Long-range transverse momentum correlations and radial flow in Pb$-$Pb collisions at the LHC with ALICE

This ALICE study introduces the new observable $v_{0}(p_\mathrm{T})$ to measure long-range transverse momentum correlations in Pb-Pb collisions at 5.02 TeV, revealing mass-dependent flow patterns consistent with hydrodynamics and quark recombination while demonstrating its sensitivity to bulk viscosity and the equation of state for constraining the properties of strongly interacting matter.

The Gist

The Big Picture: The Ultimate "Splatter" Experiment

Imagine taking two massive, heavy balls (Lead nuclei) and smashing them together at nearly the speed of light. When they hit, they don't just bounce off; they melt into a tiny, super-hot drop of liquid soup called the Quark-Gluon Plasma (QGP). This is the state of matter that existed just microseconds after the Big Bang.

For decades, scientists have studied this soup by looking at how particles fly out in different directions (like shrapnel from a bomb). They found that the soup expands and flows like a fluid. But there was a missing piece of the puzzle: How does the size and speed of this explosion fluctuate from one crash to the next?

This paper introduces a new tool, called $v_0(p_T)$, to measure those fluctuations. Think of it as a new way to listen to the "heartbeat" of the explosion.

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The New Tool: Listening to the "Heartbeat"

In previous studies, scientists measured how the soup flowed in specific directions (like a river flowing downstream). This new measurement, $v_0(p_T)$, looks at something different: Radial Flow.

• The Analogy: Imagine a balloon being inflated.
  • Standard Flow ($v_2$): If the balloon is slightly oval, it expands faster in one direction than the other. Scientists have measured this "ovalness" for years.
  • New Flow ($v_0$): This measures how fast the balloon is expanding overall in all directions at once. But here's the kicker: Every time you blow up a balloon, the speed varies slightly. Sometimes it pops out fast; sometimes slow.
  • The Measurement: $v_0(p_T)$ measures how much the "speed of the explosion" changes from one crash to the next, and how that change affects the particles flying out.

How They Did It: The "Noise-Canceling" Trick

When particles fly out of the collision, they create a lot of "noise." Some particles are just friends born from the same parent particle (like a mother and child), or they come from tiny jets of debris. These are "short-range" correlations that mess up the measurement of the big, collective flow.

To fix this, the scientists used a Pseudorapidity Gap ($\Delta\eta$).

• The Analogy: Imagine you are at a loud party trying to hear a conversation across the room. The people right next to you are shouting (short-range noise). To hear the person across the room clearly, you put on noise-canceling headphones that block out the people standing right next to you.
• In the Lab: They looked at particles in two different sections of the detector that were far apart. If two particles are far apart, they can't be "friends" from a short-range decay. If they still show a connection, it must be because the entire explosion pushed them both. This isolates the true "collective flow."

What They Found: The Mass Ordering and The "Baryon-Meson Split"

The results were fascinating and confirmed that the QGP behaves like a perfect fluid.

1. The "Heavy vs. Light" Race (Low Energy)
At lower speeds, the scientists saw a clear mass ordering.

• The Analogy: Imagine a crowd of people running out of a stadium. The heavy people (Protons) are pushed harder by the crowd's collective shove than the light people (Pions).
• The Result: The data showed that heavier particles moved differently than lighter ones, exactly as predicted by fluid dynamics. This proves the "soup" is pushing everything together, not just letting them fly randomly.

2. The "Baryon-Meson Split" (High Energy)
At higher speeds (above 3 GeV), something weird happened. The protons (heavy) suddenly started behaving more like the pions (light) than expected, or rather, they separated from the kaons in a specific way.

• The Analogy: Imagine a dance floor. At low speeds, everyone dances individually. At high speeds, the dancers start grabbing hands and forming pairs or trios before leaving the floor.
• The Result: This suggests that at high energies, particles aren't just being pushed by the fluid; they are recombining. Quarks (the building blocks) are grabbing onto each other to form protons and pions as they exit the soup. It's like the fluid is so crowded that the particles have to "stick together" to get out.

What This Tells Us About the Universe

The paper compares their data to computer simulations (like a video game of the Big Bang) to see which rules of physics are correct.

• The "Sticky" Factor (Bulk Viscosity): The new measurement is very sensitive to how "sticky" or "friction-heavy" the soup is when it expands. It turns out $v_0(p_T)$ is a great way to measure this "stickiness" (bulk viscosity), which other tools couldn't do as well.
• The "Recipe" (Equation of State): It helps scientists figure out the "recipe" of the soup—how pressure and temperature relate to each other. The data suggests the soup expands in a way that matches the most advanced theories of nuclear physics.

