Evidence for the collective nature of radial flow in Pb+Pb collisions with the ATLAS detector

This paper presents the first measurement of transverse momentum-dependent radial flow fluctuations in Pb+Pb collisions using the ATLAS detector, providing experimental evidence for the collective nature of radial flow and demonstrating its sensitivity to the quark-gluon plasma's bulk viscosity.

The Gist

Imagine smashing two giant, heavy balls together at nearly the speed of light. In the world of particle physics, this is what happens when lead nuclei collide inside the Large Hadron Collider (LHC). For a split second, the energy is so intense that the atoms melt, creating a tiny, super-hot soup of fundamental particles called Quark-Gluon Plasma (QGP).

Think of this plasma not as a static blob, but as a fluid that expands and cools down incredibly fast, much like steam escaping from a kettle. Scientists have long studied how this fluid moves in different directions (like a balloon expanding unevenly), but they have struggled to prove that the fluid expands outward in a coordinated, collective way.

This paper from the ATLAS collaboration at CERN is like a detective story where they finally found the "smoking gun" proving that this outward expansion is indeed a team effort.

Here is the breakdown of their discovery using simple analogies:

1. The Two Types of Flow

To understand the discovery, you need to know two ways the plasma moves:

• Anisotropic Flow (The "Squish"): Imagine the plasma is a balloon that isn't perfectly round. When it expands, it squishes out more in some directions than others. Scientists have known about this for a long time.
• Radial Flow (The "Blast"): This is the explosion pushing everything outward from the center. The paper focuses on this. They wanted to prove that the particles aren't just flying out randomly like shrapnel from a grenade, but are moving together like a synchronized wave.

2. The Mystery: Is it a Team or a Crowd?

Before this paper, scientists could measure the average speed of the explosion, but they couldn't easily prove that the fluctuations (the little wiggles and changes in speed from one collision to the next) were a collective phenomenon.

The Analogy: Imagine a stadium crowd.

• Non-Collective (Random): If people in the crowd start jumping randomly, the average height of the crowd might go up, but there's no pattern.
• Collective (Team): If the crowd does "The Wave," everyone jumps in a coordinated pattern. Even if the wave gets slightly faster or slower in different sections, the pattern remains the same.

The scientists wanted to prove that the radial flow in these collisions was "The Wave," not random jumping.

3. The Detective Work: The "Two-Person" Test

To prove the "Wave" theory, the ATLAS team used a clever trick called a two-particle correlation.

Imagine you are watching a dance floor. Instead of watching one dancer, you watch two dancers who are standing far apart from each other (on opposite sides of the room).

• If they are dancing randomly, their movements won't match.
• If they are part of a coordinated dance (collective flow), even if they are far apart, their movements will be linked.

The scientists looked at particles produced in the collision. They checked if the speed of a particle on one side of the collision was linked to the average speed of the whole event. They found a strong link, proving the particles were "dancing" together.

4. The Three Clues That Proved It

The paper highlights three specific pieces of evidence that confirm this is a collective "Wave":

• Clue 1: Long-Range Connection: The particles were linked even when they were very far apart in the "forward/backward" direction (pseudorapidity). This is like seeing two people at opposite ends of a stadium doing the same move at the same time. It proves the whole system is connected, not just local groups.
• Clue 2: The Shape Stays the Same: No matter how hard they smashed the balls together (changing the "centrality" or how head-on the collision was), the shape of the flow pattern remained consistent. It's like how a song sounds the same whether you play it loudly or softly; the melody (the flow) is universal.
• Clue 3: The Math Works: They found that the complex data could be broken down into simple math (factorization), just like how you can describe a complex wave by multiplying a simple "height" factor by a simple "shape" factor. This mathematical simplicity is a hallmark of collective behavior.

5. Why It Matters: The "Viscosity" of the Soup

Once they proved the flow is collective, they used it to measure a property of the plasma called bulk viscosity.

The Analogy: Think of viscosity as the "thickness" or "stickiness" of a fluid.

• Honey has high viscosity (it's thick and resists moving).
• Water has low viscosity (it flows easily).

The Quark-Gluon Plasma is the most perfect fluid known to science, but it still has a tiny bit of "stickiness." The paper shows that the way the radial flow fluctuates is extremely sensitive to this stickiness. By measuring the flow, they can now better understand how "thick" this cosmic soup is.

Summary

In short, this paper is a breakthrough because it moves from guessing that the plasma expands like a coordinated fluid to proving it with hard data. They showed that the particles move together in a synchronized, long-range pattern, and they used this pattern to measure the "thickness" of the universe's most perfect fluid.

It's like finally proving that a crowd isn't just a bunch of random people, but a synchronized dance troupe, and then using that dance to measure how slippery the floor is.

Technical Summary

Technical Summary: Evidence for the collective nature of radial flow in Pb+Pb collisions with the ATLAS detector

Problem and Motivation
While anisotropic flow ($v_n$) has been extensively studied as a probe of the quark-gluon plasma (QGP) expansion dynamics, radial flow ($v_0$), which governs the system's radial expansion and influences the average transverse momentum ($[p_T]$) of particles, has received less experimental attention. Historically, experimental studies of radial flow have been limited to model-dependent approaches using particle spectra and global moments (such as the scaled variance of $[p_T]$). These traditional methods provide only $p_T$-integrated information and do not directly probe the many-body, collective nature of radial flow fluctuations. Consequently, direct experimental evidence for the global and collective nature of radial flow fluctuations has been lacking. Furthermore, while anisotropic flow is known to be sensitive to shear viscosity, the new observable proposed to study radial flow fluctuations, $v_0(p_T)$, is predicted to be more sensitive to bulk viscosity, a transport property of the QGP that remains less constrained.

