⚛️ phenomenology

Finite $V_{\rm 2\Delta}$ puzzle in low-multiplicity pp collisions from ultra-long-range azimuthal correlations in the string-shoving model

This study utilizes the PYTHIA8 string-shoving model to demonstrate that ultra-long-range azimuthal correlations in low-multiplicity pp collisions are most sensitive to dijet events ( $N_{\rm mpi}=1$ ) and decrease with multiplicity, suggesting that string shoving explains low-multiplicity data while hydrodynamics dominates at higher multiplicities, with flattenicity proposed as a superior estimator for mitigating non-flow effects.

Original authors: Antonio Ortiz, Dushmanta Sahu, Gyula Bencedi

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Antonio Ortiz, Dushmanta Sahu, Gyula Bencedi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine two tiny, high-speed particles smashing into each other. Usually, we think of these collisions as chaotic explosions where debris flies off in random directions. But in recent years, physicists have noticed something strange: sometimes, the debris doesn't fly randomly. Instead, it seems to "flow" together, moving in coordinated patterns, almost like a fluid. This is usually seen in massive collisions (like smashing two big gold nuclei together), but scientists are now seeing hints of this "fluid-like" behavior even in tiny proton-proton collisions.

This paper investigates why this happens in the smallest collisions, using a computer simulation called PYTHIA8.

Here is the breakdown of their findings using simple analogies:

1. The Two Competing Theories

Scientists have been arguing about what causes this "flow" in tiny collisions.

Theory A (The Fluid): Maybe a tiny drop of super-hot "soup" (Quark-Gluon Plasma) forms and expands like a balloon.
Theory B (The Push): Maybe it's just the strings of energy connecting the particles pushing against each other, like people shoving in a crowded hallway, without forming a soup at all.

The authors tested Theory B (called the String Shoving model) to see if it could explain the data.

2. The Problem with the "Crowd Count" (Nch)

To study these collisions, scientists usually group them by how many particles come out. They call this the "multiplicity" (or Nch).

The Analogy: Imagine you are trying to study how well people cooperate in a room. You decide to group people by how many total items they are holding.
The Flaw: If one person is holding a giant, heavy box (a high-energy jet), they will have a high "item count," but they aren't part of a cooperative crowd. If you group them with people who are actually holding hands and moving together, your data gets messy. The paper argues that counting particles (Nch) is a bad way to sort these events because it mixes up "cooperative crowds" with "lone wolves carrying heavy boxes."

3. The New Way to Sort: "Flatness" and "Number of Pushes"

The authors tried two better ways to sort the collisions:

Nmpi (Number of Pushes): Counting how many times the particles actually bumped into each other.
Flattenicity (Flatness): A measure of how evenly the debris is spread out. If the debris is spread like a smooth pancake, it's "flat." If it's clumped in one spot (like a jet), it's "bumpy."

4. The Big Surprise: The "Dijet" Effect

The most surprising finding is where the "flow" is strongest.

Expectation: You might think the "fluid" behavior is strongest when there are lots of particles and lots of pushing (a dense crowd).
Reality in the Simulation: The "String Shoving" effect is actually strongest when there are very few interactions (specifically, just one pair of interacting strings, like a simple dijet).
The Analogy: Imagine a few people standing in a circle. If they all push against each other, they create a nice, organized rotation. But if you pack the room with hundreds of people pushing randomly, the pushes cancel each other out, and the organized rotation disappears.
The Result: The simulation showed that as the collision gets "busier" (more particles), the "shoving" effect actually gets weaker and the flow disappears.

5. Why the "Crowd Count" Failed

When the scientists used the traditional method (counting particles, Nch), they saw a confusing result: the flow seemed to drop as the event got busier.

Why? Because the "crowd count" was accidentally picking up events with "lone wolves" (jets) that didn't have the right geometry for the "shoving" to work. It was like trying to measure a dance by counting how many shoes people were wearing; the data got skewed by people wearing extra shoes for no reason.
The Fix: When they used Flattenicity (sorting by how evenly the debris was spread), they got a much clearer picture. It showed that the "shoving" mechanism works best in simple, geometric setups and fails in messy, crowded ones.

6. The Final Conclusion

The paper suggests a "hybrid" picture of reality:

In small, sparse collisions: The "flow" we see might just be String Shoving (particles pushing each other like bumper cars). It's a mechanical effect, not a fluid.
In large, dense collisions: The "flow" is likely a real fluid (hydrodynamics), where a hot soup forms and expands.

In short: The authors found that the "String Shoving" model explains the weird flow in tiny collisions, but only if you stop using the wrong tool (counting particles) to sort the data. Once you use the right tool (measuring how evenly the debris is spread), you see that this "shoving" effect is actually strongest in the simplest collisions and fades away as things get crowded. This suggests that tiny collisions might not be forming a fluid soup at all, but are just particles pushing against each other.

Technical Summary: Finite $v_{2\Delta}$ in Low-Multiplicity $pp$ Collisions from Ultra-Long-Range Azimuthal Correlations in the String-Shoving Model

Problem Statement
Recent ALICE measurements have reported ultra-long-range angular correlations ( $|\Delta\eta| > 5.0$ ) in proton-proton ($pp$) collisions at $\sqrt{s} = 13$ TeV, even at low charged-particle multiplicities ( $dN_{ch}/d\eta < 7$ ). These correlations exhibit a non-zero second-order Fourier coefficient ( $v_{2\Delta}$ ), traditionally interpreted as elliptic flow. However, theoretical models face significant challenges in explaining these observations:

Hydrodynamic models (e.g., 3D-Glauber + MUSIC + UrQMD) severely underestimate $v_{2\Delta}$ at low multiplicities, despite successfully describing high-multiplicity data.
Initial-state models (e.g., Color Glass Condensate) typically generate only short-range correlations that vanish at ultra-long ranges.
Monte Carlo generators like PYTHIA8 with the string shoving mechanism (a non-hydrodynamic model where overlapping color strings exert repulsive transverse pressure) can generate ridge-like structures. However, previous comparisons showed that this mechanism produces a $v_{2\Delta}$ that decreases with increasing multiplicity ( $N_{ch}$ ), contradicting the weakly increasing or flat trend observed in experimental data.

