Exploring differential two-particle correlations in $γp$ and low-multiplicity pp collisions using PYTHIA8

This study utilizes PYTHIA8 to investigate two-particle differential balance functions in $\gamma p$ and low-multiplicity $pp$ collisions at $\sqrt{s}=5.36$ TeV, revealing a systematic difference where the charge-dependent correlation width is narrower in $\gamma p$ events compared to $pp$ collisions, thereby offering insights into particle production mechanisms in small systems.

The Gist

Imagine you are at a massive, chaotic concert. You want to understand how the crowd behaves. Do people move in large, coordinated waves (like a fluid)? Or do they just bump into each other randomly?

In the world of particle physics, scientists do the same thing, but instead of a concert, they smash tiny particles together at near light speed. For decades, they've smashed heavy atoms (like gold or lead) to create a super-hot, super-dense soup of particles called the Quark-Gluon Plasma (QGP). In this soup, particles behave like a perfect fluid, flowing together in a coordinated dance.

But recently, scientists noticed something weird. Even when they smash small things together—like a single proton hitting another proton, or even a photon (a particle of light) hitting a proton—they see hints of that same "fluid-like" coordination. It's like seeing a synchronized dance routine in a small, crowded elevator. This is puzzling because small collisions shouldn't have enough "stuff" to create a fluid.

This paper is a simulation study (using a super-computer program called PYTHIA8) that tries to figure out why this happens. The authors, Subash Chandra Behera and Dukhishyam Mallick, decided to look at the smallest possible collisions: Photon-Proton ($\gamma p$) collisions, and compare them to standard Proton-Proton ($pp$) collisions.

Here is the breakdown of their investigation using simple analogies:

1. The "Balance Function": The Charge Detective

In these collisions, nature has a strict rule: Charge Conservation. If a positive particle is created, a negative partner must be created nearby to balance the books.

• The Analogy: Imagine a party where every time a guest arrives wearing a Red Hat (positive charge), they immediately bring a friend wearing a Blue Hat (negative charge).
• The Question: How close are these Red/Blue pairs standing to each other?
  • If they are standing right next to each other, it means they were created together in a very local, immediate event (like a quick handshake).
  • If they are far apart in the room, it means they were created early in the event and then drifted apart as the party got chaotic.

Scientists measure this "closeness" using something called a Balance Function. The narrower the peak of this function, the closer the pairs are.

2. The Two Types of Collisions

The researchers simulated two types of "parties":

• Proton-Proton ($pp$) Collisions: This is like a bustling, crowded festival. There are many interactions happening at once. People (particles) are bumping into each other, forming groups, and creating complex patterns. It's messy and full of "Multiple Parton Interactions" (MPI)—basically, many small fights happening at the same time.
• Photon-Proton ($\gamma p$) Collisions: This is like a quiet, intimate gathering. A photon is just a packet of light. When it hits a proton, it's a much cleaner, simpler interaction. There are fewer "background noises" (MPI). It's mostly just one or two main interactions happening.

3. The Big Discovery: "The Narrowing Effect"

The scientists looked at how the "Red Hat/Blue Hat" pairs behaved as they increased the number of people at the party (multiplicity).

• The Trend: In both the crowded festival ($pp$) and the quiet gathering ($\gamma p$), as the number of people increased, the Red and Blue hats ended up standing closer together.
• The Surprise: The pairs in the Photon-Proton ($\gamma p$) collisions stood significantly closer together than in the Proton-Proton collisions, even when the number of people was the same.

Why is this important?
Usually, if you see pairs standing very close together in heavy-ion collisions, scientists say, "Aha! This means the fluid formed, and the particles were created late in the game, so they didn't have time to drift apart."

But in these tiny $\gamma p$ collisions, there is no fluid. There is no "soup." So, why are the pairs so close?

4. The Explanation: The "Single String" Theory

The paper suggests that in the clean, quiet $\gamma p$ collisions, the particles are created via a single, short "string" of energy.

• The Analogy: Imagine a single, tight rubber band. If you snap it, the two pieces fly apart, but they are still very close to the center.
• In the messy $pp$ collisions, it's like having a tangled mess of rubber bands everywhere. The pieces fly off in all directions, spreading out more.

