Production of $\Xi$ and $\Omega$ hyperons in high-multiplicity proton-proton collisions at $\sqrt{s}$ = 13 TeV

This paper presents the first measurements of $\Xi$ and $\Omega$ hyperon production in high-multiplicity proton-proton collisions at $\sqrt{s} = 13$ TeV, revealing a strong correlation between multi-strange hadron yields and final-state multiplicity that extends to the highest multiplicities in pp collisions and is better described by state-of-the-art models incorporating string interactions and collective expansion.

The Gist

The Big Picture: Crashing Tiny Cars to Find Hidden Gems

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle accelerator. It smashes protons (tiny subatomic particles) together at nearly the speed of light. Usually, when you smash two protons together, it's like a gentle tap between two ping-pong balls. They bounce off, and you get a few scattered pieces.

But sometimes, the collision is a "glitch" in the system—a rare, high-energy event where the protons hit each other so hard and so densely that they create a chaotic, crowded mess. This paper is about studying those rare, high-density crashes in proton-proton (pp) collisions.

The scientists wanted to see if, in these super-crowded proton crashes, they could find strange particles (specifically called $\Xi$ and $\Omega$ hyperons) in the same way they do in massive collisions between heavy atoms (like Lead-Lead collisions).

The Analogy: The Party Room

To understand what they found, let's use a party analogy:

1. The Minimum-Bias Party (Normal Proton Collisions): Imagine a small gathering in a living room. There are maybe 10 people. It's easy to move around. If you look for a specific rare guest (let's call them "Mr. Strange"), you probably won't find them, or you'll only find one if the host is lucky.
2. The Heavy-Ion Party (Lead-Lead Collisions): Now imagine a massive stadium packed with 100,000 people. It's a mosh pit. In this chaos, "Mr. Strange" is everywhere. Scientists have known for a long time that in these massive, crowded stadiums, strange particles are produced in huge numbers. This is called "Strangeness Enhancement."
3. The New Discovery (High-Multiplicity Proton Collisions): The ALICE team asked a crazy question: What if we take our tiny living room (proton-proton) and somehow cram 30 people into it? That's what this paper does. They used special triggers to find the rare proton crashes that are four times more crowded than a normal one, making them as crowded as the edge of that massive stadium.

The Experiment: Hunting for "Multi-Strange" Guests

The scientists were looking for two specific types of particles:

• $\Xi$ (Xi): A particle with two "strange" quarks.
• $\Omega$ (Omega): A particle with three "strange" quarks.

Think of "strange quarks" as a rare flavor of ice cream. In a normal proton crash (the small living room), you almost never get the rare flavor. But in the massive stadium (Lead-Lead), you get a whole sundae bar.

The Question: If we make the small living room just as crowded as the stadium, will we suddenly start seeing the ice cream sundae bar too?

The Answer: Yes.
The paper confirms that in these super-crowded proton crashes, the production of these strange particles skyrockets. The more crowded the crash, the more strange particles appear. This proves that the "size" of the collision (whether it's a tiny proton or a giant lead nucleus) doesn't matter as much as the crowd density. If the room is packed, the physics behaves the same way.

The Twist: The "Hard" vs. "Soft" Collision

Here is where it gets interesting. The scientists compared these crowded proton crashes to crowded Lead-Proton crashes (which are like a small car hitting a truck).

• The Finding: Even though the number of particles was the same in both cases, the energy of the particles was different.
• The Analogy: Imagine two parties with the same number of people.
  • Party A (Lead-Proton): Everyone is dancing slowly and smoothly.
  • Party B (High-Multiplicity Proton): Everyone is jumping up and down, bouncing off the walls with high energy.
• The Result: The particles in the crowded proton crashes were moving faster (had higher "transverse momentum") than those in the Lead-Proton crashes. This suggests that getting that many particles in a tiny proton requires a much more violent, energetic "push" than getting them in a larger system.

The Models: Trying to Predict the Chaos

The scientists then asked their computer models (the "crystal balls" of physics) to predict what would happen.

