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Measurement of antideuteron and net- $\Lambda$ number fluctuations at the Large Hadron Collider

This paper presents the first measurement of antideuteron–net- $\Lambda$ number correlations in Pb–Pb collisions at the LHC, which align with statistical hadronization model predictions and thereby confirm that the previously observed deviation in antideuteron–antiproton correlations stems from nucleosynthesis processes rather than the hadronization mechanism.

Original authors: ALICE Collaboration

Published 2026-10-28

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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 heart of the Large Hadron Collider, where protons and heavy lead ions smash together at nearly the speed of light, scientists are trying to understand how the universe built itself from the simplest ingredients. When these particles collide, they create a fleeting, super-hot soup of energy and matter that mimics the conditions of the early universe, just moments after the Big Bang. As this soup cools down, the energy condenses into particles, much like steam turning into water droplets. Some of these particles are simple, like protons, while others are complex clusters, such as antideuterons, which are made of an antiproton and an antineutron bound together. For decades, physicists have debated how these clusters form. One idea suggests they are born from a statistical process where the universe simply decides how many of each particle to make based on temperature and volume. Another idea proposes that they are formed later, when pre-existing particles drift close enough to stick together, a process known as coalescence. Understanding which mechanism is at work is crucial because it reveals the rules governing how matter organizes itself under extreme conditions.

A researcher using the ALICE detector at CERN has now taken a fresh look at this problem by measuring how the numbers of different particles fluctuate from one collision to the next. Instead of just counting the average number of particles produced, they looked at the event-by-event correlations, asking whether the production of one type of particle is linked to the production of another. In a recent study, they found that the relationship between antideuterons and antiprotons did not fit the standard statistical models that work perfectly for other particles. This discrepancy hinted that the formation of antideuterons involves a special, local process that the standard models were missing. To solve this puzzle, the researcher needed a new way to test the theory, one that could separate the general rules of particle creation from the specific mechanics of how these clusters stick together.

In their latest work, the researcher measured the relationship between antideuterons and a different type of particle called the net-Λ. The net-Λ is a count of a specific particle called the Lambda hyperon minus its antimatter counterpart. The key feature of the Lambda is that it is not made of the same building blocks as the antideuteron; it contains a strange quark, whereas the antideuteron is made only of up and down quarks. Because they do not share the same ingredients, any connection between them should be governed purely by the general rules of how the universe creates matter, without any influence from the specific process of antideuterons sticking together. The researcher analyzed data from billions of collisions between lead ions, carefully counting the antideuterons and the net-Λ particles in each event to see if their numbers rose and fell together.

The results showed a clear, positive link between the number of antideuterons and the number of net-Λ particles. This correlation was exactly what the standard statistical model predicted, provided the model accounted for the conservation of quantum numbers across a specific volume of space. This finding is significant because it confirms that the general mechanism creating the particles that eventually form antideuterons is the same one creating all other light particles. The "soup" of matter behaves consistently, obeying the same statistical laws whether it is making a Lambda or the ingredients for an antideuteron. This ruled out the idea that the antideuteron itself is formed through some exotic, non-statistical process that breaks the universal rules.

However, the story is not complete without addressing the earlier mystery regarding antiprotons. When the researcher compared their new findings with their previous measurements of the link between antideuterons and antiprotons, a different picture emerged. The connection between antideuterons and antiprotons was much stronger than the standard model could explain on its own. This suggests that while the general environment creates the particles, the final step of forming the antideuteron involves a second, local mechanism. The data indicates that antiprotons and antineutrons, once created, must come very close together in space and time to merge into an antideuteron. This merging process, or coalescence, adds an extra layer of correlation that is not present when looking at particles that do not share the same components.

By combining these two sets of measurements, the researcher has painted a coherent picture of how these exotic particles are born. The universe first creates a sea of particles according to statistical laws, a process that is uniform and predictable. Then, in the final moments of the collision, some of these particles find each other and fuse together to form clusters. The study confirms that the statistical model is the correct foundation for understanding particle production, but it also proves that this foundation must be topped with a coalescence step to explain the formation of composite nuclei. This dual-layer understanding resolves the long-standing tension between the two competing theories, showing that both are correct but apply to different stages of the particle's life. The work provides a solid baseline for future experiments, allowing scientists to probe even more complex nuclear structures and understand the precise conditions under which matter binds itself together.

Technical Summary: Measurement of Antideuteron and Net- $\Lambda$ Number Fluctuations at the LHC

Problem Statement
The production of light nuclei and antinuclei in heavy-ion collisions presents a challenge to current theoretical frameworks. While the Statistical Hadronization Model (SHM) successfully describes the yields of light-flavored hadrons and (anti)deuterons in central Pb–Pb collisions at the LHC, it struggles to account for event-by-event fluctuations. Specifically, recent measurements of the negative correlation between antideuteron ( $\bar{d}$ ) and antiproton ( $\bar{p}$ ) numbers deviate from SHM parameterizations that describe other light-flavored hadrons. This discrepancy suggests that the formation of composite states like antideuterons may involve nucleosynthesis processes (e.g., coalescence) distinct from the standard hadronization mechanism. To resolve this, new observables are required to disentangle the effects of quantum-number conservation (hadronization) from those of nucleosynthesis (nuclear formation).

