerge in a hadronic transport model without a partonic phase, highlighting the need for controlled theoretical variations to isolate the underlying microscopic mechanisms.

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