Sequential Y(nS) suppression in high-multiplicity pp collisions: the experimental case for an early, globally correlated medium

This paper argues that the observed sequential suppression of $\Upsilon(n\mathrm{S})$ and $\psi(2S)$ states in high-multiplicity $pp$ collisions cannot be explained by standard hadronic or string-based models, but instead provides compelling evidence for the formation of an early, globally correlated partonic medium.

The Gist

Imagine you are a detective trying to solve a mystery at a massive, chaotic party. The party is a collision between two protons (tiny particles) at the Large Hadron Collider. Usually, when two protons smash into each other, they just bounce off and scatter a few crumbs (particles). But in the rare, high-energy crashes where the room gets incredibly crowded (high multiplicity), something strange happens.

The mystery involves heavy "guests" called Quarkonium (specifically the $\Upsilon$ family). Think of these as three siblings:

• $\Upsilon(1S)$: The tough, muscular older brother. He's very tightly bound and hard to break.
• $\Upsilon(2S)$: The middle sibling. A bit weaker.
• $\Upsilon(3S)$: The fragile, delicate baby. He's held together by a very weak glue.

The Mystery:
In these crowded proton collisions, the scientists noticed that the "baby" sibling ($\Upsilon(3S)$) disappears almost completely, the middle one ($\Upsilon(2S)$) gets hurt a lot, but the tough older brother ($\Upsilon(1S)$) mostly survives. This is called sequential suppression.

The big question is: Why?
Is it because the room is just full of other guests bumping into them (a "hadronic" explanation)? Or is it because a tiny, super-hot, liquid-like "soup" formed in the middle of the room that melted the fragile guests (a "partonic" explanation)?

The author of this paper, Renato Campanini, acts like a master detective who sets up four specific traps (tests) to catch the culprit. Here is how he solves it using simple analogies:

The Four Traps (Tests)

1. The "Local Crowd" Trap (Cone Isolation)

• The Theory: If the guests are being knocked out by random people bumping into them, then the fragile baby should disappear only if he is standing right in the middle of a dense crowd. If he is standing in an empty corner, he should be safe.
• The Reality: The data shows that the baby disappears just as much whether he is in a dense crowd or an empty corner.
• The Verdict: It's not just random bumps from nearby people. The danger is coming from everywhere, not just the immediate neighborhood.

2. The "Direction" Trap (Azimuthal Sectors)

• The Theory: If the danger comes from people standing in front of the guest, then guests facing a crowd should be in trouble, but guests facing away should be safe.
• The Reality: It doesn't matter which way the guest is facing. Even if the crowd is behind him, he still melts.
• The Verdict: The danger isn't coming from a specific direction. It's a global effect.

3. The "Shape" Trap (Sphericity)

• The Theory: Imagine two types of parties.
  • Party A: Everyone is running in straight lines (Jet-like).
  • Party B: Everyone is dancing in a circle, filling the whole room (Isotropic).
  • If the danger is just about "how many people are there," the fragile guest should melt the same amount in both parties.
• The Reality: The guest melts only in Party B (the round, crowded dance floor). In Party A (the straight lines), he survives.
• The Verdict: The danger depends on the shape of the crowd, not just the number of people. This suggests a fluid-like medium that forms when the room is filled uniformly, not just when people are rushing through.

4. The "Timing" Trap (Prompt vs. Non-Prompt)

• The Theory: Some guests arrive early (Prompt), and some arrive late because they are carried by a slow-moving delivery truck (Non-Prompt).
• The Reality: The early guests get melted. The late guests (who arrive after the initial chaos has settled) are perfectly fine.
• The Verdict: The "killer" must be active for a split second right at the start of the collision. If it were a slow, lingering danger, the late guests would be hurt too.

The Culprit: A Tiny, Hot Soup

When you combine all four clues, the "random bumping" theory (Hadronic models) falls apart. It can't explain why the direction, shape, and timing matter so much.

The only explanation that fits all the clues is that a tiny, super-hot, liquid-like droplet of "partonic soup" (a mini Quark-Gluon Plasma) forms instantly.

• Why it fits: This soup is everywhere at once (Global), it forms instantly (Early), and it acts like a fluid that changes based on how the room is filled (Shape).
• The "Baby" melts: The soup is hot enough to break the weak glue holding the baby together.
• The "Tough Brother" survives: The soup isn't hot enough to break the strong glue of the older brother.
• The "Late Guests" are safe: By the time the delivery truck arrives, the soup has already evaporated.

