Observation of partonic collectivity via $p_{\rm T}$-differential radial flow fluctuations in Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV

This paper reports the observation of partonic radial collectivity in Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV through $p_{\rm T}$-differential flow fluctuations ($v_0$), demonstrating that radial flow originates predominantly at the partonic stage via signatures such as mass ordering, meson-baryon separation, and robust Number of Constituent Quark scaling in central collisions.

The Gist

Imagine you are at a massive, chaotic concert where thousands of people are packed into a tiny room. Suddenly, the lights go out, and everyone starts pushing and shoving. In physics, this is what happens when two heavy atoms (like Gold) smash into each other at nearly the speed of light.

For decades, scientists have known that this crash creates a super-hot, super-dense soup of particles called Quark-Gluon Plasma (QGP). It's like a cosmic "primordial soup" where the usual rules of matter (where particles are stuck inside atoms) break down, and everything becomes a free-flowing fluid.

This paper is about a new way of looking at how this "soup" expands and cools down. Here is the story in simple terms:

1. The Old Way vs. The New Way

The Old Way (The Blast Wave):
Traditionally, to understand how this soup expands, scientists used a "Blast Wave" model. Imagine a bomb going off in a field. You look at the debris flying out, measure the average speed of all the pieces, and say, "Okay, the explosion pushed everything out at this speed." It's a good average, but it misses the details of how the explosion happened.

The New Way (The Flow Fluctuation):
The authors of this paper used a new tool called $v_0(p_T)$. Instead of just measuring the average speed, they looked at the wiggles and jitters in the crowd.

• The Analogy: Imagine a crowded dance floor. If everyone moves in perfect unison, it's smooth. But if the music changes suddenly, some people rush forward while others stumble back.
• This new tool measures how the number of people in a specific area correlates with how fast they are moving. If the crowd suddenly surges forward (collective flow), the number of people in the front changes in a specific way. By studying these tiny fluctuations, the scientists can see the "personality" of the expansion much more clearly than before.

2. The Big Discovery: The "Partonic" Party

The main question the scientists wanted to answer is: When does this collective dancing start?

• Does it start when the atoms smash together and break into smaller pieces (quarks and gluons)?
• Or does it start later, when those pieces recombine into new particles (protons and pions)?

The Answer: The study found that the "dancing" starts immediately when the atoms break apart into their smallest parts (quarks and gluons).

• The Metaphor: Think of a group of people wearing different colored shirts (Red, Blue, Green). If they all start dancing in a coordinated way before they even put on their shirts, it proves the coordination happened at the "shirt-less" stage.
• The data showed that the flow patterns follow the rules of the quarks (the fundamental building blocks), not the final particles. This is strong evidence that the "soup" behaves like a fluid right from the very first split-second of the collision.

3. The "Mass Ordering" and "Baryon-Meson" Split

When they looked at different types of particles (light ones like pions, medium ones like kaons, and heavy ones like protons), they saw a beautiful pattern:

• Low Speed: The heavier particles moved slower than the lighter ones. It's like a heavy elephant and a light mouse running; the mouse gets ahead easily.
• Medium Speed: Something weird happened. The heavy protons started "overtaking" the lighter mesons.
• The Analogy: Imagine a race where the heavy runners suddenly get a turbo boost. This "crossover" is a signature that the particles are being pushed by a collective pressure wave, and the way they combine (how many quarks are inside them) dictates how they move.

4. The "Quark Counting" Rule (NCQ Scaling)

This is the most exciting part. The scientists found a universal rule:

• If you take the flow of a particle and divide it by the number of quarks inside it, all the different particles (pions, kaons, protons) line up on the exact same curve.
• The Analogy: Imagine you have a team of 2 people (a meson) and a team of 3 people (a baryon). If you measure how fast the team runs and then divide by the number of people, both teams show the exact same "running speed per person."
• This proves that the "dancing" is happening at the individual quark level before they team up. It's like seeing the choreography of the dancers before they form the final group.

5. Why This Matters

Previously, we knew this "quark-level dancing" happened in the elliptical flow (where the soup squishes out like a football). This paper proves it also happens in the radial flow (where the soup explodes outward in a circle).

