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Strangeness enhancement at its extremes: multiple (multi-)strange hadron production in pp collisions at $\mathbf{\sqrt{\textit{s}} = 5.02}$ TeV

This ALICE study at $\sqrt{s} = 5.02$ TeV introduces a novel event-by-event counting technique to measure the full probability distribution of strange and multi-strange hadron production in proton-proton collisions, revealing that this approach significantly enhances the sensitivity to distinguish between different underlying physics mechanisms in state-of-the-art Monte Carlo models compared to traditional mean-value analyses.

Original authors: ALICE Collaboration

Published 2026-09-25

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CC BY 4.0

Original authors: ALICE Collaboration

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

In the subatomic world, matter is not a solid, unchanging thing but a dynamic soup of tiny constituents called quarks. Most of the matter we see around us is made of "up" and "down" quarks, which are relatively light and easy to produce. However, nature also contains heavier cousins known as "strange" quarks. When particles collide at incredibly high speeds, these strange quarks can be created and then immediately bind together with other quarks to form new particles called hadrons. For decades, physicists have observed a curious phenomenon: when heavy atomic nuclei smash into each other, strange particles appear far more often than they do when lighter particles collide. This "strangeness enhancement" was originally thought to be a unique signature of a state of matter called the quark-gluon plasma, a hot, dense fluid that existed just moments after the Big Bang. Yet, in recent years, scientists have found that even when simple protons collide, strange particles appear more frequently if the collision is violent enough to produce a large number of other particles. This has sparked a debate about whether the rules governing these tiny collisions are fundamentally different from what we expect, or if our current models of how particles form are missing a crucial piece of the puzzle.

To settle this, researchers from the ALICE Collaboration at CERN's Large Hadron Collider turned their attention to proton-proton collisions at a specific energy of 5.02 TeV. Instead of simply counting the total number of strange particles produced across millions of crashes and calculating an average, they adopted a much more granular approach. They looked at individual collision events one by one, asking a specific question: in a single crash, exactly how many strange particles were created? By sorting these events based on how crowded they were with other particles, the team mapped out the probability of finding zero, one, two, or even more strange particles in a single event. This method allowed them to probe the extremes of particle production, looking at rare events where a single collision might produce a handful of strange particles, or conversely, events with a high number of total particles but very few strange ones.

The results revealed a landscape of particle production that is far more complex than a simple average could ever show. The researchers found that the likelihood of producing multiple strange particles in a single event rises sharply as the overall number of particles in the collision increases. They were able to measure the probability of finding up to seven neutral kaons, five lambda particles, four cascades, and two omega particles in a single event. When they calculated the average number of these particle groups produced per event, they discovered that the production of multiple strange particles does not just increase linearly; it accelerates. The more crowded the collision, the more likely it is to produce pairs, triplets, or even larger groups of these strange particles. This behavior is a direct measure of how the strange quarks, once created, decide to group together.

A critical part of the study involved testing whether this behavior was driven purely by the number of strange quarks or if other factors, such as the total mass of the particles or the number of protons and neutrons involved, played a role. The team compared the production of different combinations of particles that contained the same total number of strange quarks but differed in their other ingredients. For instance, they looked at events containing three strange quarks arranged as a single heavy particle versus three lighter particles. They found that the enhancement pattern is dominated by the strangeness-content imbalance between the particles being compared. However, the study also uncovered a significant secondary effect: when comparing particles with the same number of strange quarks but different amounts of lighter "up" and "down" quarks, a distinct trend emerged. In collisions with fewer total particles, the formation of heavy particles containing strange quarks seemed slightly favored over lighter combinations. As the collisions became more crowded, this preference shifted, making it easier for the strange quarks to pair up with the abundant light quarks to form lighter particles. This demonstrates that while strangeness content is the primary driver, a sub-leading role is also played by the availability of light u and d quarks, which influences how strange quarks decide to assemble.

