Multiplicity dependence of prompt and non-prompt J/$\psi$ production at midrapidity in pp collisions at $\sqrt{s} = 13$ TeV

This paper presents measurements of prompt and non-prompt J/$\psi$ production yields at midrapidity in 13 TeV pp collisions, revealing a stronger-than-linear increase in self-normalized yields with charged-particle multiplicity that varies depending on the azimuthal region relative to the J/$\psi$ momentum.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. When two protons (tiny subatomic particles) crash into each other at nearly the speed of light, it's like two high-speed trains colliding. The result is a chaotic explosion of debris, creating hundreds of new particles.

This paper from the ALICE Collaboration is a detailed investigation into one specific type of debris: the J/ψ particle (pronounced "J-psi").

Here is the story of what they found, explained simply.

1. The Two Types of "J/ψ" Guests

When the crash happens, J/ψ particles are born in two different ways:

• The "Prompt" Guests: These are born instantly at the moment of the crash, like a spark flying off a firework immediately upon ignition.
• The "Non-Prompt" Guests: These are the children of a heavier, unstable particle (called a "beauty hadron"). The beauty particle is born in the crash, flies a tiny distance, and then decays into a J/ψ. It's like a parent dropping off a child at school before the child enters the classroom.

The scientists wanted to know: Does the number of "Non-Prompt" guests change depending on how chaotic the crash was?

2. The "Crowded Room" Experiment

The researchers didn't just look at one crash; they looked at thousands. They sorted these crashes into two groups:

• Quiet Crashes: Where only a few particles were created.
• Rowdy Crashes: Where hundreds of particles were created (High Multiplicity).

They asked: If we have a "rowdy" crash with lots of particles, do we get more J/ψ particles? And if so, do the "Prompt" and "Non-Prompt" types behave differently?

The Finding:
Yes! In the rowdy crashes, the number of J/ψ particles increased much faster than the number of other particles.

• The Analogy: Imagine a party. If you invite 10 people, you might get 1 extra guest. If you invite 100 people, you might get 50 extra guests, not just 10. The "J/ψ party" gets super crowded when the main party gets crowded. This is called a "stronger-than-linear" increase.

3. Looking in Different Directions (The "Flashlight" Effect)

To understand why this happens, the scientists didn't just count the whole room. They used a "flashlight" to look at the room in three specific directions relative to where the J/ψ was flying:

1. The "Toward" Zone: The direction the J/ψ was flying.
2. The "Transverse" Zone: The sides, 90 degrees away from the J/ψ.
3. The "Away" Zone: Directly opposite the J/ψ.

The Surprise:

• Toward Zone: The increase in J/ψ particles was huge. This makes sense because the J/ψ and the other particles were likely born from the same "family" or process (like a jet of particles shooting out together).
• Transverse & Away Zones: Even in the directions away from the J/ψ, the number of J/ψ particles still increased significantly when the whole room got rowdy.
• The Metaphor: It's like if you shout in a crowded room, people turn to look at you. But here, even if you look at the people not looking at you, they are still acting more excited than usual when the room gets crowded. This suggests that the "crowd" itself changes the rules of how these particles are made, not just the immediate neighborhood.

4. The "Recipe" Mystery

The scientists compared their real-world data to computer simulations (like a video game physics engine).

• The Old Recipe (Monash Tune): This computer model predicted that J/ψ particles should increase slowly. It was wrong. It underestimated the "rowdy" crashes.
• The New Recipe (OniaShower): When the scientists tweaked the computer model to include a specific process where heavy particles are created inside a "shower" of other particles, the simulation finally matched the real data.
• The Lesson: The way heavy particles (like J/ψ) are made is more complex than we thought. They aren't just made in a simple collision; they are often born inside a chaotic "storm" of other particles, and that storm makes them more likely to appear in crowded events.

5. The "Heavy" vs. "Light" Comparison

They also compared J/ψ (heavy) to D0 (a lighter cousin).

• In massive collisions (like smashing lead nuclei together), heavy particles sometimes get "regenerated" (reborn) because the environment is so dense.
• However, in these small proton-proton collisions, even in the rowdiest crashes, the ratio of J/ψ to D0 stayed mostly the same. This suggests that while the number of J/ψ goes up, they aren't being "reborn" from the soup of particles in the same way they are in massive nuclear collisions. They are just being produced more efficiently.

