Energy loss predicts no $v_2$ in small systems

This paper presents a perturbative QCD-based energy loss model calibrated on large systems that successfully predicts experimental $R_{AA}$ data in small systems like Ne+Ne and O+O, yet surprisingly forecasts a near-zero high-$p_T$ elliptic flow ($v_2$) due to a geometric decorrelation between hard and soft participant planes inherent to standard experimental measurement methods.

The Gist

Imagine you are trying to understand how a crowd of people moves through a crowded room. In physics, scientists study something similar but on a subatomic scale: they smash heavy atoms together to create a super-hot, super-dense soup of particles called the Quark-Gluon Plasma (QGP). Think of this soup as a thick, sticky fluid.

When a fast-moving particle (like a high-energy "jet" of energy) tries to shoot through this soup, it loses energy, much like a runner trying to sprint through waist-deep water. Scientists have been trying to figure out exactly how this "running through water" works.

Here is the story of this paper, broken down into simple concepts:

1. The Big Success Story (The "Big Systems")

For years, scientists have been smashing huge atoms together (like Lead-Lead or Gold-Gold). In these massive collisions, the "soup" is thick and wide.

• The Observation: When a fast particle tries to escape, it gets slowed down significantly. It also tends to exit the soup in a specific direction, creating a pattern called $v_2$ (elliptic flow).
• The Model: The authors built a computer model that simulates this "running through water." They tuned their model using data from these big collisions, and it worked perfectly. It predicted exactly how much energy the particles lost and how they flowed.

2. The New Mystery (The "Small Systems")

Recently, scientists started smashing smaller things together, like Oxygen-Oxygen or Proton-Lead.

• The Expectation: If the "running through water" theory is true, even in these tiny collisions, the fast particles should still lose energy and show that same directional flow ($v_2$).
• The Surprise: Experiments did see a directional flow ($v_2$) in these small collisions. This made scientists think, "Aha! Even tiny drops of this plasma exist, and they slow down particles just like the big ones!"

3. The Paper's Big Claim: "Wait a Minute..."

The authors of this paper took their successful "Big System" model and applied it to these "Small Systems." They wanted to see if the same physics (energy loss) could explain the results.

Their Prediction:
When they ran the numbers for small systems (Neon, Oxygen, Proton), their model said:

"If the only thing happening is particles losing energy in the soup, the directional flow ($v_2$) should be zero."

Why?
Here is the creative analogy:
Imagine a Pinball Machine.

• The Big System (Lead-Lead): The machine is a large, oval-shaped table. The bumpers (the "soup") are arranged in a clear oval shape. If you shoot a pinball (the hard particle) in, it bounces off the walls. Because the table is oval, the ball is more likely to exit in a specific direction. The "bumpers" and the "ball's path" are perfectly aligned.
• The Small System (Proton-Lead): Now, imagine the table is tiny and the bumpers are jittery. The "soup" is so small and chaotic that the direction the ball enters is completely disconnected from the direction the bumpers are facing.
  • The "Hard Sector" (the fast particle) has its own idea of where to go.
  • The "Soft Sector" (the soup) has its own idea of where to flow.
  • In small systems, these two ideas are decorrelated. They are like two people trying to dance together but completely ignoring each other's moves. Because they aren't synchronized, the "flow" averages out to zero.

4. The Conflict with Reality

The paper points out a major problem:

• The Model says: $v_2$ should be zero in small systems if it's just about energy loss.
• The Experiments say: No, we do see a strong $v_2$ in small systems (like Proton-Lead).

The authors argue that if the experiments are right and there is a flow, it cannot be caused by the simple "energy loss in the soup" mechanism that works so well for big systems.

5. What Does This Mean?

The paper suggests that our current understanding might be missing a piece of the puzzle.

• Possibility A: The "energy loss" theory is wrong for small systems.
• Possibility B: There is some other physics happening in small systems that we haven't accounted for yet. Maybe the particles aren't just "running through water"; maybe they are interacting with the "walls" of the room in a completely different way before the soup even forms.

