⚛️ phenomenology

A multi-differential constraint map for quarkonium suppression mechanisms in high-multiplicity pp and pPb collisions

By analyzing $\Upsilon(nS)$ suppression in high-multiplicity $pp$ and $p$ Pb collisions through six differential constraints, this study rules out mechanisms driven solely by local track density or total multiplicity, instead supporting an early, globally correlated, topology-sensitive suppression pattern consistent with a deconfined, pre-hadronic environment.

Original authors: Renato Campanini

Published 2026-07-01

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CC BY 4.0

Original authors: Renato Campanini

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a high-energy particle collision (like those at the Large Hadron Collider) as a chaotic, high-speed dance floor. In the center of this dance floor, heavy particles called "quarkonium" are born. These particles are like delicate couples holding hands; some couples hold on very tightly (stable), while others are barely holding on (fragile).

The paper by Renato Campanini investigates a mystery: Why do the fragile couples break up more often when the dance floor gets crowded?

Usually, scientists thought this breakup happened because the fragile couples were getting bumped by the crowd right next to them. However, this paper acts like a detective, using six different "clues" to prove that the old theory is wrong and to point toward a new explanation.

Here is the breakdown of the investigation in simple terms:

The Old Theory: The "Local Bump"

The old idea was that if you have a fragile couple (quarkonium) and a bunch of other dancers (particles) are standing right next to them, the couple gets pushed apart. It's like a crowded elevator: if you are standing right next to a pushy person, you get squished.

The Paper's First Clue (The Cone Test):
The author looked at the data and asked: "Are the fragile couples breaking up more when there are more people standing immediately around them?"

The Result: No. The couples broke up at the same rate whether they were standing in an empty corner of the dance floor or in a dense crowd right next to them.
The Metaphor: It's like realizing that the couple isn't breaking up because of the person standing next to them, but because of something happening to the whole room.

The Second Clue: The "Shape of the Room"

If it's not the people next to the couple, maybe it's just the total number of people in the room?

The Test: The author looked at the shape of the crowd. Sometimes the crowd is a tight, focused line (like a jet of particles). Sometimes the crowd is spread out evenly in a circle (isotropic).
The Result: Even if the total number of people is the same, the fragile couples break up much more often in the "spread out" crowd than in the "tight line" crowd.
The Metaphor: Imagine 100 people in a room. If they are all huddled in one corner, the couple is fine. But if those same 100 people are spread out evenly around the couple, the couple breaks up. This proves that how the energy is arranged matters more than just the count of people.

The Third Clue: The "Fast Runner"

The author also checked how fast the couples were moving.

The Result: The faster the couple moves, the less likely they are to break up, even in a crowded room.
The Metaphor: If you run through a crowded room very fast, you spend less time getting bumped. If you walk slowly, you get bumped more. This suggests the "crowd" has a physical size and the couple has to cross it.

The Fourth Clue: The "Long-Range Whisper"

This is the most surprising clue. The author looked at collisions where the "dance floor" is a bit different (proton-lead collisions). They found that the breakup of the couple is correlated with activity happening far away on the other side of the room, not just near the couple.

The Metaphor: It's as if the couple breaks up because someone whispered something from the other side of the stadium, even though no one touched them. This means the "crowd" is connected globally, like a single nervous system, rather than just a pile of independent people.

The Conclusion: What is actually happening?

Based on these clues, the paper concludes that the breakup isn't caused by local bumps or just the total number of people. Instead, it suggests that:

It happens early: The breakup happens almost instantly after the collision, before the "dancers" (particles) have even fully formed into their final shapes.
It's a "soup": The environment isn't just a pile of separate particles; it's a dense, glowing, colored "soup" (a pre-hadronic medium) that fills the space.
It's sensitive to shape: This soup is denser and more effective at breaking up couples when the event is "round" and spread out, rather than "jet-like."

The "Scissors" Constraint

The author calls the combination of the first two clues the "Scissors Constraint."

Clue 1 (Cone): It's not about the people next to you.
Clue 2 (Sphericity): It's not just about the total number of people.
The Cut: Any theory that says "more local people = more breakup" is cut out. Any theory that says "more total people = more breakup" is also cut out.

The Final Verdict

The paper doesn't claim to have found a new particle or a new law of physics. Instead, it has built a map of constraints. It tells future scientists: "If you want to explain why these particles break up, your theory must pass all six of these tests. It must be global, it must happen early, and it must care about the shape of the event."

The evidence points toward a scenario where, for a tiny fraction of a second, the collision creates a tiny, dense, hot "droplet" of matter that behaves like a fluid, affecting the fragile particles before they even have a chance to settle down. This droplet is likely made of "colored" particles (quarks and gluons) that haven't yet turned into normal matter.

In short: The fragile particles aren't breaking up because they are being pushed by their neighbors; they are breaking up because the entire room is vibrating with a specific, early-stage energy that depends on the shape of the event, not just the crowd size.

Technical Summary: A Multi-Differential Constraint Map for Quarkonium Suppression Mechanisms

Problem Statement
The suppression of quarkonium states (specifically $\Upsilon(nS)$ and $\psi(2S)$ ) in high-multiplicity proton-proton ($pp$) and proton-lead ( $p$ Pb) collisions presents a fundamental question in high-energy nuclear physics: Can the observed multiplicity-dependent hierarchy of suppression be explained entirely by hadronic final-state mechanisms (such as local comover interactions) in a small system, or does the differential structure of the data necessitate additional early-time, non-local dynamics? While sequential suppression is a classic signature of color screening in a deconfined medium in heavy-ion collisions, its presence in small systems challenges the distinction between hadronic and partonic environments.

