Observation of flow vector fluctuations in p$-$Pb collisions at $\mathbf{\sqrt{\textit{s}_{_{\bf NN}}}}=$ 5.02 TeV

This paper presents the first observation of significant transverse momentum and pseudorapidity dependent flow vector fluctuations in p$-$Pb collisions at $\sqrt{s_{_{\rm NN}}} = 5.02$ TeV, confirming collective flow in small collision systems and providing critical constraints for theoretical models of initial geometry.

The Gist

The Big Picture: Smashing Tiny Things to Find a Perfect Fluid

Imagine you are at a crowded party. Usually, when people bump into each other, they just scatter in random directions. But in the world of high-energy physics, scientists smash protons (tiny particles) into lead nuclei (heavy atoms) at nearly the speed of light.

For a long time, scientists thought that if you smashed a small object (a proton) into a big one (lead), the result would just be a chaotic mess of debris. They expected the "perfect fluid" behavior—a state of matter called Quark-Gluon Plasma (QGP) that flows like honey—to only happen in massive collisions (like Lead-Lead).

The Surprise: In smaller collisions (Proton-Lead), scientists found that the debris does flow together in an organized way, just like in the big collisions. This paper asks: How organized is this flow, and does it change depending on where you look?

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The Core Concept: The "Flow Vector"

To understand the paper, imagine the debris from the collision as a giant, expanding balloon of gas.

• The Flow: As the balloon expands, it doesn't just puff out evenly. It stretches more in one direction than another (like an oval). This stretching is called anisotropic flow.
• The Flow Vector: Think of this as an arrow pointing in the direction the "wind" is blowing inside the balloon. It has two parts:
  1. Strength: How hard is the wind blowing?
  2. Direction: Which way is it pointing?

In a perfect, smooth world, this arrow would point the same way for every single particle, no matter how fast it is moving or where it is located.

The Discovery: This paper proves that the "wind" is not the same for everyone. The direction and strength of the flow change depending on:

1. How fast the particle is moving (Transverse Momentum, or $p_T$).
2. Where the particle is located relative to the collision point (Pseudorapidity, or $\eta$).

It's like being in a storm where the wind blows one way for the people running fast, but a different way for the people walking slowly.

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The Problem: The "Noise" in the Room

Measuring this flow is incredibly hard because of "Non-flow" effects.

• The Analogy: Imagine trying to hear a specific conversation at a loud party. But there are other noises: people shouting from the same group (jets), or people echoing each other (resonance decays). These are "non-flow" noises that mimic the flow you are trying to measure.
• The Solution: The scientists used a clever trick called the "Template Fit Method."
  • Imagine you have a recording of the party when it's empty (low energy). You know exactly what the "noise" sounds like.
  • When the party is full (high energy), you subtract the "noise" recording from the total sound.
  • What's left is the pure "flow" music. This allowed them to see the flow fluctuations clearly, with a confidence level of over 99.9999% (5-sigma).

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The Findings: The Wind Changes

The paper presents three main discoveries, which they measured using special mathematical tools (observables):

1. The Speed Matters ($p_T$-dependent fluctuations)

They looked at particles moving at different speeds.

• The Result: The "wind direction" for slow particles is slightly different from the "wind direction" for fast particles.
• The Analogy: Imagine a river. The water near the bottom (slow) flows slightly differently than the water near the surface (fast). In the collision, the "river" of particles has layers that twist differently.
• Significance: This proves that the initial shape of the collision isn't a smooth, uniform blob. It's lumpy and bumpy, and those bumps affect fast and slow particles differently.

2. The Location Matters ($\eta$-dependent fluctuations)

They looked at particles moving forward vs. backward relative to the collision.

• The Result: The flow at the "front" of the explosion is not perfectly aligned with the flow at the "back."
• The Analogy: Imagine a long, twisting snake. The head might be pointing North, but the tail is pointing Northeast. The "flow vector" twists along the length of the collision.
• Significance: This tells us the initial collision wasn't just a flat pancake; it had a 3D structure that twisted as it expanded.

3. The "Lumpy" Start

The biggest takeaway is that the initial geometry (the shape of the proton and lead nucleus right before they hit) is full of fluctuations.

• The Analogy: Think of the proton not as a smooth marble, but as a bumpy potato. When it hits the lead nucleus, the "bumps" create a chaotic, twisting wind inside the resulting fireball.
• Why it matters: By measuring how the wind twists, scientists can reverse-engineer the shape of the "potato" (the proton) before the crash. This helps us understand the internal structure of protons, which is still a bit of a mystery.

