Probing hadronization with the charge correlator ratio in $p$+$p$, $Ru$+$Ru$ and $Zr$+$Zr$ collisions at STAR

This paper presents STAR measurements of the charge correlator ratio $r_c$ in $p$+$p$, $Ru$+$Ru$, and $Zr$+$Zr$ collisions at $\sqrt{s_{\rm{NN}}}=200$ GeV to probe string-like fragmentation in vacuum and investigate potential modifications to hadronization within the Quark-Gluon Plasma.

The Gist

Imagine you are a detective trying to figure out how a chaotic crowd of people (subatomic particles) organizes itself into orderly groups (particles we can see) after a massive explosion. This is the story of hadronization, and this paper is about how the STAR experiment at the Relativistic Heavy Ion Collider (RHIC) is solving the mystery.

Here is the breakdown of the paper using simple analogies.

The Big Mystery: How Particles "Dress Up"

When scientists smash particles together at near light speed, they create a shower of tiny, invisible fragments called quarks and gluons (the "partons"). These fragments don't stay invisible for long; they instantly snap together to form stable particles like protons and pions. This process is called hadronization.

The problem? The rules governing this snap-together process are written in a language called "Quantum Chromodynamics" (QCD), which is so complex that even the smartest supercomputers can't solve it from scratch. It's like trying to predict exactly how a pile of LEGOs will fall apart and reassemble without knowing the shape of the bricks.

To solve this, the scientists need to look at the "fingerprint" left behind. They use a special tool called the Charge Correlator Ratio ($r_c$).

The Detective Tool: The "Charge Correlator Ratio" ($r_c$)

Imagine you are watching a dance floor. You pick the two most energetic dancers (the "leading" and "subleading" particles) in a specific group. You ask: "Do these two dancers have the same charge (like two positive ions) or opposite charges (one positive, one negative)?"

• The "String" Theory: If particles are created by stretching a rubber band (a "string") that snaps, the two ends usually have opposite charges. If this is the only thing happening, the ratio ($r_c$) would be -1 (perfect opposites).
• The "Bath" Theory: If particles are just swimming in a giant, neutral soup where charge doesn't matter, the two dancers would be random. The ratio would be 0.

The scientists expect the real answer to be somewhere between -1 and 0. By measuring exactly where it lands, they can tell which "dance move" (fragmentation model) nature is actually using.

Part 1: The Control Group (p+p Collisions)

First, the team looked at proton-proton (p+p) collisions. Think of this as a controlled experiment in a quiet room.

• What they did: They smashed protons together and measured the charge ratio of the top two particles in the resulting jets.
• What they found: The ratio was negative (around -0.3), meaning there is a preference for opposite charges, but it's not a perfect -1.
• The Surprise: They compared their data to two famous computer simulations (called PYTHIA and HERWIG). These are like two different video game engines trying to simulate the physics.
  • PYTHIA thinks particles form like strings.
  • HERWIG thinks they form like little clusters.
  • The Twist: Even though these two programs use completely different rules, they both predicted the same wrong answer, which didn't quite match the real data. This suggests that both programs are missing a piece of the puzzle, perhaps involving how particles decay from unstable "resonances" (like a balloon popping into smaller balloons).

Part 2: The Heavy Hitters (Ru+Ru and Zr+Zr Collisions)

Next, they moved to heavy ion collisions (Ruthenium and Zirconium).

• The Analogy: If p+p is a quiet room, this is a mosh pit. When these heavy nuclei smash together, they create a Quark-Gluon Plasma (QGP)—a super-hot, dense soup of free-floating particles, similar to the state of the universe just after the Big Bang.
• The Goal: They want to see if this "soup" changes how the particles dress up. Does the QGP mess with the "string" or the "cluster"?
• The Challenge: In a mosh pit, it's hard to tell which dancer belongs to your original group and which one just bumped into you from the crowd. The "background" noise is huge.
• The Solution: They used a clever trick called embedding. They took a clean simulation (the "signal") and digitally pasted it into real heavy-ion data (the "noise").
  • They then used math to subtract the noise, separating the "Signal-Signal" pairs (the real dancers) from the "Background-Background" pairs (random bumpers).
  • They proved their math works (called "closure") by showing that when they subtracted the noise from their fake data, they got back exactly what they started with.