The Bottom Line

The authors are essentially saying:

"We have a great map for driving through a big city (large collisions). When we try to use that same map to drive through a tiny alleyway (small collisions), our map predicts you shouldn't be able to turn corners. But the drivers (experiments) say they are turning corners. Therefore, there must be a secret shortcut or a different rulebook for the alleyways that we haven't discovered yet."

They are calling for new experiments (specifically with Oxygen-Oxygen collisions) to see if the "tiny alleyway" rule applies there too. If Oxygen-Oxygen shows no flow, it proves the Proton-Lead flow is a weird anomaly. If it does show flow, then our whole theory of how particles lose energy needs a major rewrite.

Technical Summary

1. Problem Statement

The paper addresses a significant tension in high-energy nuclear physics regarding the interpretation of high-$p_T$ (transverse momentum) observables in small collision systems (e.g., $p+Pb$, $O+O$, $Ne+Ne$).

• The Context: In large systems (Au+Au, Pb+Pb), the simultaneous description of the nuclear modification factor ($R_{AA}$) and the elliptic flow coefficient ($v_2$) at high $p_T$ is successfully explained by path-length dependent partonic energy loss within a Quark-Gluon Plasma (QGP).
• The Puzzle: In small systems, experimental data presents a contradiction:
  • $R_{AA}$: Measurements in $p+Pb$ are inconsistent; some experiments (ALICE) show suppression ($R_{AA} < 1$), while others (ATLAS, CMS) show enhancement or unity ($R_{AA} \ge 1$). However, recent $O+O$ data shows suppression.
  • $v_2$: Experiments (ATLAS, ALICE, CMS) report significant, positive high-$p_T$ $v_2$ in $p+Pb$ collisions.
• The Conflict: Standard energy loss models predict that if a medium causes suppression ($R_{AA} < 1$), it must also generate anisotropy ($v_2 > 0$) due to path-length dependence. The observation of large $v_2$ without clear suppression (or with conflicting $R_{AA}$ data) challenges the interpretation that final-state energy loss is the sole driver of anisotropy in small systems.
• The Goal: The authors aim to provide a quantitative theoretical prediction for high-$p_T$ $v_2$ in small systems using a rigorous energy loss model to determine if the observed experimental $v_2$ can be attributed to energy loss.

2. Methodology

The authors employ a perturbative Quantum Chromodynamics (pQCD) based energy loss model with several advanced features:

• Energy Loss Formalism: The model combines radiative energy loss (based on the Djordjevic-Gyulassy-Levi-Vitev (DGLV) opacity expansion with short-path corrections) and collisional energy loss (based on Hard Thermal Loops (HTL) effective field theory).
• Dynamic Medium Evolution: Unlike previous "static brick" approximations, this model incorporates event-by-event hydrodynamic evolution.
  • The medium's scattering centers are modeled dynamically using a power-law density profile $\bar{\rho} \propto T^3$.
  • Initial conditions are generated via the IP-Glasma model and evolved using the MUSIC (2+1)D viscous hydrodynamics code.
  • This allows for a realistic calculation of energy loss along the full parton trajectory through a fluctuating medium.
• Calibration: The effective strong coupling constant ($\alpha_s$) is constrained via a global $\chi^2$ fit to experimental $R_{AA}$ and $v_2$ data from central and semi-central Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV.
• Anisotropy Extraction: The paper distinguishes between two definitions of $v_2$:
  1. $v_2^{hard}$: The intrinsic anisotropy of the hard parton distribution relative to the hard participant plane ($\psi_{hard}$).
  2. $v_2\{SP\}$ (Scalar Product): The standard experimental observable, which correlates the hard particle with the soft sector (bulk medium) participant plane ($\psi_{soft}$).
  • The relationship is given by: $v_2\{SP\} \propto v_2^{hard} \times \langle \cos[2(\psi_{hard} - \psi_{soft})] \rangle$.

