Measurement of $ψ(2S)$ to $J/ψ$ cross-section ratio as function of multiplicity in $p$Pb collisions at$\sqrt{s_{NN}} = 8.16$ TeV

Using LHCb data from $p$Pb and Pb$p$ collisions at $\sqrt{s_{NN}} = 8.16$ TeV, this study measures the $\psi(2S)$ to $J/\psi$ production ratio as a function of multiplicity, revealing a multiplicity-dependent suppression for prompt charmonia in the Pb-going direction that suggests the presence of additional mechanisms, potentially related to quark-gluon plasma formation, beyond standard comover effects.

The Gist

Imagine you are a detective trying to figure out what happens when two very different crowds collide. In this case, the "crowds" are subatomic particles: a single proton (a tiny, lonely traveler) smashing into a lead nucleus (a heavy, crowded city made of 200 protons and neutrons).

This paper, written by the LHCb collaboration at CERN, is about a specific mystery: How do heavy particles behave when they are born in these collisions, and does the size of the crowd around them change how they survive?

Here is the breakdown of the story, using simple analogies.

1. The Characters: The "Heavy Twins"

The scientists are studying two specific particles called charmonia. Think of them as heavy, exotic twins made of a "charm" quark and its anti-particle:

• J/ψ (J/Psi): The "Ground State." Think of this as the strong, sturdy twin. It's tightly bound together, like a rock glued with super-strong epoxy. It's hard to break apart.
• ψ(2S) (Psi-2S): The "Excited State." Think of this as the wobbly, fragile twin. It's the same type of particle, but it's vibrating with extra energy and is loosely bound, like a house of cards. It falls apart much easier if anything bumps into it.

2. The Experiment: The "High-Speed Crash"

The scientists fired protons at lead nuclei (and vice versa) at nearly the speed of light. They looked at two directions:

• pPb (Proton hitting Lead): The proton is the "bullet," and the lead is the "target." The debris flies mostly in the direction of the lead (the "Pb-going" direction).
• Pbp (Lead hitting Proton): The lead is the "bullet," and the proton is the "target." The debris flies mostly in the direction of the proton (the "p-going" direction).

They measured how many of the "fragile twins" (ψ(2S)) survived compared to the "sturdy twins" (J/ψ).

3. The Variable: The "Party Size" (Multiplicity)

The key to this experiment is multiplicity. In particle physics, this is just a fancy word for "how many other particles were created in the crash."

• Low Multiplicity: A small, quiet party. Only a few particles are flying around.
• High Multiplicity: A massive, chaotic mosh pit. Thousands of particles are flying everywhere.

The scientists wanted to see: Does the fragile twin die more often when the party gets bigger?

4. The Discovery: The "Forward-Backward" Mystery

The results were surprising and revealed a "split personality" in the data:

Scenario A: The Proton-Going Direction (The "Small System")
When the proton was the target (Pbp) or when looking at the proton side of the pPb collision:

• What happened: As the party got bigger (more particles), the ratio of fragile twins to sturdy twins stayed the same.
• The Analogy: Imagine a house of cards (fragile twin) and a rock (sturdy twin) in a room. As more people enter the room, the house of cards doesn't get knocked over any more than the rock does. The environment wasn't "hot" or "dense" enough to break the fragile one specifically.

Scenario B: The Lead-Going Direction (The "Big System")
When the lead nucleus was the target (pPb), specifically in the direction where the lead was heading:

• What happened: As the party got bigger, the fragile twins disappeared much faster than the sturdy ones. The ratio dropped significantly.
• The Analogy: Now, imagine that same house of cards and rock, but this time the room is filled with a boiling, super-dense fog (a "Quark-Gluon Plasma" or QGP). As the room gets more crowded, the fog becomes so thick and hot that it melts the house of cards, but the rock remains untouched.

5. The Big Conclusion: A "Mini-Black Hole" in a Small Room?

Usually, scientists only expect to see this "melting" effect in huge collisions, like smashing two giant lead nuclei together (PbPb), where a "soup" of free quarks and gluons (called Quark-Gluon Plasma) is formed. This soup is so hot it breaks apart the fragile particles.