The Bottom Line

This paper is like adding a new instrument to an orchestra. For years, we've been listening to the "melody" of the explosion (how it flows in directions). Now, with $v_0(p_T)$, we can hear the rhythm and volume fluctuations (how the speed of the explosion changes).

By using this new tool, the ALICE team has proven that:

1. The Quark-Gluon Plasma is a fluid that pushes particles based on their weight.
2. At high speeds, particles start sticking together (recombining).
3. We can now measure the "friction" and "stiffness" of this cosmic soup with much higher precision.

This helps us understand not just how the QGP behaves, but also the fundamental laws that governed the very first moments of our universe.

Technical Summary

1. Problem and Motivation

The study of the Quark-Gluon Plasma (QGP) relies on understanding the collective behavior of matter created in high-energy heavy-ion collisions. While anisotropic flow ($v_n$) has been extensively studied to probe azimuthal anisotropies driven by initial spatial geometry, the radial flow (isotropic expansion) and its event-by-event fluctuations remain less constrained.

Traditional methods for measuring radial flow, such as fitting transverse momentum ($p_T$) spectra with blast-wave models, yield an integrated flow parameter ($\langle \beta_T \rangle$). These methods suffer from two main limitations:

1. Lack of differential insight: They do not provide direct access to $p_T$-differential features like mass ordering or baryon-meson splitting.
2. Nonflow contamination: Inclusive $p_T$ spectrum analyses are contaminated by short-range correlations (nonflow) from resonance decays and jets, which are unrelated to hydrodynamic collectivity.

The paper introduces and measures a new observable, $v_0(p_T)$, designed to isolate long-range transverse momentum correlations analogous to anisotropic flow, thereby providing a cleaner probe of radial flow fluctuations and medium properties.

2. Methodology

Observable Definition

The observable $v_0(p_T)$ is defined as the normalized covariance between the event-by-event multiplicity fraction and the mean transverse momentum of the event:
$$v_0(p_T) = \frac{\langle f_A(p_T)[p_T]_B \rangle - \langle f_A(p_T) \rangle \langle [p_T]_B \rangle}{\langle f_A(p_T) \rangle \sigma_{[p_T]}}$$
Where:

• $A$ and $B$ are two distinct pseudorapidity ($\eta$) windows separated by a gap $\Delta\eta$.
• $f_A(p_T)$ is the fraction of particles in a specific $p_T$ bin within window $A$.
• $[p_T]_B$ is the mean $p_T$ in window $B$.
• $\sigma_{[p_T]}$ is the standard deviation of the mean $p_T$.

Key Feature: The use of a pseudorapidity gap ($\Delta\eta = 0.4$) suppresses short-range nonflow correlations (e.g., from resonance decays or near-side jets) while preserving long-range correlations driven by global pressure gradients.

Experimental Setup

• Data Source: Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV recorded by the ALICE detector in 2018.
• Event Selection: ~80 million minimum-bias events selected via V0 detector coincidence. Primary vertex reconstruction within $\pm 10$ cm; pileup events excluded.
• Centrality: Classified into intervals (e.g., 10–20%, 30–40%, 60–70%) based on V0 amplitude.
• Particle Identification (PID):
  • Inclusive charged particles ($h^\pm$).
  • Identified species: Pions ($\pi^\pm$), Kaons ($K^\pm$), and Protons ($p/\bar{p}$).
  • PID utilized specific energy loss ($dE/dx$) in the Time Projection Chamber (TPC) and time-of-flight (TOF) measurements, combined via a Bayesian approach.
  • Purity >98% for pions and protons in the relevant $p_T$ ranges.
• Systematic Uncertainties: Evaluated by varying event/track selection criteria, PID thresholds, $\Delta\eta$ gaps, and centrality definitions. A Monte Carlo (HIJING) closure test confirmed the robustness of the observable against detector efficiency effects.

