🔭 astrophysics

Light Antinuclei Coalescence: Femtoscopic Constraints via Neural-Flow Surrogates

This paper introduces a fast, differentiable normalizing-flow surrogate trained on ALICE data to precisely constrain femtoscopic source models, thereby reducing the dominant uncertainties in light antinuclei coalescence parameters ( $B_2$ and $B_3$ ) from orders of magnitude to the few-percent level and significantly improving predictions for cosmic-ray dark matter signatures.

Original authors: M. Korwieser, L. Fabbietti, B. Hashemi, L. Heinrich, M. Mahlein, D. L. Mihaylov, C. S. Zeyn

Published 2026-07-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: M. Korwieser, L. Fabbietti, B. Hashemi, L. Heinrich, M. Mahlein, D. L. Mihaylov, C. S. Zeyn

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

Imagine the universe is a giant, invisible ocean, and floating through it are tiny, ghostly particles called "dark matter." Scientists have been trying to find these ghosts for nearly a century, but they are incredibly shy and hard to catch. One of the most promising ways to spot them is to look for "antimatter" in the cosmic rays raining down on Earth. Think of antimatter as the evil twin of normal matter; when they meet, they annihilate in a flash of energy. If dark matter particles crash into each other and disappear, they might leave behind a trail of these antimatter twins, specifically "antinuclei" (tiny clusters of antimatter protons and neutrons).

However, there's a massive problem: normal collisions between cosmic rays and space gas also create antimatter. It's like trying to hear a whisper in a hurricane; the "background noise" of normal antimatter is so loud and unpredictable that it might completely hide the whisper of dark matter. To solve this, scientists need to predict exactly how much normal antimatter should be there. But their current predictions are like guessing the weather a month in advance using a broken thermometer—they have huge errors, sometimes off by a factor of 100 or even 1,000. This paper introduces a new, super-smart way to fix that broken thermometer, turning a wild guess into a precise forecast.

The authors of this paper have built a "digital twin" of a complex physics process to solve the mystery of how antimatter nuclei are formed. In the world of particle physics, when protons smash together, they sometimes stick together to form heavier particles like deuterons (a proton and a neutron holding hands). Scientists use a rule called "coalescence" to predict how often this happens. The problem is that the "glue" holding them together depends on a hidden map called the "emission source," which describes exactly where and how the particles are born. Until now, figuring out this map for the low-energy collisions that happen in deep space was like trying to map a city you've never visited using only blurry photos of a different city.

To fix this, the team used a clever trick involving machine learning. They took 49 different sets of data from the ALICE experiment at the Large Hadron Collider (LHC), which measured how protons bounce off each other at incredibly high energies. These measurements act like a high-resolution map of the "source." But there's a catch: the LHC is a high-energy machine, while cosmic rays in space are low-energy. The authors needed to stretch their high-energy map to fit the low-energy space environment.

They did this by training a "neural-flow surrogate." Imagine you have a very slow, complicated video game that simulates how particles behave, but it takes hours to run one scene. The authors built a fast, differentiable AI model (a "surrogate") that learned to mimic the slow game perfectly. This AI can now spit out the same results in a fraction of a second. By feeding it the 49 ALICE data sets, the AI learned the exact rules of how the "source" changes based on how many particles are in the collision (multiplicity) and their momentum.

The results are a game-changer for precision. Before this work, the uncertainty in predicting how many antideuterons (A=2) are created was a wild guess, varying by a factor of 10 to 100. For heavier antinuclei like antihelium-3 (A=3), the guess was even worse, off by a factor of about 1,000. With their new AI-driven method, they have shrunk these uncertainties dramatically. For antideuterons, the error is now down to just a few percent (plus a small, unavoidable 15% uncertainty from the theoretical shape of the particle's wavefunction). For antihelium-3, the uncertainty dropped from a factor of 1,000 to about 10% in the measured range.

The paper explicitly rules out the old method of using "pion" correlations (collisions involving a different type of particle) as a stand-in for proton-neutron interactions. The authors show that this old shortcut was inaccurate, sometimes overestimating the size of the source by a factor of three because it missed the influence of long-lived particles. Instead, they insist on using direct proton-proton data, which provides a much truer picture.

By combining this new, data-constrained source map with a simulation called ToMCCA, the team can now predict the production of antinuclei with a level of control never seen before. They didn't just simulate a single scenario; they created a flexible framework that can be applied to ongoing experiments like SMOG@LHCb and future space missions like AMS-02 and GAPS. While the paper doesn't claim to have found dark matter yet, it has removed the biggest obstacle in the way: the fog of uncertainty. Now, when scientists look at the cosmic rays, they will know exactly what the "background noise" should sound like, making it much easier to spot the faint, mysterious whisper of dark matter.

