System size and event shape dependence of particle-identified balance functions in proton-proton collisions at $\sqrt{s} = 13$ TeV using PYTHIA 8 and EPOS models

This study utilizes PYTHIA 8 and EPOS-LHC models to demonstrate that particle-identified balance functions in 13 TeV proton-proton collisions exhibit distinct dependencies on event multiplicity and spherocity, revealing that while PYTHIA 8 reflects fragmentation-dominated dynamics, EPOS-LHC captures collective effects like radial flow and diffusion that mimic heavy-ion behavior, thereby offering a powerful tool to disentangle hadronization mechanisms and medium-like collectivity in small collision systems.

The Gist

Imagine you are at a massive, chaotic concert. People are everywhere, bumping into each other, shouting, and moving in waves. Physicists are trying to figure out: Is this crowd moving because of a coordinated dance (a "collective" flow), or are people just bumping into each other randomly because the venue is packed?

This paper is about studying tiny subatomic "concerts" called proton-proton collisions at the Large Hadron Collider (LHC). Specifically, the researchers are looking at how electrically charged particles (like pions, kaons, and protons) behave when they are created.

Here is the breakdown of the study using simple analogies:

1. The Core Concept: The "Balance Function"

In the universe, electric charge is like a strict accounting rule: you can't create a positive charge without creating a matching negative charge. They are born as a pair.

• The Analogy: Imagine a couple holding hands (a positive and a negative charge). When they are created, they are close together. As time passes, they might drift apart.
• The Measurement: The scientists use a tool called a Balance Function to measure how far apart these "couples" end up.
  • Narrow Width: If the couples are still holding hands tightly, the "width" is narrow. This means they were created recently or were pushed together by a strong force.
  • Wide Width: If the couples are far apart, the "width" is wide. This means they had a long time to drift apart, or they were created in a chaotic, uncoordinated way.

2. The Two Competing Theories (The Models)

The researchers used two computer simulations (models) to predict what happens in these collisions, representing two different ideas about how nature works in these tiny spaces.

• PYTHIA 8 (The "Random Bumper Cars" Model):

  • This model assumes particles are created independently, like bumper cars crashing randomly.
  • The Prediction: As the crowd gets bigger (more particles), the couples get closer together. Why? Because in a crowded room, there's less space to drift apart, and the "color strings" (the forces holding them) snap quickly. It's a purely mechanical, local effect.

• EPOS-LHC (The "Mosh Pit with a Wave" Model):

  • This model is more complex. It suggests that in high-energy collisions, a tiny, dense "soup" (similar to the Quark-Gluon Plasma found in giant nucleus collisions) forms.
  • The Prediction: This soup expands like a balloon.
    • Radial Flow: The expansion pushes particles outward in all directions, squeezing the couples closer together sideways (narrowing the balance function in angle).
    • Longitudinal Diffusion: The soup also stretches out lengthwise, pulling the couples further apart forward and backward (widening the balance function in speed/rapidity).

3. The Experiment: Sorting the Crowd

The researchers didn't just look at all collisions; they sorted them into two types using a clever trick called Spherocity:

• Jet-like Events (Low Spherocity): These are like a fireworks display. Most energy shoots out in two opposite directions (like a jet).
• Isotropic Events (High Spherocity): These are like a sprinkler. Energy is spread out evenly in all directions.

They also looked at Multiplicity (how many particles are in the event), ranging from a small gathering to a massive stadium crowd.

4. What They Found

The results were a mix of both models, depending on the particle type and the event shape:

• The "PYTHIA" Behavior: In the "Random Bumper Cars" model, as the crowd got bigger, the couples stayed closer together. This happened for all particle types.
• The "EPOS" Behavior (The Surprise):
  • When the "soup" (hydrodynamic core) was active, the results changed dramatically.
  • Sideways (Azimuthal): The couples were squeezed tighter together. The "expanding balloon" pushed them into the same direction.
  • Lengthwise (Rapidity): The couples were pulled further apart. The "stretching" of the soup separated them.
  • The Twist: This "squeeze sideways, stretch lengthwise" pattern was most visible in Protons (heavy particles) and Kaons (strange particles), but less so in Pions (light particles).