Because the $\gamma p$ collision is so simple (dominated by one main interaction and no messy background noise), the "charge balancing" partners are born in a very tight, localized spot. They don't have the chaos of the "festival" to push them apart.

5. What This Means for the Future

This study is a reality check. It tells us that we don't need a giant "Quark-Gluon Plasma" soup to see particles standing close together. Sometimes, it's just because the collision was simple and clean to begin with.

• The Takeaway: When we see "fluid-like" behavior in small collisions, we have to be careful. It might not be a new state of matter; it might just be the natural result of how simple collisions work.
• The Future: The authors say we need to go to the actual experiments (like at the Large Hadron Collider) and measure these $\gamma p$ collisions for real. If the real data matches their simulation, it will help us understand exactly what is "fluid" and what is just "simple physics" in the tiny world of subatomic particles.

Summary

Think of this paper as a detective story. The detectives (physicists) noticed that even in small, simple crimes (collisions), the suspects (particles) were sticking together too well. They used a computer simulation to realize that in the simplest crimes, the suspects are born in a tiny room and stay there. In the complex crimes, they get pushed around by the crowd. This helps us understand that "sticking together" doesn't always mean "we are a fluid"; sometimes, it just means "we started very close to each other."

Technical Summary

1. Problem Statement and Motivation

The formation of the Quark-Gluon Plasma (QGP) in ultra-relativistic heavy-ion collisions is well-established through observations of collective flow and charge balance functions. A key signature of the QGP is the narrowing of the charge balance function width, interpreted as delayed hadronization where balancing charges are produced later in the system's evolution, keeping them closer in phase space.

However, recent observations in small collision systems (small $pp$, $p$-Pb) have shown similar "ridge-like" structures and narrowing of correlation widths. This challenges the conventional interpretation, as these small systems were not expected to form a QGP. The mechanism behind this narrowing in small systems remains debated, with potential contributors including local charge conservation (LCC), string dynamics, multiple parton interactions (MPI), and color reconnection.

The Core Problem: It is difficult to disentangle genuine charge conservation effects from medium-induced phenomena or complex hadronic interactions in standard $pp$ collisions. The authors propose using photon-proton ($\gamma p$) collisions as a cleaner baseline. In $\gamma p$ collisions, electromagnetic processes dominate, MPI is suppressed, and the underlying hadronic activity is minimal, offering an ideal environment to study particle production mechanisms without the "noise" of a dense hadronic environment.

2. Methodology

The study utilizes PYTHIA8 (version 8.36) event generator simulations to compare $\gamma p$ and proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 5.36$ TeV.

• Simulation Configurations:
  • $\gamma p$ Collisions: Modeled using the Equivalent Photon Approximation (EPA). Two configurations were tested:
    1. Realistic $\gamma p$: Hard QCD processes and MPI disabled (PartonLevel:MPI = off), focusing on single-string fragmentation.
    2. mb-like $\gamma p$: Configured similarly to minimum-bias $pp$ (MPI and color reconnection enabled) to isolate the effect of the collision system vs. the underlying physics tune.
  • $pp$ Collisions: Simulated with a standard minimum-bias (MB) tune (Monash tune) for comparison.
• Kinematic Selection:
  • Charged hadrons within pseudorapidity $|\eta| < 2.4$ and transverse momentum $0.3 < p_T < 3.0$ GeV.
  • Analysis performed across various charged-particle multiplicity ($N_{ch}$) intervals, specifically focusing on low ($0 < N_{ch} < 5$) and high ($40 < N_{ch} < 50$) ranges.
• Observables:
  • Two-particle Correlation Functions: Constructed using "trigger" and "associated" tracks.
  • Balance Functions:
    • Number Balance Function ($B$): Quantifies charge correlations in $(\Delta\eta, \Delta\phi)$.
    • Transverse Momentum Balance Function ($P_2^{CD}$): Quantifies momentum correlations, sensitive to $p_T$ fluctuations.
  • Components: The study extracts Charge-Dependent (CD) components (isolating balancing charges by subtracting like-sign pairs from unlike-sign pairs) and Charge-Independent (CI) components.
  • Width Extraction: The strength of correlations is quantified by the Root-Mean-Square (RMS) width ($\sigma$) of the 1D projections of $B$ and $P_2^{CD}$ onto $\Delta\eta$ and $\Delta\phi$.