1. The Old Model (PYTHIA8 Monash): This model is like a recipe book that assumes particles are just independent people bumping into each other. It failed miserably. It predicted very few strange particles, completely missing the "sundae bar" effect.
2. The Newer Model (PYTHIA8 with Ropes): This model added a new rule: "Strings" (the forces holding particles together) can overlap and interact, like tangled jump ropes. This helped! It predicted more strange particles, getting closer to reality, but still not perfect.
3. The Advanced Model (EPOS4): This model treats the collision like a fluid that expands. It did the best job of describing the shape of the data, though it still slightly underestimated the total numbers.

The Takeaway: The fact that the "Ropes" and "Fluid" models worked better tells us that in these tiny, crowded proton crashes, the particles aren't just bouncing off each other; they are interacting in a collective, fluid-like way, similar to what happens in massive nuclear explosions.

Why Does This Matter?

This paper is a big deal because it blurs the line between "small" and "large" systems.

• Old Thinking: Strange particles are only made in massive nuclear collisions (like Lead-Lead) because they create a "Quark-Gluon Plasma" (a soup of free quarks).
• New Thinking: You don't need a massive stadium to make this soup. If you pack a tiny proton room tightly enough, you get the same effect.

It suggests that the universe has a universal rule: Density is king. If you pack enough energy and matter into a small space, the laws of physics change, and you get the exotic "strange" particles, regardless of whether you started with a tiny proton or a giant lead nucleus.

Summary in One Sentence

The ALICE team proved that by cranking up the density in tiny proton collisions, they can recreate the exotic "strange particle" production usually seen only in massive nuclear collisions, showing that crowdedness, not size, is the secret ingredient to creating these rare particles.

Technical Summary

1. Problem and Motivation

The primary goal of this research is to investigate the mechanism of strangeness enhancement in high-energy collisions. Historically, the enhanced production of strange hadrons (relative to non-strange hadrons) was considered a signature of Quark-Gluon Plasma (QGP) formation in large nucleus-nucleus (A–A) collisions. However, recent observations at the LHC revealed a similar enhancement in small systems (proton-proton and proton-lead collisions) as a function of final-state charged-particle multiplicity.

The specific scientific problem addressed here is to extend these measurements to the highest multiplicities achievable in proton-proton (pp) collisions to determine:

• Whether the correlation between strangeness production and multiplicity holds at extreme multiplicities in small systems.
• If the production mechanisms in high-multiplicity pp collisions converge with those in peripheral heavy-ion collisions (where system sizes differ vastly but multiplicities are similar).
• How state-of-the-art QCD-inspired models (PYTHIA8, EPOS4) describe strange baryon production in these extreme conditions.

2. Methodology

Data Sample and Selection:

• Collision System: Proton-proton (pp) collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV.
• Dataset: Data collected by the ALICE detector during LHC Run 2 (2016–2018).
• Trigger Strategy: A dedicated High-Multiplicity (HM) trigger was used. Events were selected based on the signal amplitude in the V0 detectors (V0A and V0C), corresponding to the top 0–0.1% of minimum-bias events.
• Multiplicity Scale: The selected events have an average charged-particle multiplicity per unit of rapidity at midrapidity ($\langle dN_{ch}/d\eta \rangle$) of approximately 30. This is:
  • ~4 times higher than minimum-bias pp collisions.
  • ~2 times higher than minimum-bias p–Pb or peripheral Pb–Pb collisions.
• Event Classes: The data was divided into three multiplicity classes (I, II, III) corresponding to 0.00–0.01%, 0.01–0.05%, and 0.05–0.10% centrality intervals.

Reconstruction and Analysis:

• Particles Studied: Multi-strange hyperons $\Xi^-$, $\bar{\Xi}^+$, $\Omega^-$, and $\bar{\Omega}^+$.
• Decay Channels:
  • $\Xi \to \Lambda + \pi$ (with $\Lambda \to p + \pi$).
  • $\Omega \to \Lambda + K$ (with $\Lambda \to p + \pi$).
• Detector Usage:
  • ITS (Inner Tracking System): For precise vertexing and primary vertex determination.
  • TPC (Time Projection Chamber): For track reconstruction and particle identification via specific energy loss ($dE/dx$).
  • TOF (Time of Flight): To reject out-of-bunch pileup and aid in particle identification.
• Selection Criteria: Strict topological cuts were applied (e.g., decay radius, pointing angle, distance of closest approach) to isolate the weak decay vertices from the primary interaction vertex.
• Yield Extraction: Invariant mass distributions were fitted with a Gaussian signal plus a linear background. Yields were corrected for acceptance and efficiency using a Monte Carlo simulation based on PYTHIA8.2 (Monash 2013 tune).
• Systematic Uncertainties: Evaluated for track selection, signal extraction, material budget, pileup rejection, and efficiency dependence on multiplicity.

