Topological production of charmonia with event-shape engineering in $pp$ collisions at $\sqrt{s} = 13$ TeV using PYTHIA8

This study utilizes PYTHIA8 simulations to investigate the correlation between prompt and nonprompt $J/\psi$ production and transverse spherocity in 13 TeV $pp$ collisions, demonstrating how this event-shape observable can distinguish hard QCD processes from underlying events influenced by multiple parton interactions.

The Gist

Imagine you are a detective trying to figure out how a chaotic party was organized. You walk into a room where thousands of people (particles) have just collided, creating a massive, swirling crowd. Your job is to understand how specific, rare guests (heavy particles like charm and beauty quarks) managed to show up and form pairs (like the J/ψ particle) amidst the chaos.

This paper is a simulation of that party, run on a supercomputer using a program called PYTHIA8, which acts like a virtual physics engine. The researchers are studying collisions at the world's most powerful particle accelerator (the LHC), but instead of real data, they are looking at a perfect digital model to understand the rules of the game.

Here is the breakdown of their investigation using simple analogies:

1. The Two Types of "Guests" (Prompt vs. Non-Prompt)

In this particle party, there are two ways the star guest, the J/ψ (a heavy particle made of a charm quark and its anti-quark), can arrive:

• Prompt J/ψ: These are the "VIPs" who arrive directly from the main collision. They are born instantly when the initial crash happens. Think of them as the people who were right in the center of the explosion.
• Non-Prompt J/ψ: These are the "late arrivals." They don't come from the main crash directly. Instead, they are the children of a heavier, unstable guest (a beauty hadron). The beauty guest arrives, lives for a tiny fraction of a second, and then decays (dies) to produce the J/ψ. It's like a guest bringing a friend who shows up a moment later.

2. The "Shape" of the Party (Transverse Spherocity)

Usually, physicists sort these parties by counting how many people are in the room (multiplicity). But the authors realized that just counting heads isn't enough; you need to know the shape of the crowd.

They introduced a new tool called Transverse Spherocity (let's call it the "Party Shape Meter").

• Jetty Events (Low Spherocity): Imagine a party where everyone is rushing in two straight, opposite lines, like a high-speed train crash. This is a "Jetty" event. It's chaotic, directional, and usually caused by a single, hard, violent collision.
• Isotropic Events (High Spherocity): Imagine a party where everyone is standing in a perfect circle, chatting evenly in all directions. This is an "Isotropic" event. It's softer, more uniform, and usually caused by many smaller, gentle interactions happening at once.

3. The Big Discovery: How the Party Shape Affects the Guests

The researchers used the computer to see how the "Party Shape" changes the behavior of the J/ψ guests. Here is what they found:

• The "Soft" Crowd Makes Harder Particles: Surprisingly, they found that the Prompt J/ψ (the VIPs) were actually moving faster (had higher momentum) in the Isotropic (round/calm) parties than in the Jetty (straight-line) parties.

  • Why? In the round parties, there are many small interactions happening at once (like a crowded dance floor). The computer model suggests that these crowded conditions help the charm quarks "hug" each other and form a J/ψ with a big boost of energy. It's like a crowded dance floor pushing people together with more force than a straight hallway.

• The "Heavy" Guests Love the "Hard" Collisions: The Non-Prompt J/ψ (the late arrivals from beauty decay) behaved differently. At high speeds, they were more common in the Jetty events.

  • Why? Creating a heavy beauty quark requires a lot of energy, like a sledgehammer hitting a nail. This usually happens in those straight-line, high-energy "Jetty" collisions. Once the beauty guest is created, it flies off and eventually decays into a J/ψ.

4. The "Selfie" Problem (Autocorrelation Bias)

One of the most important lessons in the paper is about bias.

• Imagine you are trying to measure how loud a party is by asking the people in the room to shout. If you ask the people in the room to define the room, your measurement is biased because they are part of the noise.
• In physics, if you measure the "shape" of the event using particles from the same place where you are looking for the J/ψ, you get a distorted picture.
• The authors found that if you look at the "middle" of the collision (mid-rapidity) and use the middle particles to define the shape, you get a false signal. However, if you look at the "front" of the collision (forward rapidity) and use those particles to define the shape, the signal is much cleaner. It's like measuring the noise of a concert by listening to the back of the hall rather than standing right next to the speakers.