The Conclusion: What's Next?

The paper is a progress report.

1. In the quiet room (p+p): They confirmed that our current computer models aren't perfect. The real world is slightly more complex than the "string" or "cluster" theories alone suggest.
2. In the mosh pit (Heavy Ions): They have built the perfect toolkit to measure the charge ratio in the Quark-Gluon Plasma. They haven't published the final heavy-ion results yet, but they have shown that their method works and is ready to go.

Why does this matter?
If they find that the charge ratio changes in the heavy-ion collisions, it means the Quark-Gluon Plasma is actively interfering with how particles form. This would give us a brand new window into understanding the strongest force in the universe and how the early universe cooled down to form the matter we see today.

In short: They are using the "friendship" between the two most energetic particles in a crash to figure out the secret rules of how the universe builds itself, both in empty space and in the hottest soup imaginable.

Technical Summary

1. Problem Statement

The transition from partons to hadrons, known as hadronization, is a non-perturbative process in Quantum Chromodynamics (QCD) that cannot be easily calculated from first principles. Understanding this mechanism is crucial for interpreting jet evolution in high-energy collisions.

• The Challenge: Existing phenomenological models (e.g., string fragmentation vs. cluster hadronization) make different assumptions about hadronization, but experimental observables sensitive enough to distinguish between them in vacuum and in the presence of a Quark-Gluon Plasma (QGP) are needed.
• The Observable: The charge correlator ratio ($r_c$) is proposed as a novel jet substructure observable. It quantifies the charge correlation between the leading ($h_1$) and subleading ($h_2$) hadrons in a jet.
  • $r_c \to -1$: Indicates perfect charge correlation (string-like fragmentation).
  • $r_c \to 0$: Indicates no correlation (infinite charge bath).
  • The value is expected to lie between -1 and 0, with the exact value sensitive to the fragmentation mechanism.
• The Goal: To measure $r_c$ in p+p collisions to probe string-like fragmentation in vacuum and in heavy-ion (Ru+Ru, Zr+Zr) collisions to investigate potential modifications to hadronization caused by the QGP.

2. Methodology

A. Experimental Setup and Data

• Experiment: STAR detector at the Relativistic Heavy Ion Collider (RHIC).
• Collision Systems & Energies:
  • p+p: $\sqrt{s} = 200$ GeV (2012 run).
  • Heavy Ion (Isobars): Ru+Ru and Zr+Zr at $\sqrt{s_{NN}} = 200$ GeV (2018 run).
• Detectors: Tracks reconstructed from the Time Projection Chamber (TPC); neutral energy deposits measured by the Barrel Electro-Magnetic Calorimeter (BEMC).
• Jet Reconstruction:
  • Algorithm: Anti-$k_T$ sequential recombination with resolution parameter $R=0.4$.
  • Inputs: TPC tracks ($0.2 < p_T < 30$ GeV/c) and BEMC towers ($0.2 < E_T < 30$ GeV).
  • Selections: $p_T > 15$ GeV/c, $|\eta| < 0.6$, neutral energy fraction $< 0.9$, and $N_{ch} \ge 2$.

B. Analysis Strategy for p+p Collisions

• Definition of $r_c$: Calculated based on the leading and subleading tracks (charged particles) within a jet.
  • Note: Unlike previous proposals requiring the leading/subleading particles to be charged at the truth level, this analysis uses the leading/subleading tracks at the detector level to avoid complications from neutral particles (like $\pi^0 \to \gamma\gamma$) that might fragment into charged daughters.
• Corrections:
  • Mistagged Subtraction: Accounts for misidentification of tracks due to tracking inefficiency.
  • Jet Energy Scale Correction: Applied bin-by-bin to correct for jet $p_T$ resolution.
• Comparison: Results are compared against Monte Carlo (MC) event generators: HERWIG7 (cluster model), PYTHIA8 (Lund string model, Detroit tune), and PYTHIA6 (Lund string model, STAR tune).