Summary: What Does This Mean?

This paper tells us that crowds matter.
When protons collide and create a "rowdy" environment with many particles, the production of heavy, exotic particles (like J/ψ) gets a massive boost. This boost happens not just near the heavy particle, but across the whole event.

It suggests that the "soft" particles (the background noise of the crash) and the "hard" particles (the heavy J/ψ) are deeply connected. The chaos of the crowd actually helps create more heavy particles, a phenomenon that our old computer models couldn't predict until we added the right "ingredients" to the recipe.

In short: The more chaotic the crash, the more likely you are to find these special heavy particles, and they seem to thrive in the chaos in ways we are just beginning to understand.

Technical Summary

1. Problem and Motivation

The paper investigates the production mechanisms of charmonium ($J/\psi$ mesons) in proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV, specifically focusing on how these yields depend on the charged-particle multiplicity ($N_{ch}$).

• Scientific Context: While perturbative QCD (pQCD) describes heavy-quark pair production, the hadronization of these pairs into prompt $J/\psi$ mesons (directly produced or from higher charmonia states) and non-prompt $J/\psi$ mesons (from weak decays of beauty hadrons) is non-perturbative and requires phenomenological models (e.g., NRQCD, Color Evaporation Model).
• The Phenomenon: Previous measurements have shown that the self-normalized yield of quarkonia increases stronger-than-linearly with charged-particle multiplicity. This behavior is observed in high-multiplicity $pp$ events, which exhibit signs of collectivity similar to the Quark-Gluon Plasma (QGP) seen in heavy-ion collisions.
• Key Questions:
  • Does the multiplicity dependence differ between prompt and non-prompt $J/\psi$?
  • How do different azimuthal regions (toward, transverse, away relative to the $J/\psi$) affect this correlation?
  • Can current theoretical models (PYTHIA, EPOS4, CGC) reproduce these observations?
  • Does the ratio of prompt $J/\psi$ to open charm ($D^0$) change with multiplicity, indicating potential regeneration effects in small systems?

2. Methodology

Data Sample and Experimental Setup:

• Detector: ALICE experiment at the LHC.
• Collision System: $pp$ collisions at $\sqrt{s} = 13$ TeV (Run 2 data).
• Decay Channel: $J/\psi \to e^+e^-$ (dielectron channel) reconstructed in the central barrel ($|y| < 0.9$).
• Triggers: Data collected using Minimum Bias (MB), Transition Radiation Detector (TRD), and High-Multiplicity (HM, selecting the top 0.1% of events by V0 signal) triggers.
• Multiplicity Estimator: Charged-particle multiplicity ($N_{ch}$) measured within $|\eta| < 0.9$ using global tracks ($p_T > 0.15$ GeV/c) reconstructed in the ITS and TPC.

Analysis Strategy:

1. Self-Normalization: Both the $J/\psi$ yield and the multiplicity are normalized by their average values in inelastic events with at least one charged particle ($INEL>0$). This removes luminosity and efficiency uncertainties.
2. Prompt vs. Non-Prompt Separation:
   • A Boosted Decision Tree (BDT) algorithm is used to separate prompt and non-prompt components based on the pseudo-proper decay length ($x$) and other kinematic variables.
   • The separation relies on the displacement of the secondary vertex for non-prompt $J/\psi$ (from $B$-hadron decays) compared to the primary vertex for prompt $J/\psi$.
3. Azimuthal Regions: The multiplicity is measured in three regions relative to the $J/\psi$ momentum direction:
   • Toward: $|\Delta\phi| < \pi/3$ (contains particles from the same jet/process).
   • Transverse: $\pi/3 < |\Delta\phi| < 2\pi/3$ (probes underlying event activity).
   • Away: $|\Delta\phi| > 2\pi/3$ (recoil region).
4. Corrections:
   • Unfolding procedures correct for detector efficiency and bin migration.
   • Corrections are applied to account for the "autocorrelation" bias where $J/\psi$ decay daughters are included in the multiplicity count.
   • TRD trigger efficiency corrections are applied for high-$p_T$ samples.