3. Key Contributions

• First Measurement at Extreme Multiplicity: This is the first measurement of $\Xi$ and $\Omega$ yields in pp collisions with $\langle dN_{ch}/d\eta \rangle \approx 30$, pushing the boundaries of what has been observed in small collision systems.
• System Size Independence: The study provides robust evidence that strange-to-non-strange hadron ratios depend primarily on final-state multiplicity, regardless of whether the collision system is small (pp) or large (Pb–Pb).
• Model Benchmarking: The results serve as a critical benchmark for modern event generators, specifically testing the impact of "string interactions" (Ropes) and "collective expansion" (EPOS4 core-corona) on strange baryon production.

4. Key Results

Transverse Momentum ($p_T$) Spectra:

• The $p_T$ spectra of $\Xi$ and $\Omega$ become "harder" (shifted to higher $p_T$) as multiplicity increases.
• Model Comparison:
  • PYTHIA8.2 (Monash 2013): Significantly underestimates yields (by 50–90%) and fails to describe the spectral shape.
  • PYTHIA8.2 (with Ropes): Improves the description at low $p_T$ due to overlapping string interactions but underestimates yields at intermediate/high $p_T$ and predicts spectra that are too soft.
  • EPOS4: Provides the best description of the spectral shape, particularly for $\Omega$, though it still underestimates yields at high $p_T$ ($>5$ GeV/c).

Mean Transverse Momentum ($\langle p_T \rangle$):

• $\langle p_T \rangle$ increases with charged-particle multiplicity for both hyperons.
• Crucial Divergence: In the high-multiplicity region ($\langle dN_{ch}/d\eta \rangle > 20$), the $\langle p_T \rangle$ in pp collisions is significantly larger (by at least $4\sigma$ for $\Omega$ and $6\sigma$ for $\Xi$) than in p–Pb collisions at similar multiplicities. This suggests that high multiplicity in small systems arises from harder initial interactions with higher energy density compared to p–Pb.

Integrated Yields and Ratios:

• Yields: The $p_T$-integrated yields increase smoothly with multiplicity. At a given multiplicity, yields in pp, p–Pb, and Pb–Pb collisions are consistent within uncertainties, confirming that production is driven by multiplicity, not system size.
• Strangeness Enhancement ($\Xi/\pi$ and $\Omega/\pi$ ratios):
  • The ratios increase with multiplicity and are consistent across all collision systems (pp, p–Pb, Pb–Pb) at the same multiplicity.
  • The data shows a trend toward saturation in central Pb–Pb collisions. In high-multiplicity pp, the ratios continue to rise but are consistent with the saturation values seen in Pb–Pb, suggesting the mechanism is universal.
  • Model Performance: EPOS4 and the Thermal FIST model reproduce the increasing trend of the ratios well. PYTHIA8.2 with Ropes underestimates the ratios by $\sim 2\sigma$, while the standard Monash tune fails completely.

5. Significance

This paper fundamentally advances the understanding of particle production in high-energy physics by:

1. Validating Universality: It confirms that the correlation between strangeness enhancement and final-state multiplicity is a universal feature of QCD matter, independent of the initial collision system size.
2. Challenging Models: It highlights that while mechanisms like "color ropes" (in PYTHIA) and "collective expansion" (in EPOS4) improve the description of strange hadrons, current models still struggle to fully reproduce the magnitude of yields and the spectral hardness at the highest multiplicities.
3. Probing Initial States: The observed difference in $\langle p_T \rangle$ between high-multiplicity pp and p–Pb collisions suggests that the path to high multiplicity differs: pp collisions likely involve harder, more energetic initial partonic interactions, whereas p–Pb may involve different geometric or collective effects.
4. Future Outlook: The results set the stage for Run 3 data, which will offer a sample 20 times larger, potentially revealing if the strangeness ratios in pp collisions eventually exceed the thermal limits observed in heavy-ion collisions.