C. Analysis Strategy for Heavy Ion (Ru+Ru, Zr+Zr) Collisions

• Challenge: High background density in central heavy-ion collisions creates "combinatorial jets" and contaminates the leading tracks of signal jets.
• Background Estimation:
  • Background momentum density ($\rho$) is calculated using the median $p_T/A$ of jets (excluding the two hardest).
  • Embedding Technique: PYTHIA p+p jets are embedded into real isobar collision events to create a "toy sample." This allows for the separation of signal (PYTHIA) and background (isobar data).
• Decomposition Formula: The raw measured $r_c$ is decomposed into four components based on the origin of the leading two tracks:
  $$r_c(\text{raw}) = P(\text{comb})r_c(\text{comb}) + P(\text{BB})r_c(\text{BB}) + P(\text{SB})r_c(\text{SB}) + P(\text{SS})r_c(\text{SS})$$
  Where:
  • comb: Combinatorial jets (fake jets).
  • BB: Background-Background (both leading tracks are background).
  • SB: Signal-Background (one signal, one background).
  • SS: Signal-Signal (both tracks from fragmentation; the target observable).
• Validation: The decomposition method is validated using the embedding sample, showing "closure" (the calculated $r_c(\text{SS})$ matches the true $r_c$ from the embedded PYTHIA jets).
• Data-Driven Estimation: For actual data analysis, mixed-event techniques and perpendicular cone correlations are used to estimate $r_c(\text{comb})$ and $r_c(\text{BB})$.

3. Key Results

A. p+p Collision Results

• Measurement: The fully corrected $r_c$ in p+p collisions is negative (approx. -0.3) for $20 < p_T < 40$ GeV/c, lying below the charge bath limit (0).
• Model Comparison:
  • Both HERWIG7 and PYTHIA8 underpredict the magnitude of the negative correlation (i.e., they predict values closer to 0 than the data).
  • Despite using different hadronization models (Cluster vs. String), both generators show similar deviations from data.
• Physics Insight:
  • Random track pairs within jets show a negative $r_c$ (approx. -0.2) due to local charge conservation.
  • The additional negativity in the leading/subleading pair (-0.3) highlights the specific correlation from fragmentation.
  • Resonance Decays: Analysis of the origin of leading $\pi^+$ shows that ~50% come from quarks/diquarks in PYTHIA, while only ~30% do in HERWIG (the rest come from resonance decays). The difference in resonance decay fractions may explain why the two models yield similar $r_c$ predictions despite different fragmentation mechanisms.

B. Heavy Ion (Isobar) Progress

• Background Characterization: The background density $\rho$ was mapped for centralities 0–20%.
• Embedding Validation: The embedding study revealed that 21% of jets in central isobar collisions contain a leading/subleading track from the background medium, even after standard selections. This confirms the necessity of the background subtraction technique.
• Closure Test: The decomposition method successfully recovered the true $r_c(\text{SS})$ from the embedded signal, validating the approach for future data analysis.

4. Significance and Conclusions

• Vacuum Hadronization: The measurement of $r_c$ in p+p provides a stringent test for hadronization models. The discrepancy between data and current MC generators suggests that existing models (both string and cluster) may not fully capture the charge correlation dynamics or the interplay between fragmentation and resonance decays.
• QGP Modification: The development of the background subtraction framework for heavy-ion collisions is a critical step toward the first measurement of $r_c$ in the QGP.
• Future Outlook:
  • The technique allows for the isolation of the "Signal-Signal" component ($r_c(\text{SS})$) in heavy-ion collisions.
  • Comparing $r_c(\text{SS})$ in p+p vs. heavy-ion collisions will reveal if the QGP modifies the hadronization process (e.g., by altering charge correlations or fragmentation functions).
  • Further measurements of resonance production in p+p are suggested to help distinguish between hadronization models.

In summary, this work establishes $r_c$ as a robust observable for studying hadronization, demonstrates its sensitivity to fragmentation mechanisms in vacuum, and lays the technical groundwork for probing jet-medium interactions in the QGP using isobar collisions.