To understand what drives these patterns, the researchers compared their data against the most advanced computer simulations used in the field. The standard models, which rely on basic rules of particle physics, failed to reproduce the steep rise in multiple strange particle production. They predicted far fewer groups of strange particles than were actually observed. However, a more sophisticated version of the simulation, which included complex interactions between the color fields of the quarks and a mechanism that allows them to reconnect in dense environments, matched the data much more closely. Another model, which treats the collision as a mix of a hot, fluid-like core and a cooler outer region, also performed well at high densities but struggled to explain the behavior in less crowded collisions.

The findings suggest that the rules governing how strange particles form are not static but depend heavily on the density of the collision. The fact that the most advanced models can only partially reproduce the data indicates that our understanding of how quarks bind together in these extreme conditions is still evolving. By moving beyond simple averages and looking at the specific combinations of particles in individual events, the ALICE team has provided a new, sharper lens through which to view the fundamental forces that shape matter. The results do not just confirm that strange particles are enhanced in busy collisions; they reveal the intricate dance of probabilities that dictates exactly how those particles choose to form, offering a stringent new test for the theories that describe the universe at its smallest scale.

Technical Summary: Strangeness Enhancement at its Extremes in pp Collisions at $\sqrt{s} = 5.02$ TeV

Problem and Motivation
Strange-hadron production is a critical observable for understanding non-perturbative quantum chromodynamics (QCD) and the hadronization phase of colored systems. Historically, an enhanced production rate of multi-strange particles in heavy-ion collisions compared to hadronic collisions was proposed as a signature of the Quark-Gluon Plasma (QGP). While statistical hadronization models (SHM) successfully describe strangeness in heavy-ion collisions, the origin of strangeness enhancement (SE) in small collision systems (pp and p–Pb) remains uncertain. Previous ALICE measurements established that strange-to-pion yield ratios increase with charged-particle multiplicity density ( $\langle dN_{ch}/d\eta \rangle$ ), challenging the notion of pure in-vacuum hadronization. However, these measurements have been limited to the mean of the strange-particle multiplicity distribution. The origin of SE and the interplay between strange and non-strange hadron formation mechanisms require a probe beyond the average, specifically investigating events with extreme imbalances between strange and non-strange content.

Methodology
This analysis utilizes a large-statistics dataset of proton-proton collisions at $\sqrt{s} = 5.02$ TeV collected by the ALICE experiment during LHC Run 2 (2017). The study introduces a novel analysis technique: instead of measuring average yields, it determines the probability $P(n_S)$ of observing a specific number ( $n_S$ ) of strange particles per event.

Event Selection and Categorization: Events are selected based on a Minimum Bias (MB) trigger and categorized into charged-particle multiplicity density classes using the V0M estimator (forward pseudorapidity). The analysis covers the INEL > 0 class and specific V0M percentile classes ranging from low to high multiplicity.
Candidate Reconstruction: Strange hadrons ( $K^0_S$ , $\Lambda$ , $\bar{\Lambda}$ , $\Xi^-$ , $\bar{\Xi}^+$ , $\Omega^-$ , $\bar{\Omega}^+$ ) are reconstructed via their weak-decay topologies in the midrapidity region ( $|y| < 0.5$ ). Strict topological and particle identification (PID) criteria are applied to suppress combinatorial background.
Event-by-Event Counting and Weighting: A key innovation is the event-by-event counting of strange-particle candidates. Each candidate is assigned a signal weight ( $w_S$ ) based on its invariant mass, transverse momentum ( $p_T$ ), and the event's multiplicity, derived from fits to the invariant-mass distributions.
Probability Distribution Extraction: For each event with $N$ candidates, the probability distribution of having $M$ true signals (and $N-M$ background) is calculated by summing all combinations of signal/background weights. This yields a raw multiplicity distribution $P_{raw}(n_S)$ .
Unfolding and Corrections: The raw distribution is corrected for detector acceptance, efficiency, and trigger inefficiencies using a one-dimensional Bayesian unfolding procedure. The response matrix is constructed using PYTHIA 8 Monash 2013 simulations with injected strange particles, reweighted to match measured $p_T$ spectra. Systematic uncertainties are evaluated via variations in selection criteria, unfolding priors, and feed-down corrections.
Multiplet Yield Calculation: From $P(n_S)$ , the average production yield of multiplets of order $n$ ( $\langle Y_{nS} \rangle$ ) is calculated using combinatorial factors, allowing the study of doublets, triplets, and higher-order clusters.

