Probing the onset of hydrodynamization in peripheral p-Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV

Using the JETSCAPE event generator to simulate peripheral p-Pb collisions at 5.02 TeV, this study estimates the minimum size for Quark-Gluon Plasma hydrodynamization by analyzing elliptic flow fluctuations, which indicate a breakdown of fluid behavior at a charged-particle multiplicity of approximately $dN/dy \approx 14$.

The Gist

Imagine you are trying to figure out the smallest possible puddle of water that can still act like a fluid. If you have a giant ocean, it flows easily. If you have a single drop, it might just sit there or break apart. But where is the line? At what size does a collection of water molecules stop acting like a fluid and start acting like individual, chaotic particles?

This paper is about finding that exact "tipping point" for the Quark-Gluon Plasma (QGP).

What is the QGP?

Think of the QGP as the "primordial soup" of the universe. It's a state of matter that existed just fractions of a second after the Big Bang. In this state, the building blocks of atoms (quarks and gluons) are melted together and flow freely, like a super-hot, super-dense liquid.

Usually, scientists create this soup by smashing two heavy atoms (like lead) together at nearly the speed of light. But recently, scientists noticed something puzzling: even when they smash much smaller things together—like a single proton hitting a lead nucleus (p-Pb collisions)—signs of this "liquid soup" appear.

The big question is: Is it actually a liquid, or is it just a bunch of particles bouncing around chaotically?

The Experiment: Smashing Protons into Lead

The authors of this paper wanted to find the smallest size of this "soup" that can still be described by the laws of hydrodynamics (the math used to describe flowing liquids).

They used a massive computer simulation called JETSCAPE. Think of this simulation as a high-tech video game engine that recreates the entire collision process in four steps:

1. The Setup (TRENTo): They set the stage, placing the protons and lead nuclei in their starting positions.
2. The Pre-Game (Freestreaming): Before the "liquid" forms, the particles fly around freely for a tiny split second.
3. The Flow (MUSIC): This is the hydrodynamics part. The simulation tries to treat the particles as a flowing fluid.
4. The Aftermath (iSS + SMASH): As the soup cools down, the particles freeze into actual protons, pions, and other particles that detectors can see.

The Test: How "Liquid" is the Soup?

To test if the soup is really behaving like a fluid, the scientists looked at something called Elliptic Flow.

The Analogy: Imagine two cars crashing head-on. If they are perfectly round and hit dead center, the debris flies out in a circle. But if they hit slightly off-center (a glancing blow), the debris flies out more in an oval shape (like a football).

• If the matter inside acts like a perfect fluid, it will squeeze out strongly in that oval shape.
• If the matter is just chaotic particles bouncing around, the oval shape will be weak or non-existent.

The scientists ran their simulation for "peripheral" collisions (glancing blows where the overlap between the proton and lead nucleus is small). They asked: How small can this overlap get before the fluid behavior breaks down?

The Twist: The "Relaxation Time" Knob

In real fluids, there is a delay between when you push the fluid and when it responds. In physics, this is called the shear relaxation time.

The authors played a trick: they turned this "relaxation time" knob to extreme settings.

• They asked: "What if the fluid is very sluggish to respond? What if it's very quick?"
• They watched the Elliptic Flow (the oval shape) under these extreme conditions.

The Discovery: The Tipping Point

As they simulated collisions that were more and more "glancing" (meaning the amount of matter involved, or dN/dy, got smaller), they watched the fluid behavior.

• The Result: When the amount of matter dropped to about 7 particles per unit of rapidity (dN/dy ≈ 7), the fluid behavior suddenly started to wobble and break down.
• The Metaphor: Imagine a crowd of people trying to move like a fluid. If you have 100 people, they flow smoothly. If you have 10, they might still flow. But if you get down to 7 people, they start bumping into each other individually, and the smooth "flow" disappears.

The paper concludes that for proton-lead collisions at the energy they studied, hydrodynamics stops working when the system gets smaller than about 7 particles. Below that, the "soup" is too small to act like a liquid; it's just a bunch of individual particles.

Why Does This Matter?

This helps scientists understand the fundamental limits of nature. It tells us that the "liquid" state of matter isn't magic; it has a minimum size requirement. If the system is too small, the rules of fluid dynamics no longer apply, and we have to look at the individual particles instead.

The authors also noted that their results were slightly different from their previous studies on larger collisions (like lead-lead), likely because the computer models they used this time were more stable and handled the "pre-game" phase differently.

In short: They found the smallest puddle of quark-gluon plasma that can still be called a "fluid," and it turns out that puddle needs to contain at least about 7 particles to hold together.

