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Study of the interaction between $\Xi$ baryons and light mesons via femtoscopy at the LHC

This paper presents the first high-precision femtoscopic measurements of $\Xi$ -meson correlations in 13 TeV pp collisions at the LHC, revealing repulsive and shallow attractive interactions for $\Xi$ -K and $\Xi$ - $\pi$ systems respectively while characterizing the $\Xi(1620)$ and $\Xi(1690)$ resonances to constrain theoretical models of hadron dynamics.

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

At the heart of every atom lies a force so powerful it binds the very building blocks of matter together, yet it remains one of the most difficult to understand. This is the strong force, the invisible glue that holds protons and neutrons together inside the atomic nucleus. While scientists have a solid grasp of how this force works between the simplest particles, things become murky when more complex combinations are involved. Specifically, when particles containing "strange" quarks interact with lighter particles like pions or kaons, the rules of the game change. These interactions are crucial for understanding why certain exotic particles exist and how they are structured, but they are incredibly hard to study because the particles involved are unstable and decay almost instantly. To solve this puzzle, researchers must look at how these particles behave when they are born together in high-energy collisions, watching how they influence each other's paths as they fly apart.

A team of scientists at the Large Hadron Collider has taken a fresh look at this problem by studying the relationship between a specific type of heavy particle called a Xi baryon and two lighter partners: a kaon and a pion. In a recent study, the ALICE collaboration analyzed billions of high-energy collisions between protons to see how these particles interact. They focused on pairs of particles with opposite electric charges, measuring how often they appeared close together versus far apart. By looking at these patterns, the researchers could deduce the nature of the force pulling them together or pushing them apart. The results revealed a clear difference in behavior: the Xi baryon and the kaon seem to repel each other, while the Xi baryon and the pion are drawn together by a gentle, attractive force.

The experiment was conducted by smashing protons together at nearly the speed of light, creating a shower of new particles. The researchers selected only the most crowded collisions, where hundreds of particles were produced at once, because these environments are rich in the strange particles needed for the study. Using a massive detector capable of tracking the paths of these fleeting particles, the team identified pairs of Xi baryons and their lighter partners. They then calculated a correlation function, which is essentially a measure of how the distance between two particles affects the likelihood of finding them together. If the particles ignore each other, this number stays flat. If they attract, the number goes up; if they repel, it goes down. The data showed a distinct dip for the Xi-kaon pairs, indicating a repulsive force, and a rise for the Xi-pion pairs, signaling attraction.

Beyond simply measuring the strength of these forces, the study provided a detailed look at specific, short-lived states of matter known as resonances. In the data for the Xi-pion pairs, the researchers spotted clear signatures of two excited states of the Xi particle, known as the Xi(1620) and the Xi(1690). These are not stable particles but rather fleeting configurations that exist for a tiny fraction of a second before breaking apart. By analyzing the shape of the correlation peak, the team was able to determine the mass and width of these states with high precision. Their findings for the Xi(1690) matched well with previous measurements from other experiments, confirming its properties. For the less understood Xi(1620), the study provided a new, precise measurement of its mass, which was found to be slightly lower than that of its charged counterpart, a difference that aligns with theoretical expectations about how these particles behave.

The results of this study serve as a critical test for the theoretical models scientists use to describe the strong force. Theoretical frameworks that attempt to predict how these particles interact had previously struggled to match the level of repulsion observed between the Xi and the kaon. The new data shows that the repulsion is stronger than some models predicted, suggesting that our current understanding of the underlying forces needs refinement. Similarly, the attractive force between the Xi and the pion, while shallow, provides a necessary constraint for theories that try to explain how these particles might form complex, molecule-like structures. By delivering these precise measurements, the researchers have offered a new set of rules for theorists to follow, helping to narrow down the possibilities for how the universe is built at its most fundamental level.

This work represents a significant step forward in mapping the landscape of the strong interaction. While the data confirms the existence of the attractive and repulsive forces at play, it also highlights the complexity of the system, where multiple channels of interaction are linked together. The ability to measure these interactions directly, rather than inferring them from other processes, gives scientists a clearer picture of the forces at work. As the Large Hadron Collider continues to operate, collecting even more data from these high-multiplicity collisions, researchers hope to refine these measurements further and perhaps uncover even more of the hidden structures that govern the behavior of matter. For now, the study stands as a precise map of the interaction between strange baryons and light mesons, offering a solid foundation for future discoveries in the subatomic world.

