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Three-baryon femtoscopy as an effective 3 $\rightarrow$ 3 scattering experiment

This paper presents the first measurement of the three-proton correlation function in 13.6 TeV pp collisions at the LHC, demonstrating that three-hadron femtoscopy serves as an effective 3 $\rightarrow$ 3 scattering experiment that reveals a novel long-range attractive component in the isospin 3/2 three-body system and opens new avenues for studying three-body dynamics in the strangeness sector.

Original authors: ALICE Collaboration

Published 2026-08-07

📖 5 min read🧠 Deep dive

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

The Invisible Dance of Tiny Particles

Imagine the universe is a giant, chaotic dance floor where the smallest building blocks of matter—protons, neutrons, and other particles called hadrons—are constantly bumping into each other. For decades, scientists have been trying to understand the "rules of the dance," specifically the strong force, which is the invisible glue that holds atomic nuclei together. Usually, to figure out how two dancers interact, scientists set up a controlled experiment where they crash two particles together and watch how they bounce off. This is like a billiard game: you hit one ball into another and measure the angle.

However, there's a problem when you try to study groups of three dancers. In the real world, some of these particles are so short-lived they vanish before you can even set up the experiment. Furthermore, nature rarely gives us a clean "three-body" crash to study in a lab. This leaves a huge gap in our understanding: we know how two particles interact, but we don't fully understand how three of them behave together, especially when they aren't stuck together in a stable clump but are just passing through each other. This is crucial because the rules governing these three-particle interactions might explain how the dense cores of neutron stars hold together without collapsing.

The Three-Proton Party Crash

In this new study, the ALICE Collaboration at CERN's Large Hadron Collider (LHC) decided to try a different approach. Instead of crashing particles together like billiard balls, they looked at the "aftermath" of high-energy collisions. They focused on a specific, rare event: a collision that produces three protons (the positively charged cores of hydrogen atoms) that fly out together. The team measured how these three protons were correlated—essentially, how their speeds and directions were linked to one another.

Think of it like this: Imagine you are at a massive, crowded party. You can't see the people talking to each other, but you can see who ends up standing in a group of three. If three people are standing very close together and moving in a synchronized way, it suggests they were talking or interacting just before they got separated. In the world of subatomic physics, this "grouping" is called femtoscopy. It's a way of measuring the tiny distances (a few femtometers, which is a quadrillionth of a meter) between particles as they are born in a collision. By analyzing the momentum of these three protons, the scientists could reconstruct the "conversation" they had while they were still close together.

The Findings: A New Kind of Attraction

The team measured the correlation of these three protons in collisions at an energy of 13.6 TeV. What they found was a surprise. When they compared their data to the best existing computer models, they discovered that the protons were behaving in a way that standard two-particle rules couldn't fully explain.

Here is the big reveal: The data showed that the three protons were experiencing an effective long-range attraction. This is a bit counterintuitive. Protons are positively charged, so they naturally repel each other (like trying to push two north poles of a magnet together). The only thing that usually pulls them together is the strong nuclear force, but that force is supposed to be very short-range, like a sticky note that only works if you are touching it.

However, the study found that in a three-proton system, the nuclear force doesn't actually change its range. Instead, the three-body geometry creates an effective long-range attraction. The author explains this with a clever analogy of the dance floor: Even if one proton is far away from the other two, those two can stay close enough to "hold hands" (interact via the strong force). Because they are holding hands, they create a gravitational-like pull on the third proton, even from a distance. This isn't a new force or a change in the rules; it is a clever trick of three-body dynamics where the short-range force between two particles creates a lasting influence on the third.

What This Means for Physics

The paper explicitly highlights that the data strongly supports the complex three-body model. When the scientists tried to run their models without including the complex "p-wave" interactions (a specific way the particles spin and move relative to each other), the results were off by a massive margin—22.2 standard deviations away from the data. That is a statistical way of saying, "This is definitely not a coincidence; the model without p-waves is wrong."

Instead, the data matched a sophisticated three-body calculation very well, with an overall agreement within 2.5 standard deviations. This strong consistency confirms that the three-proton system acts as a real "3-to-3 scattering experiment," where three particles come in, interact, and three particles go out, all while unbound.

This is the first time scientists have directly observed this specific "isospin 3/2" three-body state. It proves that the nuclear force is more complex and far-reaching in three-particle systems than we thought. While this doesn't immediately change how we build cars or phones, it gives us a new, powerful tool to understand the most extreme matter in the universe. If we can understand how three protons dance together, we can better understand how three neutrons might behave in the heart of a neutron star, potentially solving mysteries about how these cosmic giants stay stable. The study suggests that by looking at these fleeting, three-particle groups, we are effectively turning the LHC into a giant microscope for the deepest secrets of the strong force.