3. Key Contributions

• Systematic Comparison: Provides the first detailed PYTHIA8-based comparison of differential two-particle correlations between $\gamma p$ and $pp$ collisions in the low-multiplicity regime.
• Disentangling Mechanisms: By comparing "realistic" $\gamma p$ (no MPI) with "mb-like" $\gamma p$ and $pp$, the study isolates the specific contributions of MPI and underlying event activity versus the intrinsic nature of the collision system.
• Dual Observable Analysis: Simultaneously analyzes number balance ($B$) and momentum balance ($P_2^{CD}$), revealing complementary sensitivities to particle production topology (string fragmentation vs. jet fragmentation).

4. Key Results

A. Multiplicity and Kinematics

• Multiplicity Distribution: $\gamma p$ collisions exhibit significantly lower $N_{ch}$ and a rapidly falling distribution compared to $pp$, reflecting the suppression of MPI.
• Average $p_T$: $\langle p_T \rangle$ increases monotonically with $N_{ch}$ in both systems. However, in realistic $\gamma p$ collisions, $\langle p_T \rangle$ is higher than in $pp$ at the same multiplicity, suggesting a stronger sensitivity to the underlying physics processes (e.g., string tension) than the system size itself.

B. Correlation Structures ($B$ and $P_2^{CD}$)

• Near-Side Peak:
  • In $pp$, the near-side peak grows with multiplicity, while the away-side peak (back-to-back dijets) diminishes.
  • In realistic $\gamma p$, the near-side peak is significantly stronger and narrower than in $pp$ at similar multiplicities. The away-side peak is almost entirely absent at low multiplicity due to the lack of hard dijet production.
  • The amplitude of the near-side peak in $\gamma p$ increases dramatically (from ~0.04 to ~0.4) as $N_{ch}$ rises, driven by strong local charge ordering on a single short string.
• Momentum Correlations ($P_2^{CD}$):
  • $P_2^{CD}$ shows a distinct enhancement in $\gamma p$ at low multiplicity compared to $pp$, indicating tighter momentum correlations for balancing charges in the single-string topology.
  • Unlike $B$, the amplitude of $P_2^{CD}$ generally decreases with increasing $N_{ch}$ due to the dilution of jet-dominated processes.

C. Width Analysis (The Core Finding)

• Multiplicity Dependence: Both $B$ and $P_2^{CD}$ widths ($\sigma_{\Delta\eta}$ and $\sigma_{\Delta\phi}$) decrease (narrow) as multiplicity increases in both $pp$ and $\gamma p$. This confirms a universal multiplicity-driven narrowing trend.
• System Dependence: Crucially, the widths are systematically lower in $\gamma p$ collisions than in $pp$ collisions across all multiplicity classes.
  • This indicates that in $\gamma p$, balancing charges are produced in a more localized phase space, consistent with the "single string" fragmentation model where charge partners are created close together.
  • In contrast, $pp$ collisions involve multiple strings and MPI, leading to a broader distribution of balancing charges.

5. Significance and Conclusion

• Baseline for Small Systems: The study establishes $\gamma p$ collisions as a robust baseline for understanding particle correlations in small systems. The observed narrowing in $\gamma p$ (without a QGP) suggests that local charge conservation on short strings and string dynamics are sufficient to explain the narrowing of balance functions, challenging the necessity of invoking a QGP-like medium for this effect in small systems.
• Role of MPI: The comparison between mb-like and realistic $\gamma p$ confirms that the suppression of MPI and hard scattering in $\gamma p$ leads to a cleaner, more localized correlation structure.
• Future Outlook: The authors argue that future experimental measurements of photon-induced collisions ($\gamma p$, $\gamma$Pb, $\gamma$O) at the LHC are critical. These measurements will allow physicists to separate bulk-dominated near-side correlations from jet-driven away-side correlations, providing a definitive test of the mechanisms driving the "ridge" and balance function narrowing in small collision systems.

In summary, the paper demonstrates that the narrowing of charge balance functions is a generic feature of increasing event activity driven by local charge conservation and string dynamics, which is even more pronounced in the cleaner environment of photon-induced collisions.