5. Why Does This Matter?

This study is like a "flight simulator" for particle physicists.

• Testing the Theory: It confirms that our current computer models (PYTHIA8) can explain how heavy particles behave in different types of collisions.
• Future Experiments: Now that we know how the shape of the event changes the outcome, real experiments at the LHC can use this "Party Shape Meter" to separate different types of physics. It helps them understand the "underlying event"—the invisible background noise that affects how particles are created.
• The "Underlying Event": The paper shows that even though the J/ψ is created in the initial split-second crash, the "background noise" (the underlying event) plays a huge role in shaping its final speed and direction.

Summary

Think of the universe as a giant, chaotic dance floor. This paper teaches us that how the crowd moves (the shape of the event) dictates how the rare dancers (heavy particles) move.

• If the crowd is swirling in a circle (Isotropic), the "instant" dancers move faster.
• If the crowd is rushing in straight lines (Jetty), the "heavy" dancers are more likely to appear.

By understanding these patterns, scientists can better decode the fundamental rules of how matter is built from the smallest building blocks.

Technical Summary

1. Problem Statement and Motivation

The production of heavy quarks (charm and beauty) in high-energy collisions serves as a critical testing ground for Quantum Chromodynamics (QCD). While the initial production of heavy quark pairs ($c\bar{c}$ and $b\bar{b}$) is well-described by perturbative QCD (pQCD), the subsequent formation of bound states (like $J/\psi$) involves non-perturbative soft processes that are not fully understood.

Current experimental studies often rely on charged particle multiplicity ($N_{ch}$) to select events and study the interplay between hard (jet-like) and soft (isotropic) production mechanisms. However, multiplicity-based selection suffers from autocorrelation biases, where the particles used to define the event class also contribute to the observable being measured, artificially enhancing correlations.

The paper addresses the need for a more differential and less biased method to characterize the underlying event (UE) and disentangle hard QCD processes from soft ones. It proposes using Transverse Spherocity ($S_0$), an event-shape observable, as a tool to classify events into "jetty" (hard, di-jet dominated) and "isotropic" (soft, multi-parton interaction dominated) topologies. The specific goal is to study the topological production of prompt (directly produced) and non-prompt (from beauty hadron decay) $J/\psi$ mesons in proton-proton ($pp$) collisions at $\sqrt{s} = 13$ TeV.

2. Methodology

The study utilizes the PYTHIA8 Monte Carlo event generator (version 8.308) with the 4C tune to simulate minimum bias $pp$ collisions at $\sqrt{s} = 13$ TeV.

• Event Generation:

  • Includes Multiple Parton Interactions (MPI), Color Reconnection (CR), and string fragmentation.
  • Generates 10 billion events, enabling the reconstruction of $J/\psi$ via dielectron ($e^+e^-$) and dimuon ($\mu^+\mu^-$) decay channels.
  • Prompt $J/\psi$: Reconstructed from direct production or radiative decays of higher charmonium states.
  • Non-prompt $J/\psi$: Reconstructed from the weak decay of beauty hadrons ($b \to J/\psi + X$).
  • Rapidity regions: Mid-rapidity ($|y| < 0.9$, dielectron channel) and Forward rapidity ($2.5 < y < 4$, dimuon channel).

• Event Shape Selection (Transverse Spherocity, $S_0$):

  • $S_0$ is defined based on the azimuthal distribution of charged particles in the transverse plane.
  • $S_0 \to 0$: Jetty events (hard scattering, back-to-back jets).
  • $S_0 \to 1$: Isotropic events (soft interactions, uniform particle production).
  • Events are classified into "Jetty" (lowest 20% of $S_0$) and "Isotropic" (highest 20% of $S_0$) based on specific cuts derived for different multiplicity classes (V0M).

• Observables:

  • Event-normalized transverse momentum ($p_T$) spectra.
  • Partonic modification factor ($Q_{pp}$), analogous to the nuclear modification factor $R_{AA}$, comparing jetty/isotropic yields to $S_0$-integrated yields.
  • Fraction of non-prompt $J/\psi$ ($f_B$).
  • Mean transverse momentum ($\langle p_T \rangle$) vs. charged particle multiplicity density.
  • Self-normalized yield vs. self-normalized multiplicity.