Technical Summary: Study of the interaction between $\Xi$ baryons and light mesons via femtoscopy at the LHC

Problem and Motivation
Understanding the strong interaction in the non-perturbative regime of Quantum Chromodynamics (QCD) is essential for characterizing the hadron spectrum, particularly regarding exotic states and molecular configurations. While the charm sector has revealed tetra- and penta-quark states, the light sector (involving $u, d, s$ quarks) contains predictions for meson-baryon molecular states, specifically in strangeness $S=-1$ and $S=-2$ sectors. The origin of these states is linked to coupled-channel dynamics, where transitions occur between channels sharing the same quantum numbers (e.g., $\Lambda(1405)$ arising from $\pi\Sigma$ - $K\bar{N}$ coupling).

The $S=-2$ sector features the $\Xi(1620)$ and $\Xi(1690)$ states, whose structures remain unclear. Theoretical frameworks, such as Chiral Perturbation Theory (ChPT) and Effective Field Theories (EFT), require precise experimental inputs to constrain low-energy constants and model potentials, particularly for Next-to-Leading Order (NLO) calculations. However, experimental data on these systems are scarce due to the difficulty of reconstructing unstable strange particles. Furthermore, the $S=-1$ meson-baryon interaction, specifically the $\Xi$ - $K$ channel, is poorly constrained by existing scattering data, hindering the description of the isospin-triplet component and the coupled-channel dynamics involving $\Lambda\pi$ and $\Sigma K$ channels.

Methodology
The ALICE Collaboration analyzed high-multiplicity (HM) proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV. The dataset consists of $1 \times 10^9$ events selected from the top 0.17% of inelastic collisions based on the total signal amplitude measured by the V0 detector. These events exhibit an average charged-particle multiplicity density of $\langle dN_{ch}/d\eta \rangle \approx 30$ at midrapidity, enhancing the production yield of hyperons.

The analysis focused on femtoscopic correlations between oppositely charged $\Xi$ baryons ( $\Xi^-$ and $\bar{\Xi}^+$ ) and light mesons ( $K^\pm$ and $\pi^\pm$ ).

Particle Identification: Pions and kaons were identified using specific energy loss ($dE/dx$) in the Time Projection Chamber (TPC) and timing information from the Time Of Flight (TOF) detector. $\Xi$ baryons were reconstructed via their weak decay cascade $\Xi^- \to \Lambda \pi^- \to p \pi^- \pi^-$ , employing a Boosted Decision Tree (BDT) multivariate analysis to suppress combinatorial background, achieving a purity of 97%.
Correlation Function: The experimental correlation function $C(k^*)$ was constructed as the ratio of the relative momentum distribution ( $k^*$ ) of pairs from the same event to that of mixed events. The analysis combined charge-conjugate pairs ( $\Xi^-K^+$ with $\Xi^+K^-$ , and $\Xi^-\pi^+$ with $\Xi^+\pi^-$ ) to improve statistical precision.
Modeling: The measured correlation functions were fitted using a total model $C_{tot}(k^*) = N_D \times C_{model}(k^*) \times C_{background}(k^*)$ $C_{t o t} (k^{*}) = N_{D} \times C_{m o d e l} (k^{*}) \times C_{ba c k g r o u n d} (k^{*})$ .
- $C_{model}$ included the genuine femtoscopic signal ( $C_{gen}$ ) modeled via the Lednický–Lyuboshits (LL) wavefunction approach, which incorporates both strong and Coulomb interactions in the s-wave. The LL model utilized scattering lengths ( $f_0 = \Re f_0 + i \Im f_0$ ) as free parameters, assuming a zero effective range ( $d_0=0$ ).
- Residual contributions from misidentified particles and feed-down from excited states (e.g., $\Xi(1530)$ ) were included as weighted terms.
- $C_{background}$ accounted for non-femtoscopic correlations (mini-jet background). For $\Xi$ - $K$ , the background was modeled using PYTHIA 8.2 simulations scaled by a factor $S$ to match data, while for $\Xi$ - $\pi$ , a polynomial fit to the PYTHIA simulation was used.
- The emitting source size was modeled using the Resonance Source Model (RSM), combining a Gaussian core and an exponential tail to account for long-lived resonances.