Technical Summary: Three-Baryon Femtoscopy as an Effective 3→3 Scattering Experiment

Problem Statement
While scattering experiments have long served as the primary method for constraining hadron–hadron interactions, experimental data on three-body dynamics remain limited, particularly for unbound systems and those involving short-lived hadrons. Traditional scattering experiments struggle with hyperons due to their short lifetimes ( $\tau < 10$ cm/c), and existing bound systems of hyperons with nucleons provide limited constraints on three-body forces. Furthermore, theoretical models describing the complex low-energy behavior of nuclear interactions require increasingly precise experimental benchmarks, especially regarding the angular-momentum dependence and the necessity of three-body force components. Previous attempts to measure three-particle correlations were statistically limited, and comprehensive theoretical frameworks for three-unbound-baryon scattering (3→3 reactions) were not yet available for direct comparison.

Methodology
This work presents a measurement of the three-proton ( $p$ – $p$ – $p$ ) correlation function in proton–proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 13.6$ TeV, recorded by the ALICE Collaboration during the LHC Run 3 (2024). The analysis utilizes a novel data-driven strategy to isolate the genuine three-body correlation from background channels and experimental effects.

Experimental Setup: The measurement uses the upgraded ALICE apparatus in continuous data-taking mode. A specialized software trigger was developed to record collisions containing proton triplets with low hypermomentum ( $Q_3 < 1.4$ GeV/c), a kinematic region where the correlation signal is expected. The analysis combines proton and antiproton samples to improve statistical precision, with particle identification based on specific energy loss in the Time Projection Chamber (TPC) and time-of-flight measurements in the TOF detector.
Analysis Strategy: The correlation function is defined in terms of the Lorentz-invariant hypermomentum $Q_3$ $Q_{3}$ . The analysis employs the Koonin–Pratt formula extended to three-body systems in hyperspherical coordinates.
- Source Characterization: The effective source size for the triplet ( $\rho_0$ ) is constrained by first measuring the two-proton ( $p$ – $p$ ) correlation function within the triplets. The $p$ – $p$ data is fitted using the Argonne v18 (AV18) nuclear potential, Coulomb repulsion, and proper antisymmetrization, yielding a source radius $r_0 = (1.27 \pm 0.02)$ fm. The three-body source size is derived as $\rho_0 = 2r_0 = (2.54 \pm 0.04)$ fm.
- Background Subtraction: The measured signal is decomposed into genuine $p$ – $p$ – $p$ correlations and various background contributions, including feed-down from weak decays ( $\Lambda$ , $\Sigma^+$ ), misidentified particles, and wrongly assigned collisions. These components are modeled using data-driven methods, including chiral EFT calculations for residual interactions and cumulant expansion methods for non-femtoscopic effects.
- Theoretical Comparison: The extracted genuine correlation function is compared to state-of-the-art three-body continuum calculations based on the hyperspherical adiabatic expansion. These calculations utilize the AV18 potential and treat the system as an elastic 3→3 scattering process.

Key Results

First Direct Access to Isospin 3/2: The measurement provides the first direct experimental access to the isospin 3/2 three-body system, a configuration previously inaccessible via nucleon–deuteron scattering (which probes isospin 1/2).
Sensitivity to Partial-Wave Structure: The data demonstrates high sensitivity to the partial-wave structure of the nucleon–nucleon (NN) interaction.
- Removing the $p$ -wave component of the NN interaction from the theoretical model results in a significant disagreement with the data ( $22.2\sigma$ ).
- The full calculation, including $s$ -, $p$ -, and $d$ -waves, reproduces the measurement within $2.5\sigma$ .
Slow Convergence of Three-Body Expansion: Unlike two-body systems where the nuclear interaction becomes negligible at low angular momenta due to the centrifugal barrier, the three-body correlation function requires the inclusion of nuclear interactions up to high grand-angular momentum ( $K_{max} = 7$ ) to achieve agreement with data. This indicates that the nuclear force remains relevant at higher orders in the three-body expansion.
Effective Long-Range Attraction: The measured correlation function remains above unity as it approaches the uncorrelated limit at large $Q_3$ . This observation provides the first experimental signature of an effective long-range attractive component in a three-proton continuum system. This effect arises naturally from three-body dynamics where two protons remain close enough to interact even when the third is distant, scaling as $\zeta/\rho^3$ .

Significance
The paper establishes three-hadron femtoscopy as an effective 3→3 scattering experiment, capable of probing three-body dynamics with unbound hadrons in both initial and final states. By successfully isolating the genuine three-body correlation and comparing it to rigorous theoretical calculations, the work validates the use of femtoscopy to study continuum states that are otherwise experimentally inaccessible.

The observation of the effective long-range attraction and the sensitivity to high-order partial waves offer new constraints on theoretical models of three-nucleon forces. These findings contribute to the understanding of universal physics in systems with large scattering lengths and provide a benchmark for calculations regarding possible quasi-bound states in three- and four-neutron systems. Furthermore, the methodology opens a pathway for future precision studies of three-body dynamics in the strangeness sector (e.g., $p$ – $p$ – $\Lambda$ , $p$ – $p$ – $\Sigma$ ), which is crucial for understanding hypernuclear structure and the equation of state of dense matter in neutron stars.

The Invisible Dance of Tiny Particles

The Three-Proton Party Crash

The Findings: A New Kind of Attraction

What This Means for Physics

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