Technical Summary: Light Antinuclei Coalescence: Femtoscopic Constraints via Neural-Flow Surrogates

Problem Statement
Precise predictions of cosmic-ray antinuclei fluxes are critical for indirect dark matter searches, as dark matter annihilation or decay is predicted to enhance antinuclei fluxes by factors of 10–1000 at low kinetic energies. However, establishing an unambiguous dark matter signal requires a precise understanding of the Standard Model secondary background. Current predictions for antinuclei production rates suffer from dominant systematic uncertainties (factors of 10–100 for deuterons and ~~1000 for tritons/helium-3). These uncertainties arise from the lack of direct data constraining antinuclei production mechanisms at the relevant low-multiplicity energies (~~300 GeV kinetic energy) and the reliance on approximative treatments of nucleus formation, such as using pion correlations as proxies for nucleon-nucleon sources.

Methodology
The authors present a data-driven framework to constrain the femtoscopic emission source and reduce uncertainties in coalescence-based antinuclei production rates. The methodology involves three core components:

Data-Driven Source Extrapolation: The framework exploits the empirical scaling law where the emission source is governed by event multiplicity and transverse mass ( $m_T$ ) rather than collision energy. By utilizing high-statistics proton-proton ( $p$ - $p$ ) femtoscopic correlation data from the ALICE experiment (49 correlation functions across four multiplicity classes at $\sqrt{s} = 13$ and 13.6 TeV), the authors extrapolate the source model down to the low-multiplicity regime relevant for cosmic rays.
Neural-Flow Surrogate: To overcome the computational intractability of simultaneously fitting 49 correlation functions using the Common Emission in CATS (CECA) model via direct simulation, the authors employ a conditional normalizing-flow (NF) surrogate. This differentiable neural network learns an invertible transformation between a simple latent distribution and the complex, resonance-deformed emission geometry generated by CECA. The surrogate maps CECA parameters ( $r_d$ , $h$ , $\tau$ ) and local kinematics ( $k^*$ , $m_T$ ) to the source distribution $S(r^*)$ , reducing evaluation costs by over two orders of magnitude.
Coalescence Calculation: The constrained source functions are integrated into the ToMCCA model, a fast Monte Carlo event generator using the Wigner function formalism. This allows for the calculation of coalescence parameters $B_2$ and $B_3$ for antideuterons and antitritons/helium-3, respectively. The framework accounts for two wavefunction hypotheses (N4LO and Argonne v18) to assess theoretical systematics.

Key Contributions

Surrogate Modeling: Development of a fast, differentiable normalizing-flow surrogate that emulates the CECA femtoscopic source model with sub-percent fidelity, enabling simultaneous fitting of 49 ALICE correlation functions.
Data-Constrained Source Functions: Generation of fully data-constrained emission source functions across the $m_T$ –multiplicity plane, eliminating the need for unverified proxy assumptions (e.g., using $\pi$ - $\pi$ correlations for $p$ - $n$ systems).
Uncertainty Reduction: A rigorous quantification of uncertainties in coalescence parameters, separating statistical source uncertainties from theoretical wavefunction systematics.

Results

Fidelity and Fit: The NF surrogate reproduces CECA simulations with sub-percent emulation fidelity. The simultaneous fit to 49 ALICE $p$ - $p$ correlation functions yields a $\chi^2/\text{NDF} = 1.39$ , confirming the model's ability to capture relevant source geometries, including resonance-driven non-Gaussian tails.
$B_2$ Uncertainty Reduction: The uncertainty on the deuteron coalescence parameter $B_2$ is reduced from previous factors of 10–100 to the few-percent level (specifically, source uncertainty drops to <3% for $p_T/A > 0.4$ GeV/c and up to ~23% for lower $p_T$ ). When including a ~15% wavefunction systematic (arising from the spread between N4LO and Argonne v18 hypotheses), the total uncertainty remains within the 10–25% range.
$B_3$ Uncertainty Reduction: For the triton/helium-3 parameter $B_3$ , the uncertainty is reduced from a factor of ~1000 to approximately 10% in the measured kinematic range ( $p_T/A \gtrsim 0.4$ GeV/c), degrading to ~60% in the low- $p_T$ extrapolation region.
Validation: The predicted $B_2$ values are consistent with ALICE measurements at the 0.84 $\sigma$ level and align with preliminary NA61/SHINE data within estimated uncertainties.

Significance
The paper claims to resolve the dominant source-function uncertainty that has historically prevented precise predictions of the Standard Model secondary background for cosmic-ray antinuclei. By providing a modular, data-constrained framework, the authors offer realistic inputs for ongoing and planned measurements at SMOG@LHCb, CBM@FAIR, and NA61/SHINE. These results establish a quantitatively controlled basis for future antideuteron and antihelium flux predictions essential for experiments like AMS-02 and GAPS. Furthermore, the differentiable nature of the NF surrogate is identified as a critical step toward a fully end-to-end differentiable inference pipeline for cosmic-ray physics.

Technical Summary: Light Antinuclei Coalescence: Femtoscopic Constraints via Neural-Flow Surrogates

More like this