⚛️ nuclear theory

Dipolar flow of identified hadrons at mid-rapidity using transport models

This study utilizes AMPT transport model simulations to demonstrate that the splitting between proton and anti-proton dipolar flow ( $v_{1}^{\mathrm{even}}$ ) at mid-rapidity in Au+Au collisions emerges at lower beam energies due to baryon transport and partonic dynamics, serving as a novel probe for understanding the evolution of the partonic medium.

Original authors: Abhisek Praharaj, Aradhana Panday, Sandeep Chatterjee, Md Nasim

Published 2026-07-02

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CC BY 4.0

Original authors: Abhisek Praharaj, Aradhana Panday, Sandeep Chatterjee, Md Nasim

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

Imagine two massive atomic nuclei, like gold atoms, smashing into each other at nearly the speed of light. When they collide, they don't just shatter; they create a tiny, super-hot soup of fundamental particles called quarks and gluons. This is the "primordial soup" of the universe, recreated for a split second in a particle accelerator.

Scientists want to understand how this soup behaves. Does it flow like a fluid? Does it swirl? To study this, they look at the direction particles fly out after the crash.

The "Flow" and the "Even" Split

Usually, when these nuclei collide, they are slightly off-center, like two cars grazing each other. This creates a "sideways push," sending more particles to one side than the other. This is called directed flow.

However, the collision isn't perfectly smooth. There are tiny bumps and fluctuations in the initial crash. These fluctuations create a second, subtler kind of flow that doesn't care about left or right, but rather about the "evenness" of the distribution. The scientists in this paper are studying this specific "even" flow, which they call $v_1^{even}$ .

Think of it like this:

Normal Flow: A crowd of people being pushed sideways by a wind.
The "Even" Flow: The crowd organizing itself into a pattern based on how they bumped into each other initially, regardless of the wind.

The Experiment: The "Transport" Models

To understand what's happening, the researchers used computer simulations called transport models. Think of these as video game engines for physics.

HIJING: This is a basic engine that simulates the crash and the creation of particles (like minijets) but doesn't let them interact much afterward. It's like simulating a car crash where the cars bounce off each other but don't stick or swirl.
AMPT: This is a more advanced engine. It has two modes:
- Default Mode: Particles interact a little bit, but mostly they stay as they are.
- String Melting Mode: This is the "heavy duty" mode. It assumes that when the crash is energetic enough, the "strings" holding particles together melt into a soup of free quarks. These quarks bounce around, interact, and then recombine to form new particles. This is where the real "fluid" behavior happens.

The Big Discovery: Protons vs. Antiprotons

The researchers looked at three types of particles: pions (light), kaons (medium), and protons (heavy). They also looked at their "antimatter twins" (antiprotons, etc.).

Here is what they found, using the "String Melting" (advanced) simulation:

At High Energy (200 GeV): It's like a very fast, chaotic party. Everyone is moving so fast that protons and antiprotons behave almost exactly the same. There is no difference in how they flow.
At Lower Energy (27 GeV): The party slows down. Suddenly, a clear difference appears. Protons start flowing differently than antiprotons.
- The Analogy: Imagine a crowd of people (protons) who were already in the building before the crash, and a group of people (antiprotons) who were just created by the crash. At lower speeds, the "old" people (protons) get stuck in the traffic jam near the center of the room (mid-rapidity) more than the "new" people. This "stopping" effect makes them flow differently.
The Mesons (Pions/Kaons): These light particles didn't show this difference. They flowed the same way whether they were matter or antimatter.

Why Does This Matter?

The researchers compared the "Default" and "String Melting" simulations to figure out why this happens.

In the Default simulation (where strings don't melt), protons and antiprotons looked the same.
In the String Melting simulation (where a quark soup forms), the difference appeared.

The Conclusion: The difference in flow between protons and antiprotons is a direct sign that a quark soup was formed and that baryons (heavy particles like protons) were being "stopped" and transported to the center of the collision.

The Takeaway

This study acts like a new kind of "thermometer" or "speedometer" for the early moments of a heavy-ion collision. By measuring how protons and antiprotons flow differently at lower energies, scientists can tell how much the heavy particles are getting "stuck" in the middle of the collision and how the quark soup is evolving. It confirms that the "String Melting" scenario (where a quark-gluon plasma forms) is the key to understanding these heavy-particle behaviors.