• The Takeaway: The universe, in its hottest and densest moments, behaves like a perfect fluid made of quarks. This "collective flow" isn't just a side effect; it's the main event, and it starts the instant the atoms break apart.

In a nutshell:
The authors used a new, sensitive "microscope" to watch the aftermath of a nuclear collision. They discovered that the chaos of the crash organizes itself into a smooth, coordinated flow immediately, driven by the fundamental quarks inside the atoms. It's like watching a chaotic mosh pit suddenly turn into a perfectly synchronized dance routine, and proving that the dance moves were decided by the individual dancers, not the group.

Technical Summary

1. Problem Statement and Motivation

The formation of the Quark-Gluon Plasma (QGP) in ultra-relativistic heavy-ion collisions is well-established through signatures like jet quenching and elliptic flow ($v_2$). While $v_2$ (anisotropic flow) has long been used to demonstrate partonic collectivity and Number of Constituent Quark (NCQ) scaling, isotropic radial flow has traditionally been characterized using $p_T$-integrated observables (e.g., blast-wave fits).

Recently, a new differential observable, $v_0(p_T)$, was introduced to quantify radial flow by correlating event-by-event fluctuations in charged-particle multiplicity with fluctuations in the mean transverse momentum ($[p_T]$). While $v_0(p_T)$ signatures (mass ordering, meson-baryon splitting, and NCQ scaling) have been observed at LHC energies (Pb+Pb at 5.02 TeV), it remains an open question whether these signatures persist at lower RHIC energies (Au+Au at 200 GeV) and whether the collectivity originates primarily in the partonic or hadronic stage. This paper aims to establish the existence of partonic radial collectivity at RHIC energies using the AMPT model.

2. Methodology

The study employs a multi-faceted approach combining event generation, observable definition, and comparative analysis:

• Event Generators:
  • AMPT (String Melting): The primary tool for simulating Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. The "String Melting" (SM) configuration is used, where initial strings are converted into constituent quarks/antiquarks before evolving via Zhang's Parton Cascade (ZPC) and hadronizing via quark coalescence. This setup is designed to maximize partonic interactions.
  • PYTHIA8/Angantyr: Used to simulate Pb+Pb collisions at 5.02 TeV as a non-collective baseline. This model superimposes nucleon-nucleon interactions without a hydrodynamic medium, serving to isolate collective effects from initial-state or fragmentation effects.
• Observable Definition ($v_0(p_T)$):
  • Defined as the normalized covariance between the fraction of particles in a specific $p_T$ bin ($F_A^{p_T}$) and the mean transverse momentum in a separate, longitudinally displaced pseudorapidity window ($[p_T]_B$).
  • A pseudorapidity gap ($\eta_{gap} = 0.4$) is enforced to suppress short-range non-flow correlations (e.g., resonance decays, jets).
  • The integrated observable $v_0$ quantifies the root-mean-square fluctuations of the event-wise mean $p_T$.
• Analysis Strategy:
  • Centrality Dependence: Analyzed across 9 centrality classes (0–80%).
  • Identified Particles: Studied $\pi^\pm, K^\pm, p+\bar{p}$ to test mass ordering and NCQ scaling.
  • Scaling Tests: Examined $v_0(p_T)/v_0$ for centrality independence and $v_0(p_T)/n_q$ vs. $(m_T - m_0)/n_q$ for NCQ scaling.
  • Comparison: Results are compared against ATLAS (Pb+Pb, 5.02 TeV) and ALICE (Pb+Pb, 5.02 TeV) experimental data.

3. Key Contributions

This work provides the first systematic evidence of partonic radial collectivity at RHIC energies using the differential $v_0(p_T)$ observable. Key contributions include:

1. Establishment of Three Collectivity Signatures at RHIC: Demonstrating long-range pseudorapidity correlations, factorization of two-particle correlations, and centrality-independent scaling of normalized $v_0(p_T)$.
2. NCQ Scaling of Radial Flow: Extending the NCQ scaling paradigm from anisotropic flow ($v_2$) to isotropic radial flow ($v_0$), showing that radial collectivity is established at the partonic stage.
3. Energy Dependence Analysis: Showing that NCQ scaling for radial flow is more precise at RHIC (200 GeV) than at LHC (5.02 TeV), a finding consistent with earlier $v_2$ studies.
4. Baseline Validation: Using PYTHIA8/Angantyr to prove that the observed mass ordering and scaling are absent in non-collective scenarios, confirming their origin in final-state collective dynamics.