The Shock: This paper suggests that even in a small collision (Proton vs. Lead), if you look in the right direction (the lead side) and the collision is "busy" enough (high multiplicity), you might be creating a tiny, short-lived drop of this super-hot plasma.

It's like finding a tiny, super-heated drop of lava in a snowball fight. You wouldn't expect lava in a snowball fight, but if the snowballs are packed tight enough, maybe a tiny bit of heat forms.

Why Does This Matter?

This helps us understand the transition between "small" and "large" worlds in physics.

• It tells us that the rules of the universe change depending on how crowded things get.
• It suggests that the "fragile" particles are excellent sensors. If they vanish, it means the environment got hot enough to melt them, hinting at the formation of a Quark-Gluon Plasma even in surprisingly small collisions.

In a nutshell: The scientists found that when a proton hits a lead nucleus, the "fragile" particles get crushed if the crash is messy and chaotic, but only if the crash happens in the direction of the heavy lead. This suggests that even small collisions can create tiny, super-hot "soups" of matter that we usually only see in the biggest crashes in the universe.

Technical Summary

1. Problem and Motivation

The production of heavy quarkonium states (such as charmonia $J/\psi$ and $\psi(2S)$) serves as a critical probe for understanding Quantum Chromodynamics (QCD) and the behavior of strongly interacting matter under extreme conditions.

• The Context: In heavy-ion collisions (e.g., PbPb), a Quark-Gluon Plasma (QGP) is formed, leading to the suppression of quarkonium states via mechanisms like Debye screening. However, the formation of QGP in smaller collision systems (proton-nucleus, pA) has been a subject of intense debate.
• The Specific Question: Recent observations suggest that high-multiplicity small systems might exhibit QGP-like effects. The $\psi(2S)$ state is more loosely bound than the $J/\psi$ ground state, making it more susceptible to dissociation. Therefore, the ratio of $\psi(2S)$ to $J/\psi$ production is a sensitive observable.
• The Goal: This study aims to measure the production ratio of prompt and non-prompt $\psi(2S)$ to $J/\psi$ as a function of charged-particle multiplicity in proton-lead (pPb) and lead-proton (Pbp) collisions. By comparing the two beam configurations (pPb vs. Pbp), the experiment investigates forward-backward asymmetries to distinguish between "cold nuclear matter" effects (initial state) and final-state interactions (such as comovers or QGP formation).

2. Methodology

Data and Detector:

• Experiment: LHCb detector at CERN, a single-arm forward spectrometer covering $2 < \eta < 5$.
• Dataset: Data collected in 2016 at a center-of-mass energy $\sqrt{s_{NN}} = 8.16$ TeV.
  • pPb configuration: 13.6 nb$^{-1}$ (proton beam moving forward).
  • Pbp configuration: 20.8 nb$^{-1}$ (lead beam moving forward).
• Kinematics: Measurements performed in the dimuon decay channel ($\mu^+\mu^-$) within the rapidity ranges $1.5 < y^* < 4.0$ (pPb) and $-5.0 < y^* < -2.5$ (Pbp).

Event Selection and Multiplicity:

• Candidates: Reconstructed $J/\psi$ and $\psi(2S)$ mesons with $p_T \in [0.3, 14.0]$ GeV/c.
• Multiplicity Variables: Three proxies for event multiplicity were used to avoid bias:
  1. $N_{\text{tracks}}^{\text{PV}}$: Total tracks associated with the primary vertex (PV).
  2. $N_{\text{fwd}}^{\text{PV}}$: Tracks in the forward direction (same side as charmonia).
  3. $N_{\text{bwd}}^{\text{PV}}$: Tracks in the backward direction (opposite side).
• Prompt vs. Non-prompt: Separation was achieved using the pseudo-decay time ($t_z$). Prompt mesons (directly produced) have $t_z \approx 0$, while non-prompt mesons (from $b$-hadron decays) have a broader distribution due to the $b$-hadron lifetime.