5. The Big Picture Conclusion

The study concludes that small systems (like proton collisions) can behave like big systems (like heavy-ion collisions).

• The "Smoking Gun": The fact that the balance function gets narrower sideways but wider lengthwise in the EPOS model is a signature of collective flow. It's like seeing a wave move through a stadium crowd; the people aren't just bumping randomly; they are moving together as a fluid.
• Why it matters: This helps physicists decide if the "collective behavior" seen in small proton collisions is a new state of matter (a tiny drop of Quark-Gluon Plasma) or just a complex result of random particle interactions. The fact that the "fluid" model (EPOS) explains the data better for certain particles suggests that even in tiny proton collisions, a tiny, fluid-like medium might be forming.

Summary in One Sentence

By tracking how tightly "charged couples" stay together in different types of proton collisions, the researchers found evidence that these tiny collisions might create a tiny, expanding "soup" of matter that behaves like a fluid, rather than just a chaotic mess of random particles.

Technical Summary

Here is a detailed technical summary of the paper "System size and event shape dependence of particle-identified balance functions in proton-proton collisions at $\sqrt{s} = 13$ TeV using PYTHIA 8 and EPOS models."

1. Problem Statement and Motivation

Recent experimental observations at the LHC and RHIC have revealed signs of collective behavior (such as hydrodynamic flow) in small collision systems like proton-proton ($pp$) and proton-nucleus ($p$-A) collisions. This challenges the traditional view that such phenomena are exclusive to large nucleus-nucleus ($A$-$A$) collisions where a Quark-Gluon Plasma (QGP) forms.

The central physics question is whether these collective-like signatures in small systems arise from:

• Macroscopic mechanisms: True medium formation, hydrodynamic expansion, and collective flow.
• Microscopic mechanisms: Purely QCD processes such as string fragmentation, color reconnection (CR), and multi-parton interactions (MPI).

The Charge Balance Function (BF) is a critical observable for distinguishing between these scenarios. The width of the BF encodes information about the timing of charge creation, spatial separation of balancing charges, and collective motion. A narrow BF suggests late-stage hadronization or strong collective flow (radial flow), while a broad BF suggests early creation and significant diffusion.

2. Methodology

The authors utilize Monte Carlo (MC) simulations to investigate balance functions for identified particles ($\pi$, $K$, $p$) in $pp$ collisions at $\sqrt{s} = 13$ TeV.

• Event Generators:
  • PYTHIA 8 (CP5 tune): Represents a baseline scenario dominated by microscopic QCD mechanisms (string fragmentation, MPI, color reconnection) without an explicit hydrodynamic medium.
  • EPOS-LHC: A hybrid model featuring a "core-corona" approach. The "core" undergoes viscous hydrodynamic expansion (collective flow), while the "corona" fragments independently. The study compares EPOS with the hydrodynamic core enabled ("EPOS-LHC") and disabled ("EPOS no core").
• Event Classification:
  • System Size: Selected via charged-particle multiplicity ($N_{ch}$), ranging from low ($0-20$) to high ($80-100$).
  • Event Topology: Selected via Transverse Spherocity ($S_0$). Low $S_0$ corresponds to jet-like events (dominated by hard scatterings), while high $S_0$ corresponds to isotropic events (dominated by soft/collective processes).
• Observable:
  • Balance Function ($B$): Defined as the conditional probability of observing an opposite-charge particle given a reference particle, as a function of relative rapidity ($\Delta y$) and relative azimuthal angle ($\Delta \phi$).
  • Width ($\sigma$): Calculated using the Root-Mean-Square (RMS) method for the 1D projections of $B(\Delta y)$ and $B(\Delta \phi)$.
• Kinematic Range: $0.2 < p_T < 2.0$GeV and$|y| \le 2.4$.