Methodology
This work does not present new experimental measurements or propose a new suppression model. Instead, it performs a constraint analysis using publicly available data from CMS and LHCb to determine the necessary physical properties of any successful suppression mechanism. The analysis synthesizes six complementary differential constraints:

Cone Isolation: Testing dependence on local track density ( $\Delta R < 0.5$ ) around the quarkonium.
Azimuthal-Sector Equivalence: Testing dependence on multiplicity in forward, transverse, and backward sectors relative to the quarkonium.
Transverse-Momentum Ordering: Analyzing how suppression strength varies with the quarkonium's $p_T$ .
Transverse Sphericity ( $S_T$ ): Comparing suppression in jet-like ( $S_T < 0.55$ ) versus isotropic ( $S_T > 0.85$ ) events at fixed multiplicity.
Forward- $E_T$ Long-Range Correlation: Examining suppression correlations with transverse energy measured at large rapidity gaps ( $|\eta| > 4$ ).
$p$ Pb/$Pb$p Forward-Backward Asymmetry: Contrasting suppression patterns in proton-going versus lead-going directions.

The core "scissors constraint" relies on published CMS $pp$ data at $\sqrt{s}=7$ TeV [18], with LHCb $pp$ data at 13 TeV [19, 20] and preliminary CMS $p$ Pb/light-ion results [2, 3] serving as supporting cross-system evidence.

Key Results and Constraints
The analysis establishes that no single-variable mechanism (controlled solely by local density or total multiplicity) can reproduce the full dataset. The specific constraints are:

Rejection of Local Density: The suppression ratios ( $R_{21}, R_{31}$ ) show no significant dependence on the charged-particle multiplicity inside a cone around the $\Upsilon$ direction. Events with empty cones and dense cones exhibit statistically compatible suppression trends. This disfavors mechanisms where dissociation probability scales strictly with the local hadron density near the quarkonium.
Rejection of Multiplicity-Only Models: At fixed total track multiplicity ( $N_{track}$ ), jet-like and isotropic events display significantly different suppression patterns. Isotropic events show a strong multiplicity dependence, while jet-like events show a near-flat trend. This demonstrates that event topology carries independent physical information beyond total multiplicity, ruling out models dependent solely on global $N_{track}$ .
Finite-Size and Early-Time Effects: The multiplicity dependence of suppression weakens as $\Upsilon$ $p_T$ increases, consistent with a finite-size escape effect where high- $p_T$ quarkonia traverse the active region in a shorter proper time. Furthermore, the correlation of suppression with forward transverse energy ( $E_T$ ) across a large rapidity gap ( $\Delta \eta \gtrsim 2$ ) in $p$ Pb collisions indicates a globally correlated mechanism rather than a local one.
Forward-Backward Asymmetry: In $p$ Pb collisions, the prompt $\psi(2S)/J/\psi$ ratio decreases with multiplicity in the proton-going direction but remains approximately flat (though suppressed) in the lead-going direction. This asymmetry challenges simple monotonic density-based pictures.

Key Contributions

The "Scissors" Constraint: The paper identifies a mutually exclusive set of observations: the suppression is insensitive to local density (cone test) but sensitive to global event topology (sphericity test). This simultaneously disfavors mechanisms controlled exclusively by local particle density and those controlled exclusively by total multiplicity.
Constraint Map: The work defines a rigorous, multi-dimensional benchmark that any viable microscopic description must satisfy simultaneously. To the author's knowledge, no published framework (including Comover Interaction Models, partonic CIM, pNRQCD/OQS, QGP droplet models, or SHINCHON hydrodynamics) has been explicitly tested against this complete set of six differential constraints.
Cross-System Consistency: The analysis demonstrates that the sequential suppression hierarchy and its dependence on event activity are continuous across $pp$, $p$ Pb, and light-ion (O-O, Ne-Ne) collisions when plotted against corrected multiplicity, supporting global event activity as a universal ordering variable.

Significance and Claims
The paper claims to provide a data-driven constraint map that narrows the viable parameter space for quarkonium suppression mechanisms.

Level 1 (Direct Constraints): The data disfavor local-density dissociation, purely multiplicity-driven suppression, and purely rapidity-local mechanisms.
Level 2 (Strong Inference): Any viable mechanism must be global, topology-dependent, and finite-size sensitive. Combined with formation-time arguments ( $\tau_{form} \lesssim 0.5$ fm), the suppression must act in an early, pre-hadronic environment.
Level 3 (Interpretive Context): The constraints are compatible with a dense, colored, pre-hadronic medium (potentially involving a deconfined stage) active at early times ( $\tau \lesssim 0.5$ fm). This interpretation is supported by the coincidence of the suppression onset with a qualitative change in soft-sector behavior (equation-of-state proxy) identified in independent analyses [35] and by other signatures of collectivity (strangeness enhancement, long-range ridges, flow splitting) in the same multiplicity window.

Modesty and Limitations
The authors explicitly state that this work does not identify a unique surviving model nor does it claim that any individual observable constitutes proof of deconfinement. The interpretation of a partonic medium is presented as a "physically natural description" consistent with the data, but alternative frameworks remain viable if they can satisfy the full constraint set. The paper acknowledges that the sphericity dependence could theoretically be influenced by $p_T$ composition biases, noting that a definitive separation requires a triple-differential measurement ( $R_{n1}$ vs. $N_{track}$ , $S_T$ , and $p_T$ ) which is currently absent. The core conclusions, however, rest on the robust cone-isolation and forward-backward asymmetry constraints which are independent of this caveat.