4. Key Results

A. General Features of $v_0(p_T)$

• $p_T$ Dependence: $v_0(p_T)$ is negative at low $p_T$ ($< 0.5$ GeV/c) and turns positive at higher $p_T$, crossing zero around 0.55–0.63 GeV/c. This reflects the anti-correlation between mean $p_T$ fluctuations and low-$p_T$ yields.
• Centrality Dependence: The magnitude of $v_0(p_T)$ is largest in peripheral collisions (70–80%) and smallest in central collisions (0–5%). This is attributed to larger geometric fluctuations in peripheral events.
• Factorization: The normalized distribution $v_0(p_T)/v_0$ exhibits centrality-independent scaling up to $p_T \approx 2$ GeV/c, indicating a common dynamical origin for the spectral shape across centralities.
• $\eta_{gap}$ Independence: Weak dependence on the pseudorapidity gap confirms the long-range nature of the correlations.

B. Identified Particles and Mass Ordering

• Mass Ordering: At low $p_T$, $v_0(p_T)$ follows the expected mass ordering ($\pi < K < p$), consistent with collective radial expansion.
• Meson-Baryon Splitting: At intermediate $p_T$ (2–3 GeV/c), a characteristic crossover is observed where baryons exceed mesons, consistent with quark coalescence mechanisms.
• NCQ Scaling:
  • When plotted against $(m_T - m_0)/n_q$ (transverse kinetic energy per constituent quark), the $v_0(p_T)/n_q$ spectra for different hadron species collapse onto a universal curve in central collisions.
  • Scaling Quality: The scaling is robust in central (0–20%) and semi-central (20–40%) collisions but breaks down in peripheral collisions (60–70%), where the partonic phase lifetime is too short to establish full collectivity.
  • Energy Comparison: The scaling parameter $S_f$ (quantifying deviation from the reference curve) is smaller at 200 GeV than at 5.02 TeV, indicating tighter NCQ scaling at RHIC energies.

C. Integrated Fluctuations ($v_0$)

• The integrated observable $v_0$ decreases monotonically with increasing multiplicity ($N_{ch}$), following a power law $v_0 \propto N_{ch}^b$ with $b \approx -0.42$.
• This $1/\sqrt{N_{ch}}$ scaling suggests that radial flow fluctuations are driven by geometric fluctuations in the initial collision zone, which are diluted as the number of participating sources increases.

5. Significance

• Paradigm Extension: The study successfully extends the paradigm of quark-level dynamics from anisotropic flow ($v_2$) to isotropic radial flow. It confirms that the QGP behaves as a strongly coupled fluid with collective expansion even in the radial direction at RHIC energies.
• Partonic Origin: The observation of robust NCQ scaling in $v_0(p_T)$ at 200 GeV provides strong evidence that radial collectivity is established predominantly during the partonic stage (before hadronization), rather than in the hadronic phase.
• Model Validation: The results validate the AMPT String Melting model's ability to reproduce complex collective phenomena at RHIC energies, while the failure of the non-collective PYTHIA8/Angantyr model to reproduce these features underscores the necessity of a hydrodynamic-like evolution.
• Energy Systematics: The finding that NCQ scaling is more precise at RHIC than at LHC offers new insights into the temperature and density dependence of partonic collectivity, suggesting that the system at 200 GeV may be closer to the ideal fluid limit regarding quark coalescence dynamics than the higher-energy LHC system.

In conclusion, this paper provides compelling evidence that radial flow in Au+Au collisions at 200 GeV is a collective phenomenon rooted in partonic dynamics, characterized by universal scaling laws that mirror those of anisotropic flow.