3. Key Contributions

• First Quantitative Prediction for Small Systems: The study provides the first rigorous, event-by-event hydrodynamic prediction for high-$p_T$ $R_{AB}$ and $v_2$ in symmetric small systems ($Ne+Ne$, $O+O$) and asymmetric systems ($p+Pb$).
• Identification of Geometric Decorrelation: The paper identifies a generic geometric decorrelation between the hard sector (high-$p_T$ partons) and the soft sector (bulk medium) participant planes in small systems as the primary reason for the vanishing $v_2$.
• Model Independence Argument: The authors demonstrate that the result $v_2\{SP\} \approx 0$ is robust across different energy loss models because it is driven by the decorrelation of the reference planes, not the magnitude of the energy loss itself.

4. Results

• Large Systems (Pb+Pb): The model successfully reproduces experimental $R_{AA}$ and $v_2$ data simultaneously, confirming the validity of the path-length dependent energy loss framework in large systems.
• Small Systems ($Ne+Ne$, $O+O$, $p+Pb$):
  • $R_{AB}$: The model predicts suppression ($R_{AB} < 1$) for $Ne+Ne$ and $O+O$, consistent with recent data. For $p+Pb$, the model predicts $R_{AB} \lesssim 1$, agreeing with ALICE but disagreeing with ATLAS/CMS data which show $R_{AB} \ge 1$.
  • $v_2^{hard}$: The intrinsic anisotropy of the hard partons is small but non-zero ($\sim 0.005$) due to the anisotropy of the initial temperature profiles.
  • $v_2\{SP\}$ (The Critical Finding): Despite non-zero $v_2^{hard}$, the model predicts $v_2\{SP\} \approx 0$ for all small systems.
    • Mechanism: In large systems (Pb+Pb), the hard and soft participant planes are strongly correlated ($\psi_{hard} \approx \psi_{soft}$). In small systems, these planes become decorrelated (uniform distribution of the angle difference) or even anti-correlated (in $p+Pb$).
    • Consequence: Because the experimental $v_2\{SP\}$ relies on the correlation between hard and soft planes (Eq. 6), the decorrelation causes the cosine term to average to zero, resulting in a vanishing observable $v_2$.
• Robustness: Varying the strong coupling $\alpha_s$ and the energy loss model parameters changes the magnitude of $v_2^{hard}$ but does not restore the correlation between $\psi_{hard}$ and $\psi_{soft}$. Thus, the prediction of $v_2\{SP\} \approx 0$ holds across different energy loss scenarios.

5. Significance and Implications

• Challenge to Energy Loss Interpretation: The paper argues that if the experimental high-$p_T$ $v_2$ in $p+Pb$ is indeed caused by final-state energy loss, current models are insufficient. However, since the models robustly predict $v_2\{SP\} \approx 0$, the large $v_2$ observed experimentally likely stems from non-energy-loss mechanisms.
• Alternative Origins: The authors suggest that the observed anisotropy in small asymmetric systems may arise from:
  • Initial state correlations (geometry vs. initial parton direction).
  • Sub-eikonal corrections (though likely too small).
  • Pre-thermalization energy loss (though unlikely to flip the sign of the correlation).
• Future Experimental Directions:
  • Hard-Hard Correlations: Measuring $v_2$ using two high-$p_T$ particles (removing the soft sector) could reveal the intrinsic $v_2^{hard}$.
  • Symmetric Small Systems: Measuring $v_2$ in $Ne+Ne$ and $O+O$ is crucial. If these symmetric systems show $v_2 \approx 0$, it would confirm that the large $v_2$ in $p+Pb$ is a unique feature of asymmetric collisions (likely initial state or experimental artifacts). If they show large $v_2$, the origin is likely universal to small systems.
  • Electroweak Bosons: Measuring $v_2$ for electroweak bosons (unaffected by final state energy loss) would provide a baseline.

Conclusion: The paper concludes that standard energy loss models, when applied with realistic event-by-event hydrodynamics, predict no observable high-$p_T$ $v_2$ in small systems due to the geometric decorrelation of hard and soft participant planes. This suggests that the large $v_2$ measured in $p+Pb$ experiments is not a signature of QGP formation via energy loss, but rather a result of other physical or experimental effects specific to asymmetric small systems.