Why Don't We See "Jet Quenching"?

You might ask: "If there is a hot soup, why don't we see high-speed jets (like bullets) getting stopped?"

The Analogy: Imagine a mosquito flying through a room full of fog.

• The Jets: A mosquito is tiny and fast. If the fog is thin, the mosquito flies right through without noticing. In proton collisions, the "soup" is so small and short-lived that it's like a thin mist to a fast jet. The jet doesn't lose enough energy to be noticed.
• The Quarkonium: The fragile "baby" guest is like a piece of tissue paper. Even a thin mist is enough to dissolve it.

The Big Picture

This paper argues that even in the smallest collision system (proton-proton), nature is capable of creating a tiny, fleeting drop of the same "primordial soup" that existed microseconds after the Big Bang.

The evidence isn't just one thing; it's a "scissors" of constraints. The "random bumping" theory gets cut off by the cone test, and the "global number" theory gets cut off by the shape test. The only thing left standing is the idea of a tiny, early, partonic medium.

It's like finding a puddle of water in a desert and realizing, through careful measurement, that it wasn't a leak from a hose (local) or a cloud (global), but a tiny, self-contained rainstorm that formed and vanished in a split second.

Technical Summary

1. Problem Statement

The central question addressed is the origin of the sequential suppression of excited bottomonium states ($\Upsilon(nS)$) observed in high-multiplicity proton-proton ($pp$) collisions at the LHC.

• The Phenomenon: CMS (at $\sqrt{s}=7$ TeV) and LHCb (at $\sqrt{s}=13$ TeV) have measured a monotonic decrease in the production ratios $R_{21} = \Upsilon(2S)/\Upsilon(1S)$ and $R_{31} = \Upsilon(3S)/\Upsilon(1S)$ as the charged-particle multiplicity ($N_{track}$) increases. This follows the expected hierarchy where loosely bound states ($\Upsilon(3S)$) melt before tightly bound ones ($\Upsilon(1S)$).
• The Conflict: In standard textbook physics, $pp$ collisions should not form a collective medium (like the Quark-Gluon Plasma, QGP, seen in heavy-ion collisions). Three competing explanations exist for this suppression:
  1. Hadronic Final-State Scattering (Comover Interaction Model - CIM): Dissociation via inelastic scattering with soft hadrons produced in the same rapidity region.
  2. Initial-State/String Effects: Modifications to the production step via Color Glass Condensate (CGC) or Rope Hadronization (enhanced string tension).
  3. Partonic Medium: A transient, short-lived droplet of deconfined matter causing color screening before the quarkonium forms.

The paper argues that existing hadronic and string-based models fail to explain the differential structure of the data, pointing instead toward a partonic medium.

2. Methodology: Multi-Differential Constraints

The author employs a rigorous "scissors constraint" approach, subjecting the data to four independent differential tests and one temporal test. The goal is to falsify mechanisms that cannot simultaneously satisfy all constraints.

Key Observables and Tests:

1. Cone Isolation (Local Density Test):

   • Method: Events are split based on the number of tracks inside a cone ($\Delta R < 0.5$) around the $\Upsilon$.
   • Prediction: If suppression is driven by local hadronic scattering (CIM), events with a "dense cone" should show significantly stronger suppression than "empty cone" events.
   • Result: The data shows no statistically significant difference between empty and dense cones.
   • Implication: Local hadronic scattering is ruled out.

2. Azimuthal Sectors (Near-Side Test):

   • Method: Suppression is measured relative to the azimuthal angle of tracks (forward, transverse, backward) relative to the $\Upsilon$.
   • Prediction: Local mechanisms should depend on proximity (forward tracks).
   • Result: Suppression scales identically with multiplicity in all sectors, including the "backward" sector (geometrically far from the $\Upsilon$).
   • Implication: The driving variable is a global property of the event, not local proximity.

3. Transverse Sphericity (Topology Test):

   • Method: At fixed $N_{track}$, events are separated into "jet-like" (low sphericity, $S_T < 0.55$) and "isotropic" (high sphericity, $S_T > 0.85$).
   • Prediction: Mechanisms depending only on total multiplicity (Global CIM, standard CGC, pure MPI) should yield identical suppression for both topologies.
   • Result: A massive discrepancy exists. Jet-like events show flat suppression (no dependence on $N_{track}$), while isotropic events show strong sequential suppression.
   • Implication: Any model relying solely on $N_{track}$ (without topology dependence) is falsified.

