⚛️ nuclear theory

Dynamical Coulomb effects on charged-pion HBT-radius splitting in central Au+Au collisions at few-GeV energies

This study investigates the role of dynamical Coulomb effects in explaining the observed splitting between $\pi^{+}\pi^{+}$ and $\pi^{-}\pi^{-}$ femtoscopic radii in central Au+Au collisions at few-GeV energies, finding that while baryon-meson interactions and residual-source treatments reproduce key trends, they do not fully account for the experimental data, suggesting a need to further explore charged-source geometry and its interplay with strong interactions.

Original authors: Pengcheng Li, Yongjia Wang, Qingfeng Li

Published 2026-09-22

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CC0 1.0

Original authors: Pengcheng Li, Yongjia Wang, Qingfeng Li

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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 subatomic world, where particles zip around at nearly the speed of light, scientists use a clever trick to measure things far too small to see with any microscope. This technique, known as intensity interferometry, was first used by astronomers to measure the size of distant stars by comparing the light waves arriving from them. Physicists later adapted this method to study the fleeting clouds of particles created when heavy atomic nuclei smash into each other. By looking at how pairs of identical particles, such as pions, emerge from these high-speed collisions, researchers can map out the size and shape of the fireball created in the crash, as well as how long it lasts before cooling down. These measurements act like a snapshot of the universe's most extreme moments, helping scientists understand the forces that hold matter together and how it behaves under immense pressure.

A recent study focused on a specific puzzle arising from these measurements: why do negatively charged pions appear to come from a slightly larger region than their positively charged cousins? Experiments conducted by the HADES and STAR collaborations had already noticed this difference, but the reason remained unclear. The new research, led by physicists at Huzhou Normal University and the Joint Institute for Nuclear Research, set out to determine how much of this size difference is caused simply by the electric forces between the particles and the rest of the matter in the collision. They wanted to know if the electric push and pull alone could explain the observed split, or if something more complex was happening.

To investigate this, the team used powerful computer simulations to recreate collisions between gold nuclei at energies ranging from 2.42 to 5.2 billion electron volts. They built a detailed model of the collision that tracked every particle as it formed, moved, and interacted. The researchers ran three different versions of the simulation to see which electric interactions mattered most. In the first version, they only included the electric forces between heavy particles like protons and neutrons. In the second, they added the forces between these heavy particles and the lighter pions. In the third, they also included the forces between the pions themselves. By comparing these scenarios, they could isolate exactly how the electric charge of the surrounding matter influenced the path of each pion as it flew away.

The simulations revealed that the electric forces between the heavy particles and the pions are the primary driver of the size difference. When the team included these specific interactions, the model successfully reproduced the main trend seen in the real experiments: the negatively charged pions appeared to come from a slightly larger area than the positive ones. The forces between the pions themselves played a much smaller role. The researchers also developed a second approach to check their findings. Instead of tracking every single particle interaction, they treated the leftover charged matter as a single, expanding sphere of charge that changed over time. They then calculated how this expanding sphere would push or pull on each pion as it traveled away. This method also showed an increase in the size difference, confirming that the electric environment plays a significant role.

However, the study also found that electricity alone is not the whole story. While the simulations could recreate the general pattern of the size difference, they did not fully match the exact numbers measured in the experiments, particularly for the sideways direction of the collision. The model tended to underestimate how large the difference was. This suggests that while electric forces are a major piece of the puzzle, other factors must also be at play. These could include the specific way pions are created and absorbed, the shape of the exploding fireball, or other complex dynamics inside the collision zone. The researchers concluded that their work provides a solid foundation for understanding the electric effects, but a complete explanation will require looking at these other ingredients in greater detail. The study highlights that even in the chaotic aftermath of a nuclear crash, the simple push and pull of electric charge leaves a distinct and measurable fingerprint on the particles that escape.

Technical Summary: Dynamical Coulomb Effects on Charged-Pion HBT-Radius Splitting

Problem Statement
Experiments by the HADES and STAR Collaborations have observed a significant splitting in the Hanbury Brown–Twiss (HBT) radii extracted from $\pi^+\pi^+$ and $\pi^-\pi^-$ pairs in central Au+Au collisions at few-GeV energies ( $\sqrt{s_{NN}} \approx 2.42\text{--}5.2$ GeV). Specifically, the radii for $\pi^-\pi^-$ pairs exceed those for $\pi^+\pi^+$ pairs, with the effect being most prominent in the sideward ( $R_{side}$ ) and longitudinal ( $R_{long}$ ) components at low pair transverse momentum ( $k_T$ ). While phenomenological models using effective charges and momentum corrections have successfully described this splitting, a microscopic transport treatment resolving the specific space-time histories of Coulomb interactions has been lacking. The central question addressed is the extent to which dynamical Coulomb effects alone can account for the observed charge-dependent HBT radius splitting.