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The Theoretical Check: Do the Models Work?

The scientists compared their real-world data to two supercomputer simulations:

1. AMPT: A model that treats particles like billiard balls bouncing off each other.
2. 3DGlauber+MUSIC+UrQMD: A model that treats the collision like a fluid (hydrodynamics) with complex 3D geometry.

• The Verdict: Both models got the general idea right (the wind does twist), but neither was perfect.
  • The Fluid Model was good at predicting the twist along the length of the collision but slightly underestimated the twist based on speed.
  • The Billiard Ball Model did a decent job with speed but struggled with the length.
• The Lesson: Our current theories are close, but we need better maps of the "bumpy potato" (the proton's internal structure) to get the simulation perfect.

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Summary: Why Should You Care?

This paper is like a high-resolution weather map for the smallest explosion in the universe.

1. It confirms the "Perfect Fluid": Even in tiny collisions, matter behaves like a fluid, not just a gas of random particles.
2. It reveals the "Bumpy Potato": It proves that protons aren't smooth spheres; they have a lumpy, fluctuating internal structure that dictates how the universe expands in the first fraction of a second.
3. It refines our tools: By showing exactly where our computer models fail, this paper helps physicists build better theories about how the universe began (the Big Bang) and how matter behaves under extreme pressure (like inside neutron stars).

In short: The universe is messy, lumpy, and twists in complex ways, even in the tiniest collisions, and we finally have the tools to see exactly how.

Technical Summary

1. Problem Statement

While the formation of Quark-Gluon Plasma (QGP) and collective anisotropic flow are well-established in ultra-relativistic heavy-ion collisions (e.g., Pb–Pb), their existence in small collision systems (proton–proton and proton–lead) has been a subject of intense debate. Although evidence of collective behavior (such as the "ridge" structure and mass-dependent flow) has been observed in small systems, the underlying mechanisms remain unclear.

A critical gap in understanding is the initial state geometry and its event-by-event fluctuations. In heavy-ion collisions, flow vector fluctuations (where the flow symmetry plane $\Psi_n$ and magnitude $v_n$ vary with transverse momentum $p_T$ and pseudorapidity $\eta$) have been observed with high significance. These fluctuations probe the 3D initial geometry. However, previous measurements in small systems (p–Pb) were inconclusive because:

• They relied on two-particle cumulant methods with limited pseudorapidity gaps.
• They struggled to fully disentangle non-flow effects (correlations from jets, resonance decays, and other sources unrelated to collective expansion) from genuine collective flow.
• There was a lack of precise constraints on the 3D initial conditions (longitudinal and transverse fluctuations) in small systems.

This paper aims to unambiguously observe $p_T$- and $\eta$-dependent flow vector fluctuations in p–Pb collisions and determine if they share a common origin with those in Pb–Pb collisions.

2. Methodology

The analysis utilizes data from p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV collected by the ALICE detector during LHC Run 2 (2016). The study employs specific observables and advanced analysis techniques to isolate flow fluctuations:

• Observables:

  • $v_2\{2PC\}/v_2[2PC]$: A ratio comparing the second-harmonic flow vector in a narrow $p_T$ interval ($p_T^a$) against a wide reference range ($p_T^{ref}$). A deviation from unity indicates $p_T$-dependent fluctuations.
  • $r_2(p_T^a, p_T^b)$: A differential observable comparing flow vectors between two narrow $p_T$ bins to probe finer structures of fluctuations as a function of kinematic separation.
  • $R_2(\eta_a, \eta_b)$: An observable constructed to study $\eta$-dependent fluctuations in asymmetric systems (p–Pb), utilizing correlations between mid-rapidity and forward/backward regions to suppress non-flow.

• Data Selection & Reconstruction:

  • Events selected via minimum bias triggers with primary vertices within 10 cm of the interaction point.
  • Charged tracks reconstructed using the Inner Tracking System (ITS) and Time Projection Chamber (TPC).
  • Multiplicity classes defined by the V0A detector (0–20%, 20–40%, 40–60%).
  • For $\eta$-dependent studies, correlations are made between TPC/ITS tracks and hits in the Forward Multiplicity Detector (FMD) to ensure large $\Delta\eta$ separation.

