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Strangeness production as a function of charged-particle multiplicity in proton-proton collisions at ${\bf \sqrt{s}~=~5.02}$ TeV

The ALICE experiment at the LHC measured strangeness production in proton-proton collisions at $\sqrt{s} = 5.02$ TeV as a function of charged-particle multiplicity, revealing that while most strange particle yields scale linearly with multiplicity, $\Omega$ yields increase significantly faster, a trend that state-of-the-art QCD models can only qualitatively reproduce by introducing system collectivity.

Original authors: ALICE Collaboration

Published 2026-09-29

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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, particles called hadrons are the building blocks of visible matter, formed when quarks and gluons bind together. Most everyday matter consists of hadrons made from just two types of quarks, known as up and down. However, nature also allows for the creation of "strange" hadrons, which contain a third, heavier type of quark called the strange quark. For decades, physicists have been fascinated by how these strange particles are born. In the violent collisions of heavy atomic nuclei, where temperatures soar high enough to melt protons and neutrons into a soup of free quarks and gluons, strange particles appear in abundance. This phenomenon was originally proposed as a signature of a new state of matter called the quark-gluon plasma. Yet, a puzzling discovery emerged when scientists began smashing single protons into other protons. Even in these much smaller, simpler collisions, strange particles were being produced in numbers that seemed to depend on how many other particles were created in the same crash. The question became whether the same rules governing the massive, hot soup of heavy-ion collisions also applied to the tiny, fleeting interactions of single protons, or if a completely different mechanism was at work.

To answer this, the ALICE collaboration at the Large Hadron Collider in Geneva turned their attention to proton-proton collisions at a specific energy level of 5.02 tera-electronvolts. They analyzed a massive dataset collected in 2017, containing billions of collision events. The researchers focused on measuring the production of several types of strange particles, including the neutral kaon, the lambda baryon, and the more complex cascade and omega baryons, which contain multiple strange quarks. Crucially, they did not just count the total number of particles produced; they sorted the collisions into groups based on how many charged particles emerged from each crash. This allowed them to compare the "quiet" collisions, which produced few particles, against the "noisy" ones, which produced many, effectively testing whether the density of the collision environment changed the recipe for making strange matter.

The results revealed a clear and consistent pattern. As the number of particles produced in a collision increased, the number of strange particles also increased. For the lighter strange particles, this growth was steady and proportional; if the number of charged particles doubled, the number of these strange particles roughly doubled as well. However, the story changed for the heaviest strange particles, the omega baryons. Their production did not just grow in step with the crowd; it surged much faster. In the most crowded collisions, the production of these heavy particles rose so sharply that it followed a curve rather than a straight line. This behavior suggests that the environment inside a high-multiplicity proton collision becomes dense enough to trigger a different kind of particle formation process, one that favors the creation of the heaviest, most complex strange particles.

The researchers also examined how fast these particles were moving. They found that in collisions producing many particles, the strange particles were, on average, moving faster than in collisions producing few particles. This "hardening" of the speed distribution is a feature previously seen in the massive collisions of heavy ions, where it is interpreted as a sign that the particles are pushing against each other in a collective flow, like a fluid expanding outward. The fact that this same behavior appears in single proton collisions suggests that even in these tiny systems, the particles interact strongly enough to move together as a group. When the team compared their findings to theoretical models, they discovered that standard computer simulations, which assume particles are created independently and fly apart without interacting, failed to reproduce the data. The models only matched the observations when the researchers forced them to include mechanisms that mimic collective behavior or a dense, interacting environment.

Ultimately, the study confirms that the rules governing the production of strange matter are universal across different collision sizes. Whether the collision involves two protons or two heavy lead nuclei, the yield of strange particles is determined primarily by the density of the collision, not the total energy of the impact. The data shows that as the collision environment becomes more crowded, the production of strange particles accelerates, with the most complex particles showing the strongest response. While the exact nature of the interaction driving this effect remains a subject of debate, the evidence strongly points toward the existence of collective dynamics in even the smallest high-energy collisions. This finding bridges the gap between the physics of simple particle interactions and the complex behavior of the quark-gluon plasma, suggesting that the seeds of collective fluid-like behavior are present wherever matter is compressed and heated sufficiently, regardless of the size of the colliding objects.

Technical Summary: Strangeness Production as a Function of Charged-Particle Multiplicity in Proton–Proton Collisions at $\sqrt{s} = 5.02$ TeV

Problem and Motivation
The production of strange hadrons in high-energy hadronic collisions remains a critical probe for understanding Quantum Chromodynamics (QCD) in its non-perturbative regime. Historically, an enhancement in strange hadron yields relative to non-strange particles was proposed as a signature of Quark–Gluon Plasma (QGP) formation in heavy-ion collisions. Recent observations by the ALICE Collaboration in proton–proton (pp) and proton–lead (p–Pb) collisions have revealed similar strangeness enhancement trends correlated with charged-particle multiplicity, challenging the notion that such phenomena are exclusive to large collision systems. While studies at $\sqrt{s} = 7$ TeV and $\sqrt{s} = 13$ TeV have established these trends, a comprehensive description of the underlying mechanisms—specifically whether they arise from collective effects or modified hadronization in dense environments—remains elusive. This study addresses the need to extend these investigations to a lower energy regime ( $\sqrt{s} = 5.02$ TeV) with improved statistical precision and finer granularity in multiplicity selection, particularly in previously unexplored low-multiplicity regions.

