Relative transverse activity as a probe of collectivity-like long-range correlations in pp collisions at $\sqrt{s}=13$ TeV

Using PYTHIA 8 simulations of 13 TeV proton-proton collisions, this study demonstrates that enhanced underlying-event activity, driven by multiple partonic interactions and color reconnection, can generate collectivity-like long-range correlations in the highest relative transverse activity events without requiring hydrodynamic evolution, thereby establishing $R_{\mathrm{T}}$ as a crucial differential classifier for interpreting small-system signatures at the LHC.

The Gist

Imagine you are at a massive, chaotic concert. Usually, when people talk about "collective behavior" in physics, they imagine a giant, fluid crowd moving in perfect unison, like a wave in a stadium. This happens in huge collisions (like smashing two heavy atomic nuclei together), where scientists believe a super-hot, liquid-like soup of particles (called Quark-Gluon Plasma) forms and flows together.

But here's the mystery: Scientists have started seeing similar "wave-like" patterns even in tiny collisions, like smashing two single protons (the size of a grain of sand) together. The big question is: Is this tiny collision actually forming a tiny drop of liquid, or is it just a coincidence caused by something else?

This paper acts like a detective story trying to solve that mystery using a computer simulation called PYTHIA 8.

The Detective's Tool: The "Relative Transverse Activity" (RT)

To solve the case, the researchers needed a way to sort the chaotic concert into different groups. They invented a sorting tool called Relative Transverse Activity ($R_T$).

Think of a proton collision as a firework display.

• The "Hard" Part: Sometimes, two fireworks explode right in the center, sending out bright, fast sparks (jets). This is the "hard scattering."
• The "Soft" Part: Surrounding that explosion is a cloud of smoke, sparks, and debris drifting everywhere. This is the "Underlying Event" (UE).

The researchers used $R_T$ to measure how much of that "smoke and debris" (the soft activity) is present in a specific event, relative to the main explosion.

• Low $R_T$: A clean event with mostly the main explosion and very little background smoke.
• High $R_T$: A messy event where the background smoke is thick and chaotic.

The Investigation: Looking for "Ridges"

The scientists looked at how particles pair up and move together. They were looking for a specific pattern called a "ridge."

• The Ridge: Imagine looking at the concert from above. If you see a long, continuous line of people standing shoulder-to-shoulder stretching far across the venue, that's a ridge. In physics, this "long-range" connection is usually a sign of a fluid flowing together (collectivity).

They tested two types of particle pairs:

1. Charge-Independent (CI): Looking at any two particles, regardless of whether they are positive or negative (like looking at any two people in the crowd).
2. Charge-Dependent (CD): Looking specifically at pairs that balance each other out (like a positive and a negative charge, or a person and their twin).

The Findings: The "Smoking Gun"

Here is what they discovered, which changes how we interpret the data:

1. The "Liquid" Lookalike appears only in the messiest events.
When they looked at the Charge-Independent pairs (any two particles) in the High $R_T$ events (the ones with the thickest background smoke), they found a clear "ridge." It looked exactly like the collective flow seen in giant liquid drops.

2. But the "Liquid" is a fake.
Here is the twist: This ridge only appeared in the Charge-Independent data. When they looked at the Charge-Dependent pairs (the balancing pairs), no ridge appeared, even in the messiest events.

3. The Real Culprit: "Color Reconnection."
Since the ridge didn't show up in the balancing pairs, it couldn't be caused by local conservation laws (like a positive charge needing a nearby negative charge). Instead, the paper concludes that this "collective-like" behavior is actually caused by Multiple Partonic Interactions (MPI) and Color Reconnection (CR).

The Analogy:
Imagine a crowded room where everyone is trying to talk to their specific partner (Charge-Dependent). They stay close together.
Now, imagine a different scenario where the room is so full of noise and people bumping into each other (High $R_T$) that everyone's path gets twisted. Even though they aren't holding hands, the chaos of the crowd forces everyone to drift in the same general direction. They look like they are moving together in a wave, but they aren't actually a fluid; they are just being pushed around by the crowd's chaos.

In the paper's language, "Color Reconnection" is like the invisible strings of the universe getting tangled up in the chaos, forcing particles to align without them actually forming a liquid drop.

The Conclusion

The paper claims that you do not need a liquid drop (hydrodynamics) to create these "collective" patterns.

By using the $R_T$ classifier, they showed that in proton-proton collisions, the "ridge" is just a side effect of the messy, soft background activity (the underlying event) getting so intense that it organizes the particles through standard quantum rules (QCD), not through fluid dynamics.

In short: The paper provides a "non-hydrodynamic baseline." It tells us that if we see a "ridge" in small collisions, we shouldn't immediately assume we found a tiny liquid drop. It might just be the universe's version of a chaotic crowd pushing everyone in the same direction.