3. Key Contributions

1. First Measurement of $v_0(p_T)$: This is the first experimental report of $v_0(p_T)$ for inclusive charged particles and identified hadrons (pions, kaons, protons) across various centralities in Pb–Pb collisions.
2. Validation of Hydrodynamic Scaling: The study demonstrates that $v_0(p_T)$ exhibits characteristic mass ordering at low $p_T$ and constituent quark number (NCQ) scaling, confirming its origin in hydrodynamic collectivity.
3. Sensitivity to Medium Properties: The paper establishes $v_0(p_T)$ as a sensitive probe for bulk viscosity ($\zeta/s$) and the Equation of State (EOS), distinct from its relative insensitivity to shear viscosity ($\eta/s$).
4. High-$p_T$ Physics: It provides evidence for quark recombination mechanisms at intermediate-to-high $p_T$ through the observation of baryon-meson splitting.

4. Results

$p_T$ Dependence and Mass Ordering

• Sign Change: $v_0(p_T)$ is negative at low $p_T$ ($< 0.8$ GeV/c) and becomes positive at high $p_T$. This sign change reflects the anti-correlation between event-by-event mean-$p_T$ fluctuations and the spectral shape (upward fluctuations increase high-$p_T$ fraction).
• Low $p_T$ ($< 3$ GeV/c): A clear mass ordering is observed: $v_0(p_T)$ for protons is lower than for kaons, which is lower than for pions. This is consistent with hydrodynamic models where heavier particles are pushed to higher momenta by collective radial flow.
• High $p_T$ ($> 3$ GeV/c): The trend reverses; protons exhibit larger $v_0(p_T)$ than pions and kaons. This "baryon-meson splitting" aligns with expectations from quark-recombination models, suggesting that hadrons form via the coalescence of flowing quarks.
• NCQ Scaling: When $v_0(p_T)$ is scaled by the number of constituent quarks ($n_q$) and plotted against transverse kinetic energy per quark ($(m_T - m_0)/n_q$), the data for different species collapse onto a common curve, supporting partonic collectivity prior to hadronization.

Centrality Dependence

• The magnitude of $v_0(p_T)$ scales approximately as $(dN_{ch}/d\eta)^{-1}$.
• In peripheral collisions, the data deviates from hydrodynamic scaling at high $p_T$ and shows better agreement with the HIJING model (which lacks collective flow), indicating a growing dominance of hard scatterings and jet fragmentation.

Comparison with Models

• IP-Glasma+MUSIC+UrQMD: This viscous hydrodynamic framework describes the data well up to $p_T \approx 2$ GeV/c across all centralities. It successfully reproduces the mass ordering and the sign change. Deviations at higher $p_T$ suggest the transition to a kinetic regime where hydrodynamics is less applicable.
• HIJING: Fails to describe the data in central collisions (missing collective flow) but qualitatively captures trends in peripheral collisions.

Sensitivity to Transport Coefficients

• Bulk Viscosity ($\zeta/s$): The slope of $v_0(p_T)$ at low $p_T$ is highly sensitive to temperature-dependent bulk viscosity. Models with $\zeta/s = 0$ or constant $\zeta/s$ fail to describe the data as well as those with temperature-dependent $\zeta/s$.
• Equation of State (EOS): The observable is sensitive to the squared speed of sound ($c_s^2$). Models with different EOS parametrizations (EOS1, EOS2, LQCD-based) yield distinct slopes, with the LQCD-based EOS providing the best agreement.
• Shear Viscosity ($\eta/s$): $v_0(p_T)$ shows relatively low sensitivity to variations in $\eta/s$ compared to other observables like $v_n$.
• Initial Conditions: The inclusion of sub-nucleonic fluctuations in the initial state (IP-Glasma) improves the description of the data compared to models without such fluctuations.

5. Significance

• New Probe for QGP Properties: $v_0(p_T)$ adds a crucial dimension to the set of observables used in Bayesian global analyses. It offers a unique window into bulk viscosity and the Equation of State, complementing anisotropic flow measurements which are more sensitive to shear viscosity.
• Constraint on Hydrodynamic Validity: The results help define the kinematic limits of hydrodynamic descriptions, showing where the transition to kinetic/jet-dominated regimes occurs.
• Insight into Hadronization: The observation of NCQ scaling and baryon-meson splitting at intermediate $p_T$ reinforces the quark-recombination picture of hadronization in the QGP.
• Methodological Advance: The successful application of the $\Delta\eta$-gap technique to radial flow measurements demonstrates a robust method to isolate long-range collective effects from nonflow background, setting a standard for future correlation studies.

In conclusion, this work establishes $v_0(p_T)$ as a powerful, differential observable that effectively probes the isotropic expansion and fluctuations of the QGP, providing critical constraints on the transport properties and thermodynamic nature of strongly interacting matter.