Methodology
This letter presents the first measurement of the Pearson correlation coefficient between the antideuteron number and the net- $\Lambda$ number ( $\rho_{\bar{d}\Delta\Lambda}$ ), where $\Delta\Lambda = \Lambda - \bar{\Lambda}$ . Additionally, the normalized second-order cumulant of the net- $\Lambda$ number, $\kappa_2(\Lambda-\bar{\Lambda})/\langle\Lambda+\bar{\Lambda}\rangle$ , is measured. These observables are sensitive to the hadronization mechanism because $\Lambda$ hyperons are not constituents of antideuterons; thus, their correlation is driven primarily by global quantum-number conservation rather than local nucleosynthesis.

The analysis utilizes data from Pb–Pb collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_{NN}} = 5.02$ TeV, collected by the ALICE detector during the 2018 run. The study also improves the precision of previously published $\rho_{\bar{d}p}$ results by combining 2015 and 2018 data samples.

Event Selection: Inelastic events are selected using a minimum-bias trigger with V0 scintillators. Events are categorized into eight centrality intervals (0–80%) based on V0 signal amplitude.
Particle Identification: Antideuterons and protons are identified via specific energy loss ($dE/dx$) in the Time Projection Chamber (TPC) and Time-of-Flight (TOF) measurements. $\Lambda$ hyperons are reconstructed via their weak decay ( $\Lambda \to p + \pi^-$ ).
Corrections: Cumulants are corrected for reconstruction and selection efficiencies derived from Monte Carlo (MC) simulations (HIJING + GEANT4). Volume fluctuations (VF), arising from fluctuations in the number of participant nucleons within a centrality bin, are assessed using an event-mixing technique. For net-particle cumulants up to the third order (like $\kappa_2(\Lambda-\bar{\Lambda})$ ), VF effects cancel out, whereas they are explicitly corrected for in correlation coefficients like $\rho_{\bar{d}\Delta\Lambda}$ .
Model Comparison: Results are compared with calculations from the Thermal-FIST code, which implements the SHM in the Canonical Ensemble (CE) to enforce exact conservation of quantum numbers. The model is tested with different canonical volume parameters ( $V_c$ ) and, for the $\rho_{\bar{d}p}$ observable, with a coalescence afterburner based on the Wigner formalism.

Key Contributions and Results

Net- $\Lambda$ Fluctuations: The measured normalized second-order cumulant $\kappa_2(\Lambda-\bar{\Lambda})/\langle\Lambda+\bar{\Lambda}\rangle$ shows a significant deviation from the uncorrelated baseline (unity) across all centralities. The data are well-described by Thermal-FIST calculations using a canonical volume $V_c = 3.0 \, dV/dy$ , consistent with values derived for other light-flavor hadrons. This confirms that $\Lambda$ fluctuations are governed by the same hadronization mechanism and quantum-number conservation laws as other species.
Antideuteron–Net- $\Lambda$ Correlation: The $\rho_{\bar{d}\Delta\Lambda}$ measurement reveals a positive correlation with a statistical significance of $3.4\sigma$ . This correlation is driven by baryon number conservation. The data are well-described by Thermal-FIST with $V_c = 3.0 \, dV/dy$ (within $0.8\sigma$ ), indicating that the correlation between antideuterons and non-nucleonic hadrons is primarily sensitive to the universal hadronization mechanism.
Antideuteron–Antiproton Correlation: The updated $\rho_{\bar{d}p}$ measurement confirms a strong negative correlation (anticorrelation). This observable deviates significantly ( $3.9\sigma$ ) from the Thermal-FIST prediction with $V_c = 3.0 \, dV/dy$ . However, the data are quantitatively described by the model if a smaller canonical volume ( $V_c = 1.6 \, dV/dy$ ) is assumed, or more physically, by applying a nuclear coalescence afterburner to the SHM output. The coalescence-based calculation agrees with the data within $1.5\sigma$ .

Significance
The paper establishes that the event-by-event production of antideuterons is a sensitive probe of nuclear formation processes. The consistency of the $\rho_{\bar{d}\Delta\Lambda}$ and $\kappa_2(\Lambda-\bar{\Lambda})$ results with the standard SHM ( $V_c = 3.0 \, dV/dy$ ) suggests that the nucleons composing the antideuterons originate from a locally equilibrated fireball governed by universal hadronization laws.

The discrepancy observed in $\rho_{\bar{d}p}$ is attributed to nucleosynthesis processes. The fact that a coalescence model successfully describes $\rho_{\bar{d}p}$ while the standard SHM (without coalescence) fails implies that antideuterons are formed via the coalescence of nucleons produced in statistical equilibrium. This work provides strong evidence that the antideuteron-antiproton correlation is driven by nucleosynthesis, whereas correlations between antideuterons and non-nucleonic hadrons reflect the underlying hadronization mechanism. The results support a unified picture where light nuclei formation in heavy-ion collisions involves a statistical hadronization stage followed by a coalescence step for composite states.

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