EPJ Featured Talk: First direct measurement of radial flow in heavy-ion collisions with ALICE

This paper presents the first direct measurement of radial flow in Pb-Pb collisions at 5.02 TeV using the novel observable $v_0(p_\mathrm{T})$, revealing mass ordering at low transverse momentum and quark recombination effects at high momentum that confirm the sensitivity of this probe to collective expansion and hadronization dynamics in the quark-gluon plasma.

The Gist

Imagine smashing two heavy cars together at nearly the speed of light. For a split second, the metal doesn't just crumple; it melts into a super-hot, super-dense soup of tiny particles called a Quark-Gluon Plasma (QGP). This is the state of matter that existed just microseconds after the Big Bang.

Scientists at the Large Hadron Collider (LHC) use a giant camera called ALICE to take pictures of these crashes. The big question they ask is: How does this soup expand and cool down?

For a long time, scientists could measure how the soup "wiggled" in different directions (like a drum skin vibrating), but they struggled to measure how it blowed up outward in all directions (radial flow). It's like trying to measure the wind speed inside a tornado just by looking at the swirl, without seeing how fast the air is rushing away from the center.

This paper presents a brand-new tool, a "wind speedometer" called $v_0(p_T)$, that finally lets them measure that outward push directly.

Here is the breakdown of what they found, using simple analogies:

1. The New Tool: Measuring the "Push"

Think of the collision as a crowded dance floor.

• The Old Way: Scientists used to look at the average speed of everyone on the floor. If the floor got crowded, they knew the pressure was high, but they couldn't tell if the heavy dancers (protons) were being pushed harder than the light dancers (pions).
• The New Way ($v_0$): The scientists developed a clever trick. They split the dance floor into two separate rooms (Room A and Room B) with a gap in between. They watched how the number of people in Room A changed when the average speed of people in Room B changed.
  • If the "soup" is expanding like a balloon, a sudden burst of speed in one area is linked to a specific pattern of particle counts in the other. This correlation acts as a fingerprint of the radial flow (the outward explosion).

2. The Results: The "Heavy vs. Light" Dance

When they looked at the data, two distinct patterns emerged, like a dance changing tempo:

Phase 1: The Hydrodynamic Waltz (Low Speed)
At lower speeds (low energy), the soup acts like a fluid.

• The Analogy: Imagine a strong wind blowing through a field. A light feather (a pion) gets blown away easily, but a heavy rock (a proton) resists. However, in this specific "soup," the collective pressure is so strong that it gives the heavier particles a bigger boost than the light ones.
• The Finding: The data showed a clear "mass ordering." The heavier protons were moving faster relative to their mass than the lighter pions. This confirmed that the QGP is behaving exactly like a perfect fluid, pushing everything outward together.

Phase 2: The "Recombination" Switch (High Speed)
As the particles get faster (higher energy), the rules change.

• The Analogy: Imagine the soup starts to freeze. Instead of individual particles flying solo, they start grabbing hands to form teams.
• The Finding: At high speeds, the protons suddenly got a huge speed boost compared to pions and kaons. This is because protons are made of three "quarks" (like a trio), while pions are made of two (a duo). In the cooling soup, quarks are "recombining" (joining up) to form particles. Since the trio has more "fuel" from the soup, the resulting proton flies out faster. This is a sign of how matter is being rebuilt from the soup.

3. The Models: Who Got It Right?

The scientists compared their real-world data to computer simulations:

• The "Perfect Fluid" Model (IP-Glasma+MUSIC+UrQMD): This model treats the soup like a fluid with viscosity (thickness). It matched the real data perfectly for the slow-moving particles and explained the "heavy gets a boost" effect. It's like a weather forecast that perfectly predicted the wind patterns.
• The "Jet" Model (HIJING): This model assumes the particles are just bouncing off each other like billiard balls, with no fluid flow. It failed to explain the slow particles in big collisions (central crashes) because it missed the "fluid" part. However, it worked okay for the smallest, most peripheral crashes, where the "soup" is too thin to act like a fluid and behaves more like individual particles.

Why Does This Matter?

This is the first time scientists have directly measured this specific type of outward flow.

• It proves that the Quark-Gluon Plasma is a fluid that pushes matter outward in a very specific, predictable way.
• It helps us understand how the universe cooled down after the Big Bang.
• It gives us a new way to study how quarks stick together to form the protons and neutrons that make up our world today.

In a nutshell: The scientists built a new "wind gauge" for the Big Bang's aftermath. They found that the hot soup pushes heavy particles harder than light ones, but as it cools, the particles start teaming up, giving the heavy teams a final speed boost. This confirms our theories about how the universe's most fundamental building blocks behave under extreme pressure.

Technical Summary

1. Problem Statement

While the collective behavior of the Quark-Gluon Plasma (QGP) created in heavy-ion collisions is well-described by relativistic hydrodynamics, direct measurements of radial flow remain limited.

• Current Limitations: Traditional methods, such as Boltzmann–Gibbs blast-wave fits to transverse momentum ($p_T$) spectra, provide only a single average radial flow parameter per centrality class. They fail to resolve the $p_T$-dependence of radial flow.
• The Gap: There is a need for an observable that can quantify the $p_T$-differential dynamics of radial expansion and distinguish between collective hydrodynamic flow and non-collective processes (like jet fragmentation) across different particle species and collision centralities.

2. Methodology

The study utilizes data from Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV collected by the ALICE detector at the LHC during the 2018 run.

