Dependence of two-particle azimuthal correlations on the forward rapidity gap width in pPb collisions at $\sqrt{s_\mathrm{NN}}$ = 8.16 TeV

This paper investigates the dependence of two-particle azimuthal correlations on the forward rapidity gap width in 8.16 TeV pPb collisions to determine if collective flow signatures persist in events enriched with photon-lead and pomeron-lead interactions, comparing the results against previous measurements and modern event generators.

The Gist

The Great Particle Dance: A Study of Tiny Collisions with a "Quiet" Side

Imagine you are at a massive, chaotic concert where thousands of people are dancing. Usually, when you look at the crowd, everyone is moving randomly. But in high-energy physics, scientists have discovered something surprising: sometimes, even in very small groups of particles, they start dancing in a coordinated, fluid-like pattern, as if they were part of a single, giant liquid drop. This coordinated movement is called collective flow.

For years, scientists saw this "dance" in huge collisions (like smashing two heavy lead nuclei together). But recently, they started seeing it in tiny collisions, like a proton hitting a lead atom. This was a mystery: How can such a small system act like a fluid?

This paper by the CMS Collaboration at CERN tries to solve a piece of that puzzle by looking at a specific type of proton-lead collision where one side of the room is completely empty.

The Setup: The "Silent" Proton

In a normal collision, the proton and the lead nucleus smash together, and debris flies out in all directions. But the researchers decided to look only at the "rare" collisions where the proton behaves very politely.

They selected events where the proton went one way, but nothing came out of the proton's side of the detector. It was as if the proton whispered to the lead nucleus, "I'm just passing through," without actually crashing into it hard enough to create a mess on its side.

In physics terms, they looked for a "forward rapidity gap." Think of this as a wide, empty hallway in a crowded building. If you see a wide empty space where no one is walking, you know something special happened. In these collisions, the lead nucleus breaks apart (creating a party of particles), but the proton stays intact or breaks into something so small and light it escapes detection.

This setup creates a sample rich in two specific types of interactions:

1. Pomeron Exchange: Imagine the proton sending a "ghostly messenger" (called a pomeron) to the lead nucleus. The messenger hits the lead, causing it to break up, but the proton itself remains untouched.
2. Photon-Induced: The proton acts like a flashlight, shining a beam of light (a photon) onto the lead nucleus, causing it to react without a direct crash.

The Experiment: Measuring the "Ridge"

The scientists wanted to know: Does this "quiet" collision still produce the coordinated dance (collective flow)?

To find out, they measured how the particles from the broken-up lead nucleus were moving relative to each other. They looked for a specific pattern called the "ridge."

• The Analogy: Imagine throwing a handful of confetti into the air. If the wind is random, the confetti lands in a messy pile. If there is a strong, organized wind (the "flow"), the confetti lands in a long, thin streak.
• In particle physics, if the particles form a long streak even when they are far apart in space (but close in angle), it suggests they are moving together like a fluid.

They varied the size of the "empty hallway" (the rapidity gap). They asked: If the empty space is bigger (meaning the proton was even more "gentle" and didn't interact much), does the dance pattern change?

The Findings: A Subtle, Not-So-Fluid Dance

Here is what they found, translated from complex math to plain English:

1. The Dance is Weak: In these "gentle" collisions where the proton stays quiet, the evidence for the coordinated "fluid" dance is very weak. The particles don't seem to be moving in a strong, organized pattern like they do in the big, messy collisions.
2. The "Gap" Matters: As the empty hallway (the rapidity gap) got wider, the signal for this coordinated flow actually got weaker or disappeared.
3. Comparison to Models: They compared their results to computer simulations.
   • One model (EPOS-LHC) assumes the particles act like a fluid. It predicted a stronger dance than what they saw.
   • Another model (PYTHIA) assumes the particles are just bouncing off each other like billiard balls (no fluid). This model was closer to the data, though not perfect.

The Bottom Line

The paper concludes that when you isolate collisions where the proton barely interacts (creating a large empty gap), the "collective flow" or fluid-like behavior largely vanishes.

Why does this matter?
It helps scientists decide between two competing theories about how these tiny systems work:

• Theory A: The particles form a tiny drop of liquid (Quark-Gluon Plasma) that flows.
• Theory B: The patterns we see are just the result of initial conditions (how the particles were arranged before they hit) and don't require a fluid state.

By showing that the "dance" disappears when the collision is very "exclusive" (quiet on one side), this paper suggests that the fluid-like behavior seen in other small collisions might depend heavily on the specific way the particles interact. It puts a constraint on models that claim this fluid behavior happens universally, regardless of how the collision happens.

In short: If you want to see the "fluid dance" in these tiny collisions, you need a bit more chaos. When the proton stays too polite and the collision is too quiet, the dance stops.

Technical Summary

Technical Summary: Dependence of two-particle azimuthal correlations on the forward rapidity gap width in pPb collisions at $\sqrt{s_{NN}} = 8.16$ TeV

Problem Statement
Relativistic heavy ion collisions are characterized by collective flow, described by Fourier coefficients ($v_n$) of azimuthal angular distributions, often attributed to the formation of a quark-gluon plasma (QGP). However, similar non-zero Fourier coefficients have been observed in small systems, including proton-proton (pp), proton-lead (pPb), and photon-proton ($\gamma$p) collisions. The microscopic origin of these correlations in small systems remains debated, with competing explanations involving hydrodynamic expansion (collective final-state response) versus initial-state correlations (e.g., gluon saturation). To distinguish between these scenarios, it is necessary to study systems where multiparton interactions and color reconnection are suppressed. This paper addresses the need to characterize azimuthal correlations in pPb collisions enriched with semi-exclusive topologies, specifically those mediated by color-singlet exchange (pomeron) or photo-induced processes, by varying the forward rapidity gap width ($\Delta\eta_F$).