Key Contributions

First Measurement of $P(n_S)$ : This work presents the first measurement of the full strange-particle multiplicity distribution $P(n_S)$ in pp collisions, extending the study of strangeness production beyond the mean.
Extreme Regime Probing: The analysis accesses extreme kinematic regimes, measuring $P(n_S)$ up to $n_S=7$ for $K^0_S$ , $n_S=5$ for $\Lambda$ , $n_S=4$ for $\Xi$ , and $n_S=2$ for $\Omega$ .
Strangeness-Induced Bias Quantification: The paper explicitly quantifies the "strangeness-induced charged-particle multiplicity bias," demonstrating that selecting events with high $n_S$ shifts the underlying charged-particle multiplicity distribution to higher values. This bias is shown to be model-dependent, varying significantly between PYTHIA 8 Monash 2013, PYTHIA 8 QCD-CR + Ropes, and EPOS LHC.
Multiplet Ratios with $\Delta S = 0$ : The study calculates ratios of multiplets with equal total strangeness content (e.g., $\langle Y_{n\Lambda} \rangle / \langle Y_{nK^0_S} \rangle$ ) to isolate non-strangeness-related mechanisms, such as light quark ( $u, d$ ) availability and baryon/mass effects.

Results

Multiplicity Dependence: $P(n_S)$ increases with event multiplicity, with the rise being steeper for higher $n_S$ . The distributions are well-described by Negative Binomial Distributions (NBD).
Multiplet Yields: The average yields of multiplets $\langle Y_{nS} \rangle$ increase more than linearly with multiplicity. For high $n$ , the yields span several orders of magnitude from low to high multiplicity classes.
Model Comparison:
- PYTHIA 8 Monash 2013: Shows significant discrepancies, underestimating baryon yields and failing to reproduce the steep rise of multiplet yields.
- PYTHIA 8 QCD-CR + Ropes: Shows improved agreement for baryons compared to the Monash tune, particularly at high multiplicity, but still struggles with $K^0_S$ yields. It successfully reproduces the trends of $\Delta S = 0$ ratios.
- EPOS LHC: Agrees well with data at high multiplicity but severely underestimates yields at low multiplicity, suggesting limitations in modeling the transition between core (hydrodynamic) and corona (string fragmentation) regimes.
Strangeness Enhancement ( $\Delta S$ ): Ratios of multi-strange baryon multiplets to $K^0_S$ multiplets show an enhancement factor of two orders of magnitude from low to high multiplicity, reaching a strangeness imbalance of $\Delta S = 5$ .
$\Delta S = 0$ Evolution: Ratios with equal strangeness content (e.g., $\langle Y_{n\Lambda} \rangle / \langle Y_{nK^0_S} \rangle$ ) exhibit a non-trivial evolution with multiplicity. Specifically, $\langle Y_{n\Lambda} \rangle / \langle Y_{nK^0_S} \rangle$ increases with multiplicity for $n > 1$ , while ratios involving baryons in the numerator and mesons in the denominator (e.g., $\langle Y_{\Xi} \rangle / \langle Y_{K^0_S} \rangle$ ) decrease. This suggests that light quark availability and coalescence probabilities play a sub-leading but significant role in the enhancement pattern.

Significance
The paper claims that this new approach "dramatically enhances the sensitivity to the different underlying physics mechanisms modeled by each generator." By moving beyond average yields to full multiplicity distributions and multiplet ratios, the study provides a stringent test bench for Monte Carlo event generators. The results indicate that while current models capture some aspects of strangeness production, the specific implementation of Color Reconnection (CR) and Rope Hadronization in PYTHIA 8 QCD-CR + Ropes is crucial for describing multi-strange baryon production. Furthermore, the observation of multiplicity-dependent trends in $\Delta S = 0$ ratios challenges the view that strangeness enhancement is driven solely by strangeness content, pointing to the importance of light quark dynamics and coalescence mechanisms in small collision systems. The author states that these results pave the way for studying the relative probability of hadronizing into different strange-hadron combinations for a given number of produced strange quarks.

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