3. Key Contributions

• Particle Identification (PID): The study differentiates dynamics for pions (lightest, most abundant), kaons (strangeness), and protons (baryon number), revealing species-specific transport mechanisms.
• Multidimensional Analysis: It combines system size ($N_{ch}$) and event shape ($S_0$) to disentangle the effects of hard scattering (jets) from soft collective processes.
• Model Comparison: By contrasting PYTHIA 8 (microscopic only) with EPOS-LHC (microscopic + hydrodynamic), the study isolates the specific signatures of collective flow in small systems.

4. Key Results

A. Model Differences in Correlation Structure

• PYTHIA 8: Produces broad, flat balance functions. As multiplicity increases, the width decreases monotonically. This is attributed to enhanced local charge conservation and reduced spatial diffusion in a fragmentation-dominated scenario. Jet-like events (low $S_0$) show narrower widths than isotropic events, but this distinction fades at high multiplicity.
• EPOS-LHC (with Core): Exhibits a distinct "signature of collectivity."
  • $\Delta \phi$ (Azimuth): The balance function becomes narrower in high-multiplicity events compared to the "no-core" scenario. This is caused by radial flow, which collimates balancing partners in the same direction.
  • $\Delta y$ (Rapidity): The balance function becomes broader in high-multiplicity events. This is due to longitudinal diffusion and flow in the hydrodynamic core, which separates balancing charges over a wider rapidity range.
• EPOS-LHC (No Core): Behaves similarly to PYTHIA 8, lacking the narrowing in $\Delta \phi$ and broadening in $\Delta y$ seen in the core scenario.

B. Species Dependence

• Pions ($\pi$): Show the broadest widths due to large yields and resonance decays. They are sensitive to both models but show less dramatic differences between core/no-core scenarios compared to heavier particles.
• Kaons ($K$): Exhibit the narrowest widths. Strangeness conservation and associated production (e.g., $\phi \to K^+K^-$) keep balancing charges localized. They show strong sensitivity to event shape.
• Protons ($p$): Show intermediate widths but the strongest sensitivity to event shape and hydrodynamic core. In EPOS-LHC, protons show a significant narrowing in $\Delta \phi$ and broadening in $\Delta y$ with the core, suggesting strong coupling between baryon number transport and collective expansion.

C. Event Shape Sensitivity

• Jet-like events (Low $S_0$): Consistently yield narrower balance function widths across all models, reflecting back-to-back partonic scattering and collimated fragmentation.
• Isotropic events (High $S_0$): Yield broader widths. In EPOS-LHC, the distinction between jet-like and isotropic events persists even at high multiplicities for pions and kaons, indicating that event shape selection remains a powerful tool to probe underlying dynamics even in high-density environments.

5. Significance and Conclusion

The study demonstrates that particle-identified balance functions are a powerful tool to disentangle microscopic and macroscopic mechanisms in small collision systems.

1. Evidence of Collectivity: The specific pattern observed in EPOS-LHC (narrower $\Delta \phi$ and broader $\Delta y$ with increasing multiplicity) serves as a characteristic signature of collective hydrodynamic expansion, distinct from the monotonic narrowing seen in purely microscopic models like PYTHIA 8.
2. Role of Baryon Number: The strong response of protons to the hydrodynamic core suggests that baryon number transport is highly sensitive to collective flow, providing a unique probe for medium-like behavior.
3. Methodological Insight: The results validate that selecting events by transverse spherocity allows researchers to isolate jet-like vs. isotropic dynamics, offering a way to study the emergence of collectivity in high-multiplicity $pp$ collisions.

Conclusion: The paper concludes that multidimensional balance function measurements (dependent on species, multiplicity, and event shape) are essential for understanding the transition from independent fragmentation to collective medium-like behavior in high-energy $pp$ collisions. The results suggest that high-multiplicity $pp$ collisions may indeed host a transient, medium-like phase characterized by hydrodynamic flow, particularly evident in the transport of baryons and strange quarks.