• Non-Flow Suppression (Key Innovation):

  • Template Fit Method: Instead of simple peripheral subtraction, the analysis uses a template fit. The two-particle correlation function in high-multiplicity events is fitted using a combination of a non-flow template (derived from low-multiplicity events) and a flow-modulated component (Fourier series). This effectively disentangles collective flow from non-flow correlations (jets, resonances).
  • Pseudorapidity Gaps: Strict requirements on $\Delta\eta$ ($>1.0$ for $p_T$ studies, $>0.8$ for $r_2$) are applied to further suppress jet-related correlations.

• Systematic Uncertainties:

  • Evaluated by varying event/track selection criteria (vertex position, TPC space points, $\chi^2$).
  • Validated using Monte Carlo closure tests with the AMPT model and GEANT3 simulations.
  • Residual non-flow contributions estimated using DPMJET III and PYTHIA8 models.

3. Key Contributions

• First Unambiguous Observation in Small Systems: The paper provides the first definitive observation of $p_T$- and $\eta$-dependent flow vector fluctuations in p–Pb collisions with a significance exceeding 5$\sigma$.
• Advanced Non-Flow Control: The application of the template fit method in this context significantly reduces biases from non-flow effects compared to previous studies, allowing for a cleaner extraction of flow fluctuations.
• 3D Initial Geometry Constraints: By measuring fluctuations in both transverse ($p_T$) and longitudinal ($\eta$) directions, the study provides unique constraints on the 3D initial geometry of small collision systems, a regime previously poorly understood.
• Multiplicity Dependence: The analysis extends these measurements across different multiplicity classes (0–20% to 40–60%), revealing how fluctuations evolve with system size.

4. Results

Transverse Momentum ($p_T$) Dependent Fluctuations

• Observation: The ratio $v_2\{2PC\}/v_2[2PC]$ deviates significantly from unity for $p_T > 1$ GeV/c. The deviation increases with $p_T$, reaching over 10% for $p_T > 2.5$ GeV/c.
• Significance: The deviation from unity is observed with 7.9$\sigma$ confidence for $p_T > 1$ GeV/c.
• Multiplicity Dependence: The effect is more pronounced in lower multiplicity classes (40–60%), suggesting stronger fluctuations in peripheral-like collisions.
• Model Comparison:
  • 3DGlauber+MUSIC+UrQMD: Predicts a smaller deviation (few percent) than observed, suggesting it may underestimate the strength of fluctuations or the initial geometry variations.
  • AMPT (with string melting): Generates slightly stronger fluctuations and describes the data better, though statistical uncertainties in the model are large.
  • Conclusion: The agreement with models that include partonic interactions supports the presence of partonic flow in high-multiplicity p–Pb collisions.

Pseudorapidity ($\eta$) Dependent Fluctuations

• Observation: The observable $R_2(\eta_a, \eta_b)$ shows a clear decreasing trend as $|\eta_a|$ increases, indicating significant $\eta$-dependent flow vector fluctuations.
• Significance: Deviations from unity are observed with 7.2$\sigma$ confidence for $|\eta_a| > 0.4$.
• Multiplicity Dependence: Unlike $p_T$ fluctuations, $\eta$-dependent fluctuations show no significant difference between multiplicity classes within uncertainties, though models suggest a reduction in peripheral collisions.
• Model Comparison:
  • 3DGlauber+MUSIC+UrQMD: Reproduces the trend qualitatively but significantly underestimates the magnitude of fluctuations, particularly for specific $\eta_b$ ranges (1.8 < $|\eta_b|$ < 2.6).
  • AMPT: Captures the trend but slightly overestimates the magnitude.
  • Conclusion: Neither model quantitatively reproduces the longitudinal fluctuations, indicating a gap in the theoretical understanding of the 3D initial state in small systems.

5. Significance

• Confirmation of Collective Flow: The results confirm that the mechanisms driving anisotropic flow in small systems (p–Pb) are fundamentally similar to those in large systems (Pb–Pb), specifically pointing to initial geometry fluctuations as the driver.
• Evidence of QGP-like Behavior: The observation of flow vector fluctuations, which are sensitive to the initial state and less affected by complex final-state evolution, strongly supports the hypothesis that a short-lived, collectively expanding medium (potentially a QGP droplet) is formed in high-multiplicity p–Pb collisions.
• Theoretical Constraints: The measurements provide critical new constraints for theoretical models. While models can describe average flow coefficients, they struggle to simultaneously reproduce the magnitude of both $p_T$ and $\eta$ dependent fluctuations. This highlights the need for improved modeling of the fluctuating 3D initial geometry and the proton's internal structure.
• Future Directions: These results serve as essential inputs for future 3D Bayesian analyses aimed at precisely determining the transport properties and initial conditions of matter created in small collision systems at the LHC.