Methodology
The analysis utilizes a large dataset ( $L_{int} = 2.3 \text{ nb}^{-1}$ ) collected by the ALICE experiment during the 2017 pp data-taking campaign at $\sqrt{s} = 5.02$ TeV. The study focuses on the production of strange and multi-strange hadrons: $K^0_S$ , $\Lambda$ , $\Xi$ , and $\Omega$ (including antiparticles, which are summed due to compatible yields).

Event Selection: Events were selected with at least one charged particle in $|\eta| < 1$ (INEL > 0), corresponding to approximately 75% of the total inelastic cross-section. The sample was divided into 12 multiplicity classes based on the amplitude of the V0 detector (V0M), covering a wide range of charged-particle densities.
Particle Reconstruction: Strange hadrons were reconstructed via their weak decay topologies ( $K^0_S \to \pi^+\pi^-$ , $\Lambda \to p\pi^-$ , $\Xi \to \Lambda\pi$ , $\Omega \to \Lambda K$ ) using the Inner Tracking System (ITS), Time Projection Chamber (TPC), and Time-of-Flight (TOF) detectors. Strict topological and kinematic selection criteria were applied to suppress combinatorial background.
Corrections and Unfolding: Raw yields were corrected for detector acceptance, tracking efficiency, and secondary particle contamination (specifically feed-down from $\Xi$ decays to $\Lambda$ ). Monte Carlo (MC) simulations using PYTHIA 8 and GEANT 3/4 were employed to estimate efficiencies. The $p_T$ spectra were extrapolated to zero momentum using a Lévy-Tsallis function to calculate integrated yields and mean transverse momentum ( $\langle p_T \rangle$ ).
Systematic Uncertainties: Sources included signal extraction stability, selection criteria variations, detector material description, and feed-down corrections. Uncertainties were generally found to be independent of multiplicity.

Key Contributions and Results

Transverse Momentum Spectra Evolution: The $p_T$ distributions for all measured particles exhibit a hardening trend as multiplicity increases. The spectral maximum shifts to higher $p_T$ values, and the ratio of high-multiplicity spectra to the inclusive (INEL > 0) spectrum approaches a saturation region around $4 \text{ GeV}/c$ . This behavior mirrors observations in nucleus–nucleus collisions.
Mean Transverse Momentum ( $\langle p_T \rangle$ ): $\langle p_T \rangle$ increases with charged-particle multiplicity for all species. This trend is consistent with results at $\sqrt{s} = 7$ TeV and $13$ TeV, suggesting that the collision energy does not significantly alter the multiplicity dependence of $\langle p_T \rangle$ .
Strangeness Enhancement and Yield Trends:
- The integrated yields of $K^0_S$ , $\Lambda$ , and $\Xi$ show a linear dependence on charged-particle multiplicity density.
- The $\Omega$ yield follows a significantly faster-than-linear (quadratic) increasing trend within the measured multiplicity range.
- When compared across energies ( $\sqrt{s} = 5.02, 7, 13$ TeV), the production rates for a given multiplicity density are consistent, reinforcing the idea that strange particle production is driven by multiplicity rather than collision energy.
$\Lambda/K^0_S$ Ratio: The ratio of $\Lambda$ to $K^0_S$ spectra displays a characteristic peak at intermediate $p_T$ ( $1.5\text{--}3 \text{ GeV}/c$ ). The position and magnitude of this peak evolve with multiplicity, becoming more pronounced in high-multiplicity events, a feature reminiscent of collective radial flow in larger systems.
Model Comparison:
- PYTHIA 8: The standard "Monash 2013" tune fails to describe the data. However, the "QCD-CR+Ropes" tune, which introduces Color Reconnection (CR) with 3-leg junctions and string tension modification (ropes) in dense environments, qualitatively reproduces the $\Lambda/K^0_S$ ratio and the yield trends for baryons, though it underestimates the $\langle p_T \rangle$ hardening.
- EPOS 4: This model, utilizing a core-corona mechanism with hydrodynamic expansion in the "core," provides a good description of baryon yields and $\langle p_T \rangle$ , though it tends to overshoot $K^0_S$ and $\Omega$ yields and predicts softer spectra for $K^0_S$ .
- DCCI: The Dynamical Core-Corona Initialization model describes $\langle p_T \rangle$ well but underpredicts the multiplicity dependence of baryon yields.
- Conclusion on Models: None of the models quantitatively describe all observables simultaneously. However, the paper concludes that models can only qualitatively describe the data if they incorporate mechanisms for collectivity (either parton flow or Color Reconnection) and modified hadronization in high-density environments. Pure vacuum hadronization models are insufficient.

Significance
This work extends the precision of strangeness production measurements to lower energies and lower multiplicities, confirming that the observed enhancement and spectral hardening are universal features of high-multiplicity pp collisions, independent of the center-of-mass energy. The results challenge standard perturbative QCD descriptions and string fragmentation models that do not account for final-state interactions in dense environments. The finding that $\Omega$ yields follow a quadratic trend, while other strange hadrons follow a linear one, provides new constraints for phenomenological models. Ultimately, the paper asserts that the successful description of these phenomena requires the introduction of collective effects or modified hadronization mechanisms in high-density pp collisions, bridging the phenomenological gap between small (pp) and large (AA) collision systems.

Technical Summary: Strangeness Production as a Function of Charged-Particle Multiplicity in Proton–Proton Collisions at s=5.02\sqrt{s} = 5.02s​=5.02 TeV

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Technical Summary: Strangeness Production as a Function of Charged-Particle Multiplicity in Proton–Proton Collisions at $\sqrt{s} = 5.02$ TeV