Methodology
The authors employ a combined framework using the UrQMD transport model (version 4.0) and the CRAB correlation analysis program. The study focuses on 0–10% central Au+Au collisions at $\sqrt{s_{NN}} = 2.42, 3.0, 3.2, 3.5, 3.9, 4.5,$ and $5.2$ GeV, utilizing a hard Skyrme Equation of State ( $K_0 = 380$ MeV).

Two complementary approaches are used to model Coulomb dynamics:

Microscopic Two-Body Scenarios: Three transport scenarios are simulated to isolate specific Coulomb contributions:
- Case I (Reference): Includes only baryon–baryon (BB) Coulomb interactions.
- Case II: Adds baryon–meson (BM) interactions.
- Case III: Further adds meson–meson (MM) interactions.
  In these scenarios, pairwise Coulomb forces are calculated event-by-event during the transport evolution, modifying pion trajectories and freeze-out correlations.
Dynamical Residual-Source Treatment: Based on the Case-I phase-space output (where pions do not experience direct BM or MM forces), the authors reconstruct a time-dependent effective charged source.
- The residual source is defined as the ensemble of charged participant baryons and charged mesons at a given time $t$ .
- The source is modeled as an expanding uniform sphere characterized by a time-dependent effective charge $Z_{\text{eff}}(t)$ and an effective radius $R_{\text{eff}}(t)$ , reconstructed from UrQMD snapshots.
- Each charged pion is propagated from its individual last strong-interaction point through this evolving Coulomb field using a relativistic velocity-Verlet algorithm. The accumulated Coulomb impulse modifies the pion's final momentum, which is then fed into CRAB for HBT analysis.

Key Contributions

Quantification of Coulomb Contributions: The study systematically separates the effects of BB, BM, and MM Coulomb interactions on HBT radii.
Dynamical Effective Source: The paper implements a novel approach where the residual source is not static but evolves in time ( $Z_{\text{eff}}(t)$ and $R_{\text{eff}}(t)$ ), and pions are propagated individually through this field from their specific freeze-out points.
Comparison of Scales: It contrasts the microscopic, event-by-event pairwise Coulomb treatment with a macroscopic, event-averaged monopole field treatment to assess their respective impacts on charge splitting.

Results

Momentum Dependence: The calculations reproduce the general trend of HBT radii decreasing with increasing $k_T$ . The inclusion of BM interactions in the microscopic transport (Case II) generates the majority of the additional charge splitting observed between $\pi^-\pi^-$ and $\pi^+\pi^-$ pairs. MM interactions (Case III) contribute only marginally.
Residual Source Effects: The dynamical residual-source calculation enhances the splitting in $R_{long}$ and $R_{side}$ relative to the BB-only reference. However, the effect on $R_{out}$ is minimal.
Energy Dependence: Both the microscopic and residual-source calculations show that the charge splitting decreases as collision energy increases, consistent with experimental data. This is attributed to the residual source remaining compact and generating a strong field for a shorter duration at higher energies.
Quantitative Discrepancy: While the models reproduce the trend of the splitting, they do not fully account for the magnitude of the experimental data.
- At $\sqrt{s_{NN}} = 2.42$ GeV, the residual-source calculation yields $R_{long}$ and $R_{side}$ ratios ( $R_{\pi^-\pi^-}/R_{\pi^+\pi^+}$ ) of 1.128 and 1.085, respectively, compared to experimental values of approximately 1.23 and 1.20.
- The sideward splitting ( $R_{side}$ ) is consistently underestimated across the energy range, particularly for negative pions.
- The model underestimates absolute radii at higher energies, suggesting that agreement in ratios does not imply a complete description of the space-time emission structure.

Significance and Claims
The paper claims that dynamical Coulomb interactions, specifically the coupling between pions and the charged baryonic medium (BM interactions), make a non-negligible contribution to the observed HBT-radius splitting at low collision energies. The study demonstrates that an evolving Coulomb environment can generate finite charge splitting.

However, the authors are modest in their conclusions, stating that Coulomb dynamics alone do not fully account for the experimental data. The remaining discrepancy suggests that other factors—such as isospin-dependent pion production/absorption, charge-dependent hadronic potentials, resonance decays, non-spherical source geometry, and event-by-event charge-density fluctuations—likely play significant roles. The paper concludes that further investigation into the interplay between charged-source geometry and strong-interaction dynamics is required to fully disentangle electromagnetic acceleration from strong-interaction modifications of the emission geometry.

Technical Summary: Dynamical Coulomb Effects on Charged-Pion HBT-Radius Splitting

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