3. Key Contributions

• First Differential Measurement: This is the first measurement to separate prompt and non-prompt $J/\psi$ yields as a function of multiplicity in $pp$ collisions at 13 TeV, extending previous inclusive measurements.
• Azimuthal Decomposition: The study uniquely decomposes the multiplicity dependence into "toward," "transverse," and "away" regions, disentangling autocorrelation effects from underlying event properties.
• Model Constraints: The results provide stringent constraints on event generators (PYTHIA 8, EPOS4) and theoretical frameworks (Color Glass Condensate) regarding heavy-flavor hadronization in high-density environments.
• Ratio Analysis: The paper presents the first measurement of the prompt $J/\psi$ to prompt $D^0$ ratio as a function of multiplicity in $pp$ collisions, comparing it to $p$-Pb and Pb-Pb systems.

4. Results

Multiplicity Dependence of Yields:

• Stronger-than-Linear Increase: Both prompt and non-prompt self-normalized yields exhibit a stronger-than-linear increase with self-normalized multiplicity.
• Azimuthal Dependence:
  • Toward Region: The increase is strongest here, driven by autocorrelations (particles from the same production process, e.g., jet fragmentation or common mother particles).
  • Transverse/Away Regions: The increase is weaker but still present. This suggests that the underlying event activity is correlated with hard processes, or that the definition of these regions still captures some associated radiation.
• $p_T$ Dependence: The slope of the multiplicity dependence increases with $J/\psi$ transverse momentum ($p_T$), particularly in the toward region, suggesting a link to harder jet production.

Non-Prompt Fraction ($f_B$):

• The fraction of non-prompt $J/\psi$ ($f_B$) shows a slight hint of increasing with multiplicity (significance $\sim 2.9\sigma$ in a linear fit excluding the first point), though the trend is mild.
• This suggests that beauty production mechanisms may have a slightly different multiplicity dependence than charm, or that $B$-hadron decays contribute more significantly to high-multiplicity events.

Comparison with Models:

• PYTHIA 8:
  • The standard Monash tune underestimates the prompt $J/\psi$ yield at high multiplicities.
  • The oniaShower setting (where quarkonia are produced within parton showers) reproduces the prompt data well, indicating that higher-order corrections and parton shower effects are crucial.
  • PYTHIA reproduces the non-prompt trend well.
• EPOS4:
  • Overestimates prompt yields in the toward region (especially with hydrodynamic evolution).
  • Underestimates non-prompt yields at high multiplicities.
• CGC Models:
  • The 3-Pomeron CGC model describes prompt data well over the full multiplicity range.
  • CGC+ICEM describes low-$p_T$ data but fails at higher $p_T$.

Prompt $J/\psi$ / $D^0$ Ratio:

• The ratio of prompt $J/\psi$ to prompt $D^0$ yields remains constant within uncertainties across the multiplicity range in $pp$ collisions.
• This contrasts with Pb-Pb collisions, where the ratio increases in central collisions (attributed to $c\bar{c}$ regeneration). The lack of increase in $pp$ suggests that regeneration effects are negligible in small systems, even at high multiplicities.

5. Significance and Conclusions

• Autocorrelations vs. Medium Effects: The study concludes that the stronger-than-linear increase in $J/\psi$ yields is significantly driven by autocorrelations (particles produced in the same process as the $J/\psi$) rather than solely by medium-induced effects. This is evidenced by the strong dependence on the "toward" region and the $p_T$ dependence.
• Hadronization Mechanisms: The success of the oniaShower model in PYTHIA suggests that the production of prompt quarkonia is intimately linked to the parton shower evolution, challenging models that treat $J/\psi$ production purely as a hard scattering process.
• Small System Collectivity: While high-multiplicity $pp$ events show collectivity-like features (e.g., strangeness enhancement), the constant $J/\psi/D^0$ ratio implies that the specific mechanism of $J/\psi$ regeneration (observed in large QGP systems) is not active in $pp$ collisions, even at the highest multiplicities.
• Future Outlook: The results highlight the need for high-statistics, trigger-bias-free measurements in LHC Run 3 to further disentangle the effects of the underlying event from the hard scattering process.

In summary, this paper provides a comprehensive dissection of heavy-flavor production in high-multiplicity $pp$ collisions, demonstrating that while multiplicity correlations are strong, they are largely driven by event topology and parton shower dynamics rather than the formation of a thermalized medium capable of regenerating charmonia.