Analysis Technique:

• Signal Extraction: An extended two-dimensional unbinned maximum-likelihood fit was performed on the dimuon invariant mass ($m_{\mu\mu}$) and pseudo-decay time ($t_z$) distributions.
  • Mass models: Crystal Ball functions for signal, exponential for background.
  • $t_z$ models: Dirac $\delta$ (prompt) and exponential (non-prompt) convolved with resolution functions.
• Efficiency Correction: Yields were corrected for acceptance, reconstruction, particle identification (PID), and trigger efficiencies. The ratio of cross-sections was normalized to the integrated cross-section to cancel branching fractions and luminosity uncertainties.

3. Key Contributions

1. First Measurement of Multiplicity Dependence in Pbp: This paper provides the first detailed study of the $\psi(2S)/J/\psi$ ratio as a function of multiplicity specifically for the Pbp configuration (where the lead nucleus travels toward the detector).
2. Forward-Backward Asymmetry: By comparing pPb (proton-going direction) and Pbp (lead-going direction), the study isolates the role of the nuclear environment. The lead-going direction in Pbp corresponds to the same kinematic region as the proton-going direction in pPb, but with a significantly higher baryon density.
3. Disentanglement of Effects: The use of $N_{\text{bwd}}^{\text{PV}}$ (multiplicity measured opposite to the charmonium) allows the authors to disentangle "comover" effects (interactions with particles produced in the same rapidity region) from other suppression mechanisms.

4. Results

Prompt Production ($J/\psi$ and $\psi(2S)$ directly produced):

• pPb Configuration (Proton-going direction): A clear decreasing trend is observed in the normalized $\psi(2S)/J/\psi$ ratio as multiplicity increases.
  • Linear fit slope: $p_1 = -0.281 \pm 0.057$ (for $N_{\text{tracks}}^{\text{PV}}$).
  • The hypothesis of a constant ratio is strongly disfavored ($p\text{-value} \approx 5 \times 10^{-6}$).
  • This behavior is consistent with observations in $pp$ collisions and is attributed to comover interactions (final-state effects where excited states are dissociated by surrounding particles).
• Pbp Configuration (Lead-going direction): No significant dependence on multiplicity is found.
  • The ratio remains flat across the multiplicity range.
  • The linear fit slope is consistent with zero ($p_1 = -0.055 \pm 0.054$).
  • This result is distinct from $pp$ and pPb but aligns more closely with trends seen in large systems (PbPb) where QGP formation is expected.

Non-Prompt Production (from $b$-hadron decays):

• No significant multiplicity dependence was observed in either pPb or Pbp configurations. This is expected as the ratio largely cancels out variations in $b$-hadron production across multiplicity bins.

Comparison with Other Systems:

• When comparing the Pbp results to PbPb data (from ALICE), the Pbp suppression pattern (lack of multiplicity dependence in the ratio) resembles the PbPb behavior more than the pPb/$pp$ behavior. This suggests that the high baryon density in the lead-going direction of Pbp collisions creates an environment where additional suppression mechanisms (beyond comovers) are active.

5. Significance

• Evidence for QGP-like Effects in Small Systems: The absence of the expected multiplicity-dependent suppression in the Pbp configuration (lead-going) suggests that the suppression mechanisms observed in large heavy-ion collisions (likely related to QGP formation or strong color screening) may also be present in small systems when the nuclear density is sufficiently high.
• Transition from Small to Large Systems: The results highlight a transition in collision dynamics. The p-going direction behaves like a "small system" dominated by comover effects, while the Pb-going direction in Pbp collisions exhibits behavior characteristic of "large systems" where QGP-like effects may dominate.
• Theoretical Implications: These findings challenge models that attribute all suppression in pA collisions solely to cold nuclear matter effects or comovers. They support the hypothesis that high-multiplicity events in asymmetric collisions can create a transient, hot, and dense medium (a "droplet" of QGP) capable of suppressing excited quarkonium states.

In conclusion, this paper provides crucial experimental evidence that the suppression of charmonium states in proton-nucleus collisions is not uniform; it depends heavily on the direction of the collision and the resulting baryon density, offering a unique window into the onset of QGP formation in small collision systems.