Technical Summary

Technical Summary: Probing the Onset of Hydrodynamization in Peripheral p-Pb Collisions

Problem Statement
While relativistic hydrodynamics has successfully modeled the Quark-Gluon Plasma (QGP) in large heavy-ion collisions (Pb-Pb, Au-Au), its applicability to small collision systems (high-multiplicity proton-proton and proton-nucleus) remains a subject of intense debate. The central question is whether the observed collective flow signatures in these small systems arise from true QGP-like hot nuclear matter effects or cold nuclear matter effects. Specifically, the authors aim to determine the smallest system size (quantified by particle multiplicity, $dN/dy$) at which hydrodynamic descriptions break down. Previous work by the authors established an onset of hydrodynamization at $dN/dy \approx 10$ for peripheral Pb-Pb and Au-Au collisions; this study extends that investigation to the smaller p-Pb system at $\sqrt{s_{NN}} = 5.02$ TeV.

Methodology
The study utilizes the JETSCAPE framework (version 3.6.4), a modular simulation tool designed to consistently model both soft and hard sectors of high-energy collisions. The simulation chain for the soft sector includes:

1. Initial Conditions: The TRENTo model generates the initial energy density based on a generalized mean of nuclear thickness functions, incorporating nucleon fluctuations.
2. Pre-equilibrium: A Freestreaming module based on the collisionless Boltzmann equation bridges the gap between the initial state and the hydrodynamic phase.
3. Hydrodynamics: The MUSIC solver implements second-order viscous hydrodynamics (BRSSS formalism). The shear relaxation time ($\tau_\pi$), a second-order transport coefficient regulating non-hydrodynamic modes, is the primary variable of interest.
4. Hadron Afterburner: The iSS (particlization) and SMASH (hadronic transport) modules handle the freeze-out and subsequent hadronic rescattering.

To probe the onset of hydrodynamization, the authors vary the shear relaxation time ($\tau_\pi$) to extreme values. Since $\tau_\pi$ is related to the shear viscosity to entropy density ratio ($\eta/s$) by $\tau_\pi(T) = b_\pi \frac{\eta}{s(T)} \frac{1}{T}$, they employ two distinct variation strategies:

1. Varying the normalization constant $b_\pi$ (from 1 to 20) while keeping the temperature-dependent $\eta/s$ fixed.
2. Varying the temperature-dependent $\eta/s$ bounds (using the lower KSS limit and upper Bayesian limits) while keeping $b_\pi$ fixed.

The breakdown of hydrodynamic behavior is identified by monitoring the elliptic flow ($v_2$) and its fluctuations. Theoretical arguments suggest that if the contribution of non-hydrodynamic modes (regulated by $\tau_\pi$) exceeds that of hydrodynamic modes, the fluid description fails, leading to abrupt deviations in flow observables.

Key Contributions and Results

• Benchmarking: The model successfully reproduces experimental data from ALICE, ATLAS, and CMS for charged particle rapidity spectra, transverse momentum ($p_T$) spectra, and average transverse momentum as a function of centrality (defined by $N_{track}$).
• Fluctuation Analysis: By simulating peripheral p-Pb collisions and varying $\tau_\pi$, the authors observe that elliptic flow fluctuations increase as the system moves from central to peripheral collisions.
• Onset Determination:
  • When varying $b_\pi$, an abrupt increase in elliptic flow fluctuations is observed in the centrality range of 75–85% to 70–80%.
  • When varying $\eta/s$, fluctuations begin to increase below the 70–80% centrality range.
  • These fluctuations correspond to a charged particle multiplicity of $dN/dy \approx 7$.
• Comparison to Previous Work: Unlike the authors' previous study on larger systems (where the onset was found at $dN/dy \approx 10$), the transition in p-Pb appears at a lower multiplicity. The authors note that the deviation below the inferred onset is less abrupt than in previous studies, potentially due to the use of the more stable MUSIC hydrodynamic solver compared to the previously used ECHO-QGP.

Significance and Claims
The paper claims to provide an estimate for the smallest QGP volume in p-Pb collisions at 5.02 TeV that can be satisfactorily modeled by low-order hydrodynamics. The primary conclusion is that hydrodynamic behavior breaks down at approximately $dN/dy \approx 7$.

The authors maintain a modest tone regarding the nature of this transition, acknowledging that it remains an open question whether this represents a sharp onset or a smooth transition region. They also highlight that their study isolates the soft sector; a definitive confirmation of the onset would ideally require simultaneous investigation of the hard sector (e.g., jet quenching) to see how hard and soft observables mutually influence the determination of hydrodynamization. The work serves as a specific application of non-hydrodynamic mode analysis to constrain the validity limits of hydrodynamic models in small collision systems.