Methodology
The analysis utilizes pPb collision data recorded by the CMS experiment at the LHC with an integrated luminosity of 174.5 nb$^{-1}$ at $\sqrt{s_{NN}} = 8.16$ TeV. The study focuses on events selected to enhance semi-exclusive topologies where the proton remains intact or dissociates into a low-mass state, while the lead nucleus breaks up.

• Event Selection: Events are selected based on the presence of a "forward rapidity gap," defined as a region in the proton-going direction (starting at $\eta = 3$) with no detected particles. The gap width, $\Delta\eta_F$, is varied from 0.5 to values greater than 2.5. The selection requires activity in the hadronic forward (HF) calorimeter on the lead-going side and no activity above specific thresholds on the proton-going side.
• Sample Composition: The selected sample contains a mixture of single-diffractive (IPpPb), photon-lead ($\gamma$Pb), and nondiffractive interactions. For $\Delta\eta_F > 2.5$, the sample is "diffraction-enhanced," with Monte Carlo (MC) simulations (EPOS-LHC) suggesting a dominant diffractive component (43.5%) and a small nondiffractive contribution (5%).
• Correlation Measurement: Two-particle azimuthal correlations are measured for charged particles within $|\eta| < 2.4$ and $0.3 < p_T < 3$ GeV. The analysis employs a mixed-event technique to construct the background distribution, correcting for tracking inefficiencies.
• Fourier Decomposition: Long-range correlations ($|\Delta\eta| > 2$) are extracted to suppress short-range jet fragmentation effects. The resulting $\Delta\phi$ distributions are fitted with a Fourier series to extract the coefficients $V_{n\Delta}$ (specifically $V_{1\Delta}$ and $V_{2\Delta}$). The elliptic flow coefficient $v_2$ is derived as $\sqrt{V_{2\Delta}}$.
• Comparisons: Results are compared against inclusive pPb data, $\gamma$p data, and predictions from event generators: PYTHIA 8.3.10 (based on the ANGANTYR model, lacking collective effects) and EPOS-LHC (which includes collective effects).

Key Contributions

• First Measurement of $\Delta\eta_F$ Dependence: This work presents the first search for long-range azimuthal correlations as a function of the forward rapidity gap width in pPb collisions.
• Diffraction-Enhanced Sample Analysis: The paper provides detailed measurements for a sample enriched in diffractive and $\gamma$Pb events, offering a complementary view to inclusive small-system measurements.
• Systematic Constraints: The analysis provides constraints on models by comparing data against generators with and without collective flow, specifically in a regime where initial-state correlations might dominate if collective flow is absent.

Results

• $V_{1\Delta}$ and $V_{2\Delta}$ Trends: The measured $V_{1\Delta}$ coefficients are negative and decrease (become more negative) as $\Delta\eta_F$ increases. The central values of $V_{2\Delta}$ increase monotonically with $\Delta\eta_F$, though they remain consistent with zero within uncertainties in two bins.
• Multiplicity Dependence: For the diffraction-enhanced sample ($\Delta\eta_F > 2.5$), measurements are presented as a function of charged particle multiplicity ($N_{ch}$). The measured $V_{1\Delta}$ values are consistently lower than inclusive pPb results but qualitatively agree with $\gamma$p data. The $V_{2\Delta}$ values agree with both pPb and $\gamma$p results within similar multiplicity ranges.
• Model Comparisons:
  • PYTHIA 8.3.10: Predictions for $V_{1\Delta}$ are generally higher than the data. For $V_{2\Delta}$, predictions are consistent with data in most bins but overestimate results in the lowest $\Delta\eta_F$ bin.
  • EPOS-LHC: Predictions for $V_{1\Delta}$ are consistent with data except in specific $\Delta\eta_F$ bins where they are higher. For $V_{2\Delta}$, the model is consistent with data bin-by-bin, except for the lowest $\Delta\eta_F$ bin where it overestimates the data.
• Elliptic Flow ($v_2$): For $\Delta\eta_F$ bins $[0.5, 1)$, $[1, 1.5)$, and $[2, 2.5)$, non-zero $v_2$ values are measured (e.g., $0.0617 \pm 0.0099$ for $0.5 \le \Delta\eta_F < 1.0$). In other bins, the data are consistent with zero, and 95% confidence level (CL) upper limits are derived. These limits are stable across $\Delta\eta_F$ and multiplicity bins, reaching up to 0.13 for the most inclusive bin. These limits are comparable to those observed in $\gamma$p interactions.

Significance
The paper claims that these results constrain scenarios where ridge-like correlations are expected to persist universally across small systems regardless of event topology. By demonstrating that the correlation strength varies with the forward rapidity gap width—a proxy for the degree of exclusivity and suppression of multiparton interactions—the study provides a reference for models predicting a reduced collective response when such interactions are suppressed. The results support the investigation of whether the observed collectivity in small systems is a universal hydrodynamic phenomenon or dependent on specific initial-state conditions. The paper does not claim to definitively resolve the origin of collectivity but rather provides necessary data to test theoretical models (such as Ingelman-Schlein based approaches) in a regime complementary to inclusive measurements.