Technical Summary

Technical Summary: Relative Transverse Activity as a Probe of Collectivity-like Long-Range Correlations in pp Collisions at $\sqrt{s} = 13$ TeV

Problem Statement
A central open question in high-energy nuclear physics is the origin of collectivity-like signatures, specifically long-range, ridge-like correlations, observed in small collision systems such as high-multiplicity proton-proton (pp) and proton-lead (p–Pb) collisions. While such structures are well-described by relativistic hydrodynamics in large systems (e.g., Pb–Pb), their presence in small systems has sparked debate. Competing explanations include the emergence of collective dynamics in limited spatial extents versus QCD-driven mechanisms, such as multiple partonic interactions (MPI), color reconnection (CR), and gluon saturation, which can mimic hydrodynamic flow without requiring a hydrodynamic medium. To resolve this, precision observables sensitive to particle production dynamics across different event-activity regimes are required to establish a non-hydrodynamic baseline.

Methodology
This work presents a simulation study using PYTHIA 8 (Monash 2013 tune) to investigate two-particle correlation functions in pp collisions at $\sqrt{s} = 13$ TeV. The analysis focuses on final-state charged hadrons within the kinematic acceptance $|\eta| < 0.8$ and $0.2 < p_T < 2.0$ GeV/c.

The core methodological innovation is the classification of events based on Relative Transverse Activity ($R_T$). $R_T$ is defined as the ratio of the charged-particle multiplicity in the transverse region ($60^\circ < |\Delta\phi| < 120^\circ$ relative to the leading particle) to the inclusive average multiplicity in that region. By selecting events with a leading particle in the range $5 \le p_T^{\text{lead}} \le 40$ GeV/c, the study isolates the "transverse plateau" regime where the underlying event (UE) is well-defined and independent of the hard scattering scale.

Events are categorized into four $R_T$ classes:

1. $0 \le R_T \le 0.5$ (Jet-dominated)
2. $0.5 < R_T \le 1.5$
3. $1.5 < R_T \le 2.5$
4. $2.5 < R_T \le 5.0$ (UE-dominated)

The study analyzes two correlation functions:

• $R_2(\Delta\eta, \Delta\phi)$: The two-particle number correlation function, sensitive to multiplicity fluctuations.
• $P_2(\Delta\eta, \Delta\phi)$: The two-particle transverse-momentum correlation function, sensitive to $p_T$ fluctuations.

These are further decomposed into Charge-Independent (CI) and Charge-Dependent (CD) combinations to distinguish between collective-like effects and local charge conservation dynamics. The Zero-Yield-At-Minimum (ZYAM) procedure is employed to subtract uncorrelated pedestals and isolate near-side excess yields.

Key Results

1. Emergence of Long-Range Structure in CI Correlators: A distinct, finite long-range near-side component (ridge-like structure) is observed in the charge-independent number correlator ($R_2^{CI}$) exclusively for the highest $R_T$ class ($2.5 < R_T \le 5.0$). This structure persists at large pseudorapidity separations ($1.2 \le |\Delta\eta| \le 1.6$) and is confirmed to extend beyond the jet-fragmentation region.
2. Absence in CD Correlators: No corresponding long-range structure appears in the charge-dependent correlators ($R_2^{CD}$ or $P_2^{CD}$) for any $R_T$ class. The CD correlators remain localized near $(\Delta\eta, \Delta\phi) = (0,0)$, consistent with local charge balancing via string fragmentation.
3. Peak Width Evolution:
   • For CI correlators, the near-side peak width in $\Delta\eta$ remains constant across all $R_T$ classes, while the width in $\Delta\phi$ systematically narrows as $R_T$ increases. This narrowing suggests growing azimuthal coherence driven by MPI and CR.
   • For CD correlators, peak widths show only a mild systematic broadening with increasing $R_T$, with no long-range development.
4. $P_2$ vs. $R_2$ Behavior: Across all classes, $P_2$ exhibits systematically narrower near-side peaks than $R_2$. This is attributed to $P_2$'s sensitivity to $p_T$ fluctuations, which suppresses contributions from soft pairs near the mean $p_T$, whereas $R_2$ weights all pairs equally, retaining contributions from soft, isotropic UE particles.

Key Contributions and Significance
The primary contribution of this work is establishing $R_T$ as a differential event classifier capable of isolating collectivity-like long-range correlations in small systems without invoking hydrodynamic evolution.

• Non-Hydrodynamic Baseline: The findings demonstrate that enhanced UE activity, driven by multiple partonic interactions and color reconnection within the PYTHIA 8 framework, is sufficient to generate ridge-like, long-range azimuthal correlations. This provides a crucial non-hydrodynamic baseline for interpreting experimental data from the LHC.
• Disentangling Mechanisms: The contrasting behavior between CI and CD correlators serves as a diagnostic tool. The presence of a long-range ridge only in CI (and not CD) indicates that the observed structures in small systems arise from charge-independent QCD dynamics rather than local conservation laws or hydrodynamic flow.
• Role of Underlying Event: The study clarifies that the underlying event is not merely a background to be subtracted but an active driver of correlation structures. Specifically, the interplay of MPI and CR at high $R_T$ generates azimuthal coherence that mimics collective expansion.

In conclusion, this paper argues that collectivity-like signatures in small collision systems can emerge from microscopic QCD dynamics (MPI and CR) alone, challenging the necessity of hydrodynamic interpretations for such observations in pp collisions.