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Tracing Electromagnetic Response through Charge Splitting of Directed Flow in the Quark-Gluon Plasma

This study utilizes a unified viscous hydrodynamic model incorporating electromagnetic effects to demonstrate that the beam-energy-dependent sign reversal and amplitude changes in the charge splitting of directed flow ( $\Delta v_1$ ) arise from the competition between electric and magnetic field-induced momentum distortions, thereby establishing $\Delta v_1$ as a quantitative probe of the quark-gluon plasma's electromagnetic response and space-time evolution.

Original authors: Ankit Kumar Panda, Zhu Meng, Long-Gang Pang, Xin-Nian Wang

Published 2026-10-30

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CC BY 4.0

Original authors: Ankit Kumar Panda, Zhu Meng, Long-Gang Pang, Xin-Nian Wang

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 a particle accelerator, scientists smash heavy atomic nuclei together at speeds approaching the speed of light. These collisions create a fleeting, extreme state of matter known as the quark-gluon plasma. For a fraction of a second, the protons and neutrons that usually hold atomic nuclei together melt away, freeing their internal components—quarks and gluons—to roam in a hot, dense soup. This state of matter existed just microseconds after the Big Bang, and recreating it allows physicists to study how the universe cooled and formed the structure we see today. However, these collisions are not just about heat and density; they also generate intense, rapidly changing magnetic and electric fields. Because the plasma is made of charged particles, it reacts to these fields in complex ways, creating subtle imbalances in how the particles fly apart. Understanding these reactions is like listening to the echo of the early universe, offering a way to measure the fundamental properties of the plasma, such as how easily electricity flows through it.

A team of researchers has now used a sophisticated computer model to trace how these electromagnetic fields shape the movement of particles in the quark-gluon plasma. They focused on a specific phenomenon called the "directed flow," which describes a slight tilt in the direction particles move as they exit the collision zone. When the researchers looked at the difference in this tilt between positively charged particles and negatively charged particles, they found a surprising pattern that changes depending on the energy of the collision. At the lower energies used at the Relativistic Heavy Ion Collider (RHIC) in the United States, the tilt for protons points in one direction. But at the much higher energies of the Large Hadron Collider (LHC) in Europe, the tilt for charged particles flips and points the opposite way. This sign reversal had been observed in experiments but remained a puzzle for theoretical models, which struggled to explain how the same physical laws could produce opposite results at different energy levels.

To solve this puzzle, the researchers built a unified model that simulates the entire life cycle of the plasma, from the moment of impact to the moment the particles freeze out and stop interacting. Their simulation included the dynamic evolution of the electric and magnetic fields generated by the colliding nuclei, as well as how the plasma conducts electricity. A key ingredient in their model was the electrical conductivity of the plasma, a measure of how well the medium allows electric current to flow. The team found that by adjusting this conductivity to match the different energy scales of the two colliders, they could perfectly reproduce the experimental data. At the lower energy of the RHIC, the electric field dominates the interaction, pushing the particles in one direction. At the higher energy of the LHC, the magnetic field becomes more influential due to the longer lifetime of the field in the more conductive plasma, pushing the particles in the opposite direction. The researchers discovered that the flip in direction is not a contradiction but a natural result of a competition between these two forces, where the balance shifts as the energy of the collision increases.

The study also made specific predictions about how this effect should appear for different types of particles, such as pions, kaons, and protons. Because these particles have different masses, they respond to the electromagnetic fields in distinct ways. The model suggests that lighter particles like pions are the most sensitive to these fields, while heavier particles like protons show a different pattern depending on how long they take to react to the changing environment. By comparing these predicted patterns with future experimental measurements, scientists will be able to pin down the exact transport properties of the quark-gluon plasma. This work establishes the charge splitting of directed flow as a precise tool for probing the electromagnetic response of the early universe, turning a subtle wobble in particle trajectories into a clear signal of the plasma's inner workings. The findings confirm that the behavior of the quark-gluon plasma is governed by a delicate interplay of electric and magnetic forces, controlled by the medium's ability to conduct electricity, and that this interplay changes fundamentally as the energy of the collision rises.