Methodology
The ATLAS Collaboration presents the first measurement of the transverse momentum ($p_T$) dependence of radial flow fluctuations, denoted as $v_0(p_T)$, using Pb+Pb collision data at $\sqrt{s_{NN}} = 5.02$ TeV collected in 2015 (integrated luminosity of 470 $\mu$b$^{-1}$). The analysis utilizes charged particle tracks reconstructed in the inner detector ($0.5 < p_T < 10$ GeV, $|\eta| < 2.5$).

The observable $v_0(p_T)$ is defined based on the correlation between the event-by-event (EbE) $p_T$-differential yield spectrum, $n(p_T)$, and the EbE average transverse momentum, $[p_T]$. To isolate shape variations from total multiplicity fluctuations, the fractional spectrum $n(p_T) = N(p_T) / \int N(p_T) dp_T$ is used in each event. The analysis employs a two-subevent method, separating particles into two pseudorapidity regions ($\eta_a$ and $\eta_b$) with varying gaps ($\eta_{gap} = 0, 1, 2, 3$) to suppress short-range non-flow correlations (e.g., resonance decays, jet fragmentation).

The measurement relies on the factorization hypothesis, where the normalized covariance between the spectrum and the average momentum is expressed as:
$$\frac{\langle \delta n(p_T) \delta [p_T] \rangle}{\langle n(p_T) \rangle \langle [p_T] \rangle} = v_0(p_T) v_0$$
Here, $v_0$ represents the global radial flow fluctuation magnitude. The analysis checks for three hallmarks of collectivity:

1. Long-range correlation: Independence of the signal from the pseudorapidity gap between subevents.
2. Factorization: The extracted $v_0(p_T)$ should be independent of the reference $p_T$ range ($p_T^{ref}$) used to calculate $[p_T]$.
3. Centrality-independent shape: The normalized shape $v_0(p_T)/v_0$ should exhibit universal behavior across different centrality classes, reflecting the hydrodynamic response.

Systematic uncertainties are evaluated regarding track selection, reconstruction efficiency, residual pileup, centrality definition, and Monte Carlo closure tests. The results are compared with hydrodynamic model predictions (Trento+MUSIC framework) incorporating different viscosity scenarios (ideal, constant shear viscosity, and temperature-dependent bulk viscosity).

Key Results

• Observation of $v_0(p_T)$: The data reveal a characteristic pattern for $v_0(p_T)$: a rise up to $p_T \approx 3\text{--}4$ GeV, a sign change (zero-crossing) near $p_T \approx 1$ GeV (consistent with the mean $[p_T]$ of the 0.5–10 GeV range), and a decrease at higher $p_T$.
• Collective Nature:
  • Factorization: The extracted $v_0(p_T)$ is nearly independent of the $p_T^{ref}$ range used for calculation up to $p_T \approx 3$ GeV, confirming the factorization property analogous to anisotropic flow.
  • Long-range Correlation: Varying the pseudorapidity gap ($\eta_{gap}$) from 0 to 3 results in little change to $v_0(p_T)$ in central collisions, and only a slight decrease in peripheral collisions at high $p_T$. This supports the interpretation of radial flow as a long-range, global correlation.
  • Universality: While the magnitude of $v_0(p_T)$ depends on centrality, the normalized shape $v_0(p_T)/v_0$ is nearly independent of centrality for $p_T \lesssim 2.5$ GeV. This suggests the shape is governed by a universal hydrodynamic response, while the magnitude is driven by initial-state fluctuations in nuclear overlap area and density.
• Viscosity Sensitivity: Comparisons with hydrodynamic models show that calculations without bulk viscosity underestimate the data at high $p_T$. Including a temperature-dependent bulk viscosity improves agreement with the data, particularly regarding the zero-crossing point and the high-$p_T$ behavior. The data indicate that $v_0(p_T)$ is sensitive to the bulk viscosity of the QGP.
• Non-flow Contributions: At $p_T \gtrsim 3$ GeV and in peripheral collisions, the data show dependence on $p_T^{ref}$ and $\eta_{gap}$, consistent with increasing contributions from non-flow correlations such as jet quenching and fragmentation.

Significance and Claims
The paper claims to present the first measurement of the $p_T$-differential radial flow fluctuations $v_0(p_T)$ and provides the first direct experimental evidence for the collective nature of radial flow. By establishing the three hallmarks of collectivity (long-range correlation, factorization, and centrality-independent shape) for radial flow, the study validates $v_0(p_T)$ as a powerful new tool for probing the QGP.

The authors emphasize that this observable offers a unique opportunity to constrain the bulk viscosity of the QGP, a transport coefficient that is less well-determined than shear viscosity. The results establish a foundation for quantitative constraints on QGP transport properties and demonstrate that radial flow fluctuations, previously inferred only through model-dependent spectral analyses, can be directly measured via correlation techniques. The paper notes that these findings are consistent with a subsequent study by the ALICE Collaboration, further reinforcing the validity of the observations.