4. $p_T$-Dependent Escape (Kinematic Test):

   • Method: Analyzing the survival ratio as a function of the $\Upsilon$ transverse momentum ($p_T$).
   • Result: Suppression weakens as $p_T$ increases; at high $p_T$, the ratio becomes flat.
   • Implication: High-momentum quarkonia escape the medium before it dissociates them (kinematic escape), implying a finite-size medium with a finite lifetime.

5. Temporal Constraint (Non-Prompt Flatness):

   • Method: LHCb data separates prompt quarkonia (produced at the primary vertex) from non-prompt quarkonia (from displaced $b$-hadron decays, $\sim 450 \mu m$ away).
   • Result: Prompt $\psi(2S)/J/\psi$ ratios show suppression; non-prompt ratios are flat across all multiplicities.
   • Implication: The suppression mechanism must act at early proper times (pre-resonance stage, $< 1$ fm/c), before the $b$-hadron decays. Late-stage hadronic rescattering is ruled out.

3. Key Contributions and Results

Falsification of Existing Frameworks:
The paper systematically evaluates published models against the five constraints (Table 1 in the paper):

• Local CIM: Fails the Cone and Sphericity tests.
• Global CIM (density $\propto N_{track}$): Fails the Sphericity test (cannot explain why jet-like events don't suppress).
• Rope Hadronization / PYTHIA MPI: Fails the Sphericity test (cannot reproduce the jet-like vs. isotropic gap) and lacks a native $p_T$-escape mechanism.
• CGC (Initial State): Fails the Sphericity test (standard saturation scales depend on global density, not topology).
• Two-Component Models (TCM): Fail to simultaneously fit the cone equality and sphericity gap without fine-tuning that lacks predictive power.

The Surviving Mechanism:
The only class of mechanisms consistent with all constraints is an early, globally correlated medium with partonic degrees of freedom.

• It acts globally (explaining sphericity dependence).
• It acts early (explaining non-prompt flatness).
• It is finite in size (explaining $p_T$ escape).
• It is not driven by local hadron density (explaining cone independence).

Consistency with Other Observables:
The onset of $\Upsilon$ suppression ($dN_{ch}/d\eta \approx 4-6$) coincides with:

• Strangeness Enhancement: A known QGP signature.
• The "Ridge": Long-range correlations indicating early-time gluon field interactions.
• Partonic Flow: At higher multiplicities, ALICE observes baryon-meson $v_2$ grouping, a fingerprint of partonic collectivity.

Energy Density Estimate:
A Bjorken-type estimate for the highest multiplicities yields an energy density $\epsilon_{BJ} \approx 1.7$ GeV/fm$^3$ and temperature $T \approx 180$ MeV. This sits above the lattice-QCD deconfinement crossover ($\sim 0.5$ GeV/fm$^3$) but below the threshold where jet quenching would be observable.

4. Significance and Conclusion

Why Jet Quenching is Absent:
The paper resolves the apparent paradox of why jet quenching is not seen in $pp$ despite the presence of a medium.

• Path Length: The medium in $pp$ is small ($L \sim 1-2$ fm) compared to PbPb ($L \sim 5-6$ fm). Radiative energy loss scales as $L^2$, making the effect in $pp$ roughly 1/25th to 1/36th of that in heavy ions (hundreds of MeV vs. tens of GeV), falling below current detection thresholds.
• Sensitivity: While too weak to quench high-$p_T$ jets, the medium is dense enough to dissolve loosely bound quarkonia ($\Upsilon(3S)$ binding energy $\sim 200$ MeV).

Conclusion:
The paper concludes that the sequential suppression of $\Upsilon(nS)$ in high-multiplicity $pp$ collisions is not driven by ordinary hadronic final-state interactions or initial-state string effects. Instead, the multi-differential data provides strong evidence that the smallest collision systems at the LHC produce a transient, partonic-like medium (a "droplet") that exhibits color screening and collective behavior. This finding bridges the gap between small-system collectivity and heavy-ion QGP physics, suggesting that deconfinement effects emerge at much lower multiplicities than previously thought.

Impact:
This work serves as a "constraint map" for future theoretical models, demanding that any successful explanation of small-system collectivity must incorporate early-time, global, partonic degrees of freedom that are sensitive to event topology and kinematic escape, while remaining invisible to standard jet quenching measurements.