Technical Summary: Tracing Electromagnetic Response through Charge Splitting of Directed Flow in the Quark–Gluon Plasma

Problem Statement
Experimental observations of the charge splitting of directed flow, defined as $\Delta v_1 \equiv v_1(h^+) - v_1(h^-)$ , present a significant challenge for theoretical descriptions of the Quark-Gluon Plasma (QGP). Data from RHIC ( $\sqrt{s_{NN}} = 200$ GeV, Au+Au) and the LHC ( $\sqrt{s_{NN}} = 5.02$ TeV, Pb+Pb) exhibit a distinct sign reversal at midrapidity: the slope is negative for protons at RHIC but positive for inclusive charged hadrons at LHC. Previous theoretical approaches, ranging from non-conducting models to magnetohydrodynamic (MHD) frameworks with finite conductivity, have struggled to provide a simultaneous quantitative description of these measurements, particularly the change in the $\Delta v_1$ slope. A consistent connection between the evolving electromagnetic (EM) fields, the QGP response, and charge-dependent particle distributions at particlization is required to resolve this.

Methodology
The authors employ a unified (3+1)-dimensional viscous hydrodynamic framework, CLVisc, to simulate the QGP evolution. The methodology integrates electromagnetic effects through two primary mechanisms:

Bulk Evolution: The Lorentz force is introduced as a source term in the energy-momentum conservation equation ( $\nabla_\mu T^{\mu\nu} = F^{\nu\lambda}J_\lambda$ ). The electric current $J^\mu$ includes a conduction term proportional to the electrical conductivity ( $\sigma_{el}$ ), which governs the induced currents and the subsequent evolution of EM fields.
Particlization: A leading-order electromagnetic correction derived from kinetic theory is applied to the Cooper–Frye particlization distribution function. The equilibrium distribution $f_0$ is modified by a charge-odd term $\delta f_{EM} \propto \tau_c q f_0(1 \pm f_0) \frac{E \cdot p}{T_{frz}(u \cdot p)}$ , where $\tau_c$ is the relaxation time linked to conductivity. This correction imparts momentum distortions dependent on the particle's charge and the local electric field in the fluid rest frame.

The study utilizes TRENTo initial conditions for Au+Au (50–80% centrality) and Pb+Pb (5–40% centrality) collisions. Electromagnetic fields are calculated from the relativistic motion of spectator and participant protons using a Green's-function formulation, mapped onto the hydrodynamic grid, and evolved with the medium. The model validates its implementation against semi-analytic resistive-MHD solutions.

Key Results

Reproduction of Sign Reversal: By varying the effective electrical conductivity ( $\sigma_{el}$ ) between RHIC and LHC energies (consistent with lattice-QCD scales), the model successfully reproduces the experimental data. Specifically, it captures the negative midrapidity slope for protons at RHIC and the positive slope for inclusive charged hadrons at LHC.
Mechanism of Sign Reversal: The sign change arises from the competition between electric and magnetic field contributions to the momentum distortion.
- At RHIC energies, the electric field contribution dominates, driving a negative slope.
- At LHC energies, an enhanced conductivity extends the lifetime of the magnetic field on the freeze-out hypersurface. The magnetic contribution, which favors a positive slope, becomes dominant over the electric contribution, resulting in a net positive slope.
Mass-Dependent Predictions: The framework predicts specific charge splittings for identified pions, kaons, and protons.
- At RHIC, thermal distribution weights favor larger splitting for lighter hadrons (pions).
- At LHC, harder momentum spectra increase the weight of the $E \cdot p$ projection, altering the mass ordering.
- The model demonstrates that introducing a mass hierarchy in the relaxation time ( $\tau_c$ ) can significantly modify these splittings, potentially reversing conventional mass orderings.

Significance and Claims
The paper establishes the charge splitting of directed flow ( $\Delta v_1$ ) as a quantitative probe of the electromagnetic response and the space-time evolution of the QGP. The authors claim that their unified framework successfully disentangles electric and magnetic contributions, explaining the observed beam-energy dependence through the interplay of conductivity and relaxation time. Furthermore, the model provides testable predictions for the mass dependence of $\Delta v_1$ for identified hadrons, suggesting that precision measurements of these splittings can offer sensitive constraints on the transport properties (specifically relaxation dynamics) of the QGP during the particlization process. The study emphasizes that while constant effective conductivity was used as an average value, future improvements should account for the local temperature and time dependence of these transport parameters.

Technical Summary: Tracing Electromagnetic Response through Charge Splitting of Directed Flow in the Quark–Gluon Plasma

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