Technical Summary: Dipolar Flow of Identified Hadrons at Mid-Rapidity Using Transport Models

Problem Statement
The study of collective behavior in relativistic heavy-ion collisions offers critical insights into the properties of strongly interacting matter. While anisotropic flow coefficients ( $v_n$ ) are established tools for probing initial geometry and transport properties, the directed flow coefficient ( $v_1$ ) is particularly sensitive to early-time dynamics. Traditionally, $v_1$ is dominated by a rapidity-odd component arising from collective sideward deflection. However, initial-state fluctuations can induce dipole-like asymmetries, generating a rapidity-even component ( $v_1^{even}$ ). Recent hydrodynamical studies suggest that $v_1^{even}$ for identified hadrons could serve as a sensitive probe for baryon stopping and diffusion over rapidity. This paper addresses the need to investigate these effects using transport-based models to understand the underlying mechanisms of baryon transport and partonic dynamics.

Methodology
The authors employ two widely used transport models to simulate Au+Au collisions at center-of-mass energies ( $\sqrt{s_{NN}}$ ) of 27, 62.4, and 200 GeV:

HIJING (Heavy Ion Jet INteraction Generator): Used primarily to quantify non-flow contributions. It incorporates perturbative QCD, minijet production, and string fragmentation but lacks mechanisms to generate collective flow.
AMPT (A Multi-Phase Transport Model): Used as the primary tool for studying collective behavior. The study compares two configurations:
- AMPT-Default: Minijet partons scatter before hadronizing via Lund string fragmentation.
- AMPT-String Melting (AMPT-SM): Assumes that at high energy densities ( $>1$ GeV/fm³), strings melt into constituent quarks and antiquarks. These partons undergo a parton cascade (ZPC) and subsequently hadronize via quark coalescence.

Analysis Method
The rapidity-even component of directed flow ( $v_1^{even}$ ) is extracted using two-particle correlations in relative azimuthal angle ( $\Delta\phi$ ). The analysis involves:

Calculating the two-particle Fourier coefficients ( $v_{11}$ ) from the correlation function $C_r(\Delta\phi)$ , defined as the ratio of same-event to mixed-event pair distributions.
Applying a pseudorapidity gap ( $|\Delta\eta| \geq 0.7$ ) to suppress non-flow effects such as resonance decays and jets.
Extracting $v_1$ via a simultaneous fit of $v_{11}$ as a function of transverse momentum ( $p_T$ ) for different particle selections, using an equation that accounts for non-flow correlations induced by global momentum conservation.
Since the analysis is performed within a rapidity-symmetric acceptance ( $|y| < 1.0$ ), the extracted $v_1$ effectively corresponds to the rapidity-even component ( $v_1^{even}$ ), as the rapidity-odd component averages to zero.

Key Results

Validation of Non-Flow: Comparisons with the HIJING model confirm that $v_1^{even}$ is consistent with zero within statistical uncertainties, indicating that residual non-zero values in AMPT arise from collective flow rather than non-flow artifacts.
Particle Species Dependence: At $\sqrt{s_{NN}} = 200$ GeV, no significant difference is observed between particles and anti-particles for identified hadrons ( $\pi, K, p$ ). However, as beam energy decreases to 27 GeV, a clear splitting develops between protons and anti-protons in $v_1^{even}$ . In contrast, mesons ( $\pi^{\pm}$ and $K^{\pm}$ ) show no significant particle-antiparticle difference across the energy range.
Model Configuration Dependence: The proton-antiproton splitting is observed exclusively in the AMPT-String Melting (SM) configuration. In the AMPT-Default configuration, this distinction is largely absent.
Energy Dependence: The magnitude of the proton-antiproton $v_1^{even}$ splitting increases with decreasing beam energy.

Mechanism and Interpretation
The paper attributes the observed splitting to baryon transport and early-stage partonic dynamics. In the AMPT-SM scenario, transported quarks from the incoming nuclei reach mid-rapidity and undergo substantial partonic rescattering before hadronizing via coalescence. Protons formed from these transported quarks develop a different flow pattern compared to anti-protons, which are primarily formed from newly produced quarks. The AMPT-Default model, which retains strings during partonic evolution and limits the partonic phase, does not facilitate sufficient baryon transport to generate this splitting. Furthermore, net-proton rapidity distributions in AMPT-SM show marked changes at lower energies compared to high energies, reflecting stronger baryon stopping, whereas the Default model shows relatively weak changes.

Significance
The study concludes that the proton-antiproton difference in $v_1^{even}$ is a sensitive probe of baryon stopping and the evolution of the partonic medium. The results highlight the potential of identified-particle $v_1^{even}$ measurements at RHIC Beam Energy Scan energies to constrain the physics of baryon transport and deposition at mid-rapidity. The findings suggest that the string melting scenario, where partonic interactions and quark coalescence dominate, is essential for reproducing the observed baryon transport effects.

The "Flow" and the "Even" Split

The Experiment: The "Transport" Models

The Big Discovery: Protons vs. Antiprotons

Why Does This Matter?

The Takeaway

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