This discrepancy suggests that the choice of event activity estimator (specifically $N_{ch}$ ) may introduce biases that obscure the true behavior of collective-like effects in small systems.

Methodology
The authors conducted a systematic investigation using PYTHIA8 (version 8.312) with the string shoving mechanism enabled.

Event Generation: 10 billion $pp$ collisions were simulated at $\sqrt{s} = 13$ TeV using the Monash tune baseline, modified to include string shoving with a repulsive strength parameter $g=10$ (conservative estimate) and variations up to $g=40$ .
Correlation Analysis: Two-particle correlations were constructed using charged particles in forward ( $2.6 < \eta < 3.2$ ) and backward ( $-3.0 < \eta < -2.0$ ) pseudorapidity intervals, selecting pairs with $5.0 < |\Delta\eta| < 6.0$ .
Non-Flow Subtraction: A template fit method was employed to extract the $v_{2\Delta}$ coefficient. High-multiplicity distributions were fitted as a superposition of a low-multiplicity template (representing non-flow) and a Fourier series representing flow-like modulation. The study validated this implementation by reproducing ALICE's reported PYTHIA8 results.
Event Classifiers: The analysis compared three distinct event activity estimators to assess selection biases:
1. $N_{ch}$ : Traditional mid-rapidity charged-particle multiplicity ( $|\eta| < 0.8$ ).
2. $N_{mpi}$ : The number of multiparton interactions (a direct proxy for initial-state string density).
3. Flattenicity ( $1-\rho_{nch}$ ): A global event-shape observable designed to isolate events dominated by MPIs while minimizing bias from localized hard processes (jets).

Key Results

Multiplicity Dependence and Bias:
- When classified by $N_{ch}$ , the string shoving model reproduces the previously observed trend: $v_{2\Delta}$ decreases as $N_{ch}$ increases, eventually converging with the Monash tune (no shoving) at high multiplicities.
- When classified by $N_{mpi}$ or flattenicity, the behavior changes significantly. The strongest ultra-long-range correlations (and the most distinct near-side ridge structures) appear in the lowest $N_{mpi}$ classes (specifically $N_{mpi} \approx 1-3$ , corresponding to dijet-like events).
- As $N_{mpi}$ increases, the correlation strength diminishes. This indicates that the string shoving mechanism is most effective in sparse, geometrically anisotropic environments (few overlapping strings) and becomes inefficient in dense, isotropic environments.
Template Subtraction Artifacts:
- The study found that low-multiplicity templates derived from the string shoving model already contain significant flow-like correlations. When these templates are used to subtract non-flow from higher multiplicity classes, an over-subtraction occurs, artificially suppressing the extracted $v_{2\Delta}$ values and exacerbating the decreasing trend.
Comparison with Data:
- While the string shoving mechanism explains the existence of correlations in low-multiplicity events, it fails to reproduce the magnitude and trend of ALICE data at higher multiplicities when using $N_{ch}$ as the classifier.
- The hydrodynamic model fails at low multiplicities but shows a rising trend at high multiplicities, suggesting a transition in the dominant physical mechanism.

Key Contributions
The paper makes three primary contributions to the understanding of collectivity in small systems:

Systematic Comparison of Estimators: It provides the first systematic comparison of $N_{ch}$ , $N_{mpi}$ , and flattenicity within the string-shoving framework for ultra-long-range correlations, revealing that $N_{ch}$ introduces a significant bias by conflating jet-dominated events with isotropic, MPI-rich events.
Identification of Saturation: The study identifies a "built-in saturation" in the string shoving mechanism: the effect peaks in low- $N_{mpi}$ (dijet-like) events and diminishes in dense environments, contrary to the expectation that collective effects scale linearly with activity.
Validation of Flattenicity: The analysis demonstrates that flattenicity is a superior estimator for isolating collective-like effects in small systems. It selects event topologies with reduced bias from hard processes, revealing a cleaner correlation structure that better reflects the underlying string density.

Significance and Claims
The authors conclude that the observed finite $v_{2\Delta}$ in low-multiplicity $pp$ collisions can be explained by initial-state effects (string shoving) without invoking a thermalized Quark-Gluon Plasma (QGP). However, the mechanism has limitations:

Low Multiplicity: String shoving dominates, providing a non-hydrodynamic explanation for collectivity in sparse systems.
High Multiplicity: The string shoving mechanism alone cannot explain the data; hydrodynamic expansion becomes increasingly relevant as system size and density grow.

The paper advocates for moving beyond traditional $N_{ch}$ -based analyses in favor of global, topology-sensitive estimators like flattenicity. This shift is necessary to avoid biases that artificially distort the observed trends and to achieve a more physically meaningful interpretation of collective phenomena in small collision systems. The work supports a picture of a gradual onset of collectivity, where initial-state mechanisms dominate in small systems and final-state hydrodynamic expansion takes over in larger, denser environments.