• The Observable ($v_0(p_T)$): The paper introduces and measures a novel observable, $v_0(p_T)$, which quantifies the normalized covariance between event-wise fluctuations of the mean transverse momentum ($[p_T]$) and the fraction of particle yield ($f(p_T)$) in specific $p_T$ bins.
  • Formula: $v_0(p_T) = \frac{\langle f_A(p_T)[p_T]_B \rangle - \langle f_A(p_T) \rangle \langle [p_T]_B \rangle}{\langle f_A(p_T) \rangle \sigma_{[p_T]}}$
  • Non-flow Suppression: To isolate long-range collective correlations, the calculation uses a pseudorapidity gap ($\Delta\eta$). Particle yields are measured in window A, while mean $p_T$ is calculated in window B (and vice versa), suppressing short-range non-flow correlations.
• Event Selection:
  • Minimum-bias events triggered by V0 detectors.
  • Primary vertex constrained to $\pm 10$ cm of the interaction point.
  • Pileup events rejected.
  • Centrality determined via V0 amplitude distribution (analyzed in 10–20%, 30–40%, and 60–70% intervals).
• Particle Identification: Measurements include inclusive charged hadrons, as well as identified pions ($\pi^\pm$), kaons ($K^\pm$), and protons ($p/\bar{p}$) up to $p_T \approx 6$ GeV/c.
• Theoretical Comparisons: Results are compared against:
  • IP-Glasma+MUSIC+UrQMD: A hybrid model combining IP-Glasma initial conditions, viscous hydrodynamics (MUSIC), and hadronic afterburner (UrQMD).
  • HIJING: A model including mini-jets and nuclear effects but lacking collective flow.

3. Key Contributions

• First Direct Measurement: This work presents the first direct measurement of the $v_0(p_T)$ observable in heavy-ion collisions.
• $p_T$-Differential Radial Flow: It successfully maps the radial flow dynamics as a function of transverse momentum, moving beyond the single-parameter average provided by blast-wave fits.
• Particle Species Dependence: It provides the first $v_0(p_T)$ measurements for identified hadrons (pions, kaons, protons), allowing for the study of mass ordering and hadronization mechanisms.
• Model Validation: It validates the IP-Glasma+MUSIC+UrQMD framework as a robust description of radial flow dynamics up to intermediate $p_T$.

4. Key Results

A. Inclusive Charged Hadrons

• Low $p_T$ ($< 0.8$ GeV/c): $v_0(p_T)$ is negative across all centralities. This indicates an anti-correlation between mean $p_T$ fluctuations and low-$p_T$ particle production (events with higher mean $p_T$ have fewer low-$p_T$ particles).
• Intermediate $p_T$ ($0.8 - 4.0$ GeV/c): The observable rises approximately linearly. The slope increases from central to peripheral collisions, reflecting larger event-by-event fluctuations in radial flow in smaller systems.
• High $p_T$ ($> 4.0$ GeV/c): The linear rise deviates (slope decreases) in central/semicentral collisions but remains more linear in peripheral collisions.
• Model Agreement: The IP-Glasma+MUSIC+UrQMD model accurately describes data up to $p_T \approx 2.0$ GeV/c for all centralities. The HIJING model fails to describe central/semicentral data (lacking flow) but agrees with peripheral data where hard processes dominate.

B. Identified Hadrons (Mass Ordering & Baryon-Meson Splitting)

• Low $p_T$ ($< 3$ GeV/c): A clear mass ordering is observed: $v_0(p_T)_\pi > v_0(p_T)_K > v_0(p_T)_p$. This is consistent with hydrodynamic expectations where heavier particles receive a stronger boost from the collective expansion.
• Intermediate $p_T$ ($> 3$ GeV/c): A baryon-meson splitting occurs where protons exhibit significantly larger $v_0(p_T)$ than pions and kaons.
  • This phenomenon mirrors the splitting seen in anisotropic flow ($v_2$) and suggests quark recombination (coalescence) is the dominant hadronization mechanism at these momenta.
  • The splitting is strongest in central collisions and negligible in peripheral ones, indicating a system-size dependence (recombination favored in dense systems).
• Model Performance: The hydrodynamic model reproduces the mass ordering up to $\sim 3$ GeV/c for protons, $\sim 2$ GeV/c for pions, and $\sim 1.5$ GeV/c for kaons. HIJING fails to capture both the low-$p_T$ mass ordering and the high-$p_T$ splitting.

5. Significance

• Novel Probe: $v_0(p_T)$ serves as a sensitive, complementary probe to anisotropic flow ($v_n$) for studying QGP properties. It is particularly sensitive to the QCD equation of state and bulk viscosity, while being largely insensitive to shear viscosity.
• Dynamics Insight: The results confirm that radial flow is a collective phenomenon that can be resolved differentially in $p_T$. The transition from hydrodynamic behavior (mass ordering) to recombination dominance (baryon-meson splitting) provides a detailed picture of the QGP evolution and hadronization.
• Future Applications: The successful application of this method to light hadrons paves the way for future studies involving heavy-flavor and rare particles, offering deeper insights into parton-medium interactions.

In conclusion, this paper establishes $v_0(p_T)$ as a powerful tool for dissecting the collective expansion dynamics of the QGP, validating hydrodynamic models at low-to-intermediate $p_T$, and identifying the onset of non-collective hadronization mechanisms at higher momenta.