• Validation:

  • Results are compared with experimental data from ALICE and LHCb.
  • Robustness is tested using an alternative PYTHIA8 configuration (CR-BLC 2) which includes beyond-leading-colour effects and junction formation.

3. Key Contributions

1. First Application of Event-Shape Engineering to $J/\psi$: This is the first study to utilize transverse spherocity to investigate the topological production of both prompt and non-prompt $J/\psi$ in $pp$ collisions, moving beyond traditional multiplicity-based selections.
2. Quantification of Autocorrelation Bias: The study explicitly demonstrates how autocorrelation biases affect measurements when event selection (multiplicity or spherocity) is performed in the same rapidity region as the observable, contrasting mid-rapidity and forward-rapidity results.
3. Decoupling Hard and Soft Mechanisms: By separating events into jetty and isotropic topologies, the paper isolates the influence of Multiple Parton Interactions (MPI) and Color Reconnection (CR) on heavy-flavor production.
4. Model Robustness: The findings are validated against the CR-BLC 2 model, confirming that while absolute yields vary, the qualitative trends regarding event topology and $p_T$ dependence are robust across different non-perturbative QCD modeling assumptions.

4. Key Results

• $p_T$ Spectra Hardening:

  • Non-prompt $J/\psi$ exhibits a harder $p_T$ spectrum than prompt $J/\psi$, consistent with the large mass of the parent beauty hadrons.
  • Isotropic events show a harder $p_T$ spectrum for prompt $J/\psi$ compared to jetty events. This is attributed to Color Reconnection (CR) effects in high-MPI environments, where charm quarks from independent scatterings combine to form high-$p_T$ charmonium states.
  • Conversely, jetty events favor the production of non-prompt $J/\psi$ at high $p_T$, reflecting the dominance of initial hard scatterings in di-jet topologies.

• Partonic Modification Factor ($Q_{pp}$):

  • At mid-rapidity, $Q_{pp}$ for prompt $J/\psi$ in isotropic events peaks at lower $p_T$ ($\sim 5$ GeV/c) compared to jetty events, indicating significant MPI-driven hardening.
  • At forward rapidity, the dependence on spherocity diminishes, and $Q_{pp}$ remains close to unity. This suggests that beauty hadron production at forward rapidity is less sensitive to the event shape defined by mid-rapidity particles, effectively reducing autocorrelation bias.

• Non-Prompt Fraction ($f_B$):

  • At low $p_T$ ($< 6$ GeV/c), isotropic events (high MPI) show a larger $f_B$, indicating MPI enhances beauty production.
  • At high $p_T$ ($> 6$ GeV/c), the trend reverses: jetty events dominate $f_B$. This confirms that high-$p_T$ beauty production is driven by initial hard scatterings (di-jet topology) rather than soft multi-jet environments.

• Autocorrelation Bias:

  • The self-normalized yield of $J/\psi$ vs. multiplicity shows a steeper-than-linear increase.
  • This effect is significantly stronger when $J/\psi$ and multiplicity are measured in the same rapidity region (forward-forward or mid-mid) due to autocorrelation.
  • Measurements in forward rapidity (where $S_0$ is defined in mid-rapidity) show reduced bias, validating the utility of cross-rapidity event shape selection.

5. Significance and Conclusion

This work establishes transverse spherocity as a powerful, less biased tool for studying heavy-flavor production mechanisms in small collision systems ($pp$).

• Physics Insight: It reveals that the underlying event activity (MPI) plays a crucial role in shaping the $p_T$ spectra of prompt $J/\psi$ via Color Reconnection, while non-prompt $J/\psi$ production is more sensitive to the initial hard scattering topology (di-jet vs. multi-jet).
• Experimental Guidance: The study warns against the pitfalls of autocorrelation in multiplicity-based analyses and suggests that event-shape engineering, particularly when combining mid-rapidity event classification with forward-rapidity measurements, provides a cleaner probe of QCD dynamics.
• Future Outlook: These findings provide a baseline for future experimental studies in LHC Run 3 and Run 4, where high-statistics data will allow for the exploration of charmonia production within specific jet topologies, offering deeper insights into hadronization mechanisms from $pp$ to Pb-Pb collisions.