Measurement of the charged-particle-jet transverse-momentum fraction carried by prompt and non-prompt J/$ψ$ mesons in pp collisions at $\sqrt{s}=13$ TeV

The ALICE Collaboration reports the first measurement of the charged-particle jet transverse-momentum fraction ($z^{\rm ch}$) carried by prompt and non-prompt J/$\psi$ mesons in 13 TeV proton-proton collisions, revealing that while PYTHIA 8 simulations qualitatively reproduce the data for $z^{\rm ch} < 0.9$, they significantly overestimate the fraction of isolated J/$\psi$ mesons at high $z^{\rm ch}$ values, highlighting challenges in modeling the hadronization of low-momentum jets.

The Gist

The Big Picture: Catching the "Ghost" in the Machine

Imagine you are at a massive, high-speed fireworks display. Every time two fireworks collide, they explode into a chaotic spray of sparks, smoke, and debris. Physicists call these collisions "jets."

Usually, when these fireworks explode, the debris is a messy mix of thousands of tiny particles. But sometimes, hidden inside that mess, a very specific, heavy, and rare particle called a J/ψ meson is born. It's like finding a golden coin inside a pile of gravel.

This paper is about a team of scientists (the ALICE Collaboration) at the Large Hadron Collider (LHC) who decided to look very closely at these "fireworks" to answer two big questions:

1. Where did the golden coin come from? Was it made right at the moment of the explosion (prompt), or did it fall out of a heavier, slower-moving rock that broke apart later (non-prompt)?
2. How much of the explosion's energy did the coin carry? Did it take the whole show with it, or just a tiny spark?

The Setup: The High-Speed Camera

To see this, the scientists used a special camera setup called the Transition Radiation Detector (TRD). Think of this detector as a super-sensitive motion sensor that only triggers when it sees a specific type of fast-moving electron.

They collected data from billions of collisions (about 1.63 "inverse picobarns" of data, which is a fancy way of saying "a huge amount of stuff"). They focused on collisions where the resulting "fireworks" (jets) had a moderate amount of energy—not the biggest, most violent explosions, but the medium-sized ones.

The Detective Work: Sorting the Coins

Once they found a J/ψ meson inside a jet, they had to figure out its origin. This is where the "ghost" analogy comes in.

• Prompt J/ψ (The Instant Maker): These are created directly in the crash. They appear immediately, like a spark flying out the second two cars collide.
• Non-Prompt J/ψ (The Late Bloomer): These are created when a heavier "beauty" particle (a B-hadron) is created first. This heavy particle flies a tiny distance away from the crash site before it decays and turns into a J/ψ. It's like a heavy rock flying off the car, rolling a few inches, and then cracking open to reveal the golden coin.

The scientists used the Inner Tracking System (ITS)—essentially a super-high-resolution microscope—to measure exactly where the J/ψ appeared. If it appeared right at the crash site, it was "prompt." If it appeared a tiny bit further away, it was "non-prompt."

The Main Discovery: The "Z" Score

The scientists measured a value called $z_{ch}$. Imagine the jet is a delivery truck carrying a heavy load of cargo (energy). The J/ψ is one specific package in that truck.

• $z_{ch} = 1.0$ means the J/ψ took 100% of the truck's cargo. The truck is empty except for this one package. This is called an "isolated" J/ψ.
• $z_{ch} = 0.1$ means the J/ψ only took 10% of the cargo, and the rest is shared with hundreds of other particles.

What they found:

1. The Trend: As the scientists looked at jets where the J/ψ carried more and more of the energy (approaching $z_{ch} = 1$), they found a lot of these "isolated" J/ψ mesons.
2. The Problem with the Computer Simulations: The scientists compared their real-world data to computer simulations (using a program called PYTHIA 8).
   • For the "messy" jets (where the J/ψ shares the energy with others), the computer simulation was spot on. It was like the computer correctly predicted how a messy pile of gravel would look.
   • However, when the J/ψ carried almost all the energy (approaching $z_{ch} = 1$), the computer simulation went crazy. It predicted way too many of these isolated, lonely J/ψ mesons. The computer thought they were common; the real data showed they were rarer than the computer guessed.

Why Does This Matter? (The "Hamburger" Analogy)

Think of the computer simulation as a recipe for making a hamburger.

• The recipe says: "Take a patty (the J/ψ) and put it in a bun (the jet)."
• In the real world, when you make a burger, you usually have a patty, some lettuce, some cheese, and some sauce all mixed together.
• The computer simulation, however, keeps predicting that you will end up with a burger that is 99% patty and 1% bun. It thinks the patty is so dominant that it pushes everything else out.

The fact that the computer is wrong about these "super-patty" burgers tells us that our understanding of how particles stick together (hadronization) is incomplete, especially when the particles are moving relatively slowly. The computer doesn't quite know how to simulate the "glue" that holds the messy parts of the jet together when the main particle tries to take over.

The Conclusion

This paper is a crucial piece of the puzzle. It tells us that while our current computer models (like PYTHIA 8) are great at describing the messy, average collisions, they struggle to describe the rare, high-energy "lonely" particles.

By finding this gap between the real data and the simulation, the ALICE team has given theoretical physicists a new target. They need to rewrite the "recipe" for how heavy particles form and interact, especially in the low-energy, messy environments of the early universe or inside heavy-ion collisions (like the quark-gluon plasma).

In short: We found a lot of "golden coins" in the fireworks, but the computer predicted even more than we actually saw. This means our computer models need a software update to better understand how the universe builds these heavy particles.

Technical Summary

1. Problem and Motivation

The production mechanism of charmonium states (bound states of charm-anticharm quark pairs, specifically $J/\psi$) remains a significant challenge in Quantum Chromodynamics (QCD). While perturbative QCD (pQCD) describes the creation of $c\bar{c}$ pairs, the subsequent hadronization into a bound state involves non-perturbative physics that is not yet fully understood.

• The Gap: Existing models (Color Evaporation, Color Singlet, NRQCD) struggle to universally describe $J/\psi$ production, particularly at low transverse momentum ($p_T$).
• The Observable: To probe the hadronization mechanism, the paper investigates $J/\psi$ production within jets. Specifically, it measures the fraction of the jet's transverse momentum carried by the $J/\psi$ meson, denoted as $z_{ch}$.
  • High $z_{ch}$ (near 1): Indicates "isolated" $J/\psi$ production, where the meson carries most of the jet momentum. This is sensitive to the relative contributions of color-singlet vs. color-octet hadronization mechanisms.
  • Low $z_{ch}$: Indicates "non-isolated" production, where the $J/\psi$ is accompanied by other hadrons from the fragmentation process.
• Context: Previous measurements by LHCb and CMS at high jet $p_T$ ($>20$ GeV/c) showed that simulations (PYTHIA 8) overestimate the fraction of isolated $J/\psi$. This paper extends the investigation to a low jet $p_T$ regime ($7 < p_{T}^{ch\ jet} < 15$ GeV/c), a region where factorization theorems may break down and where heavy-quark fragmentation fractions deviate from those measured in $e^+e^-$ collisions.

2. Methodology

Data and Simulation

• Data Sample: Proton-proton ($pp$) collisions at $\sqrt{s} = 13$ TeV recorded by the ALICE detector during 2017–2018.
• Trigger: A Transition Radiation Detector (TRD) trigger requiring at least one track with $p_T > 2$ GeV/c compatible with an electron hypothesis.
• Luminosity: Integrated luminosity of $L = 1.63 \pm 0.03$ pb$^{-1}$.
• Monte Carlo (MC): PYTHIA 6.4 (for underlying event) with injected prompt and non-prompt $J/\psi$ mesons. PYTHIA 8.311 (Monash 2013 tune) is used for comparison with data.

Reconstruction and Selection

• $J/\psi$ Reconstruction: Reconstructed via the $e^+e^-$ decay channel at midrapidity ($|y| < 0.9$) with $p_T^{J/\psi} > 1$ GeV/c.
• Jet Reconstruction: Jets are reconstructed using the anti-$k_T$ algorithm with a resolution parameter $R=0.4$.
  • Input: Only charged particles within $|\eta| < 0.9$ and $p_T > 0.15$ GeV/c.
  • Jet Selection: $7 < p_T^{ch\ jet} < 15$ GeV/c and $|\eta_{jet}| < 0.5$.
  • Handling $J/\psi$ in Jets: The decay electrons of a reconstructed $J/\psi$ are removed from the jet constituents and replaced by the $J/\psi$ four-momentum to ensure the $J/\psi$ is included in the jet definition.
• Prompt vs. Non-Prompt Separation:
  • Prompt: Directly produced $J/\psi$ or feed-down from higher charmonium states.
  • Non-Prompt: $J/\psi$ originating from beauty-hadron decays ($b \to J/\psi$).
  • Method: A 2D maximum-likelihood fit is performed on the invariant mass ($m_{e^+e^-}$) and the pseudo-proper decay length ($x$). The displacement of the secondary vertex allows statistical separation of the prompt and non-prompt components.

Analysis Techniques

• Unfolding: A 2D Bayesian unfolding procedure (using the RooUnfold package) corrects for detector resolution and bin migration. A response matrix maps generator-level truth to detector-level measurements.
• Efficiency Corrections: Corrections are applied for acceptance, reconstruction efficiency, and TRD trigger efficiency. The efficiency for prompt and non-prompt $J/\psi$ is treated separately due to their different $p_T$ spectra.

3. Key Contributions

1. First Measurement in Low-$p_T$ Jets: This is the first measurement of $J/\psi$ production within charged-particle jets in the low jet-$p_T$ range ($7-15$ GeV/c) at the LHC. This regime is crucial for testing the universality of parton fragmentation and potential factorization breaking.
2. Separation of Production Mechanisms: The analysis provides distinct distributions for prompt and non-prompt $J/\psi$ mesons, allowing for a differential study of charm vs. beauty fragmentation within jets.
3. Comparison with Theory: The results are compared against:
   • PYTHIA 8: Both "SoftQCD" (fixed-order NRQCD) and "CharmoniumShower" (production within parton shower) settings.
   • pQCD Calculation: A specific calculation by Zhang and Xing based on NRQCD factorization.

4. Results

Prompt $J/\psi$

• Data Trend: The distribution of $z_{ch}$ shows a rising trend as $z_{ch}$ increases, with a distinct peak as $z_{ch} \to 1$. This indicates that isolated $J/\psi$ production is the dominant mechanism in this low jet-$p_T$ range.
• Comparison with PYTHIA 8:
  • For $z_{ch} < 0.9$, PYTHIA 8 (both settings) qualitatively reproduces the rising trend.
  • For $z_{ch} \to 1$, PYTHIA 8 significantly overshoots the data. This suggests the simulation overestimates the fraction of isolated $J/\psi$ mesons.
• Comparison with pQCD: The Zhang and Xing calculation (valid for $0.5 < z_{ch} < 0.9$) shows very good compatibility with the data, though it carries large theoretical uncertainties from Long-Distance Matrix Elements (LDMEs).

Non-Prompt $J/\psi$

• Data Trend: The distribution is compatible with a rising trend within uncertainties, though less pronounced than for prompt $J/\psi$.
• Comparison with PYTHIA 8: Similar to the prompt case, PYTHIA 8 agrees well with data up to $z_{ch} \approx 0.9$. However, for $z_{ch} > 0.9$, the simulation exhibits a pronounced peak not observed in the data.
• Physical Interpretation: Since non-prompt $J/\psi$ come from beauty decays, they are expected to be accompanied by other decay products, leading to a larger fraction of non-isolated production (lower $z_{ch}$). The data supports this, showing a suppression of the isolated component compared to simulations.

Comparison with Other Experiments

• The ALICE results (low $p_T$, charged jets) differ significantly from CMS results (high $p_T$, full jets), where the CMS distribution peaks at $z \approx 0.5-0.6$ with no isolated peak.
• The trend is consistent with LHCb measurements of prompt $\psi(2S)$, which show an evolution from an isolated-dominant shape at low $p_T$ to a non-isolated shape at high $p_T$.

5. Significance and Conclusion

• Hadronization Challenge: The tension between data and PYTHIA 8 simulations at high $z_{ch}$ (isolated region) highlights the difficulty in simulating the hadronization of low-momentum jets. The simulations fail to correctly model the suppression of isolated heavy quarkonia in this kinematic regime.
• Factorization Breaking: The unique kinematic range probed ($7 < p_T < 15$ GeV/c) is sensitive to potential breaking of the factorization theorem, offering new constraints on heavy-quark fragmentation functions.
• Future Outlook: These measurements provide a baseline for future heavy-ion collision studies. Understanding $J/\psi$ production in $pp$ jets is essential for disentangling medium effects (like color screening and recombination) in the Quark-Gluon Plasma (QGP).
• Conclusion: The ALICE Collaboration successfully measured the $z_{ch}$ distribution for prompt and non-prompt $J/\psi$ in low-$p_T$ jets. While PYTHIA 8 captures the general shape for $z_{ch} < 0.9$, it fails to reproduce the data at high $z_{ch}$, indicating an overestimation of isolated production. This discrepancy underscores the need for improved theoretical descriptions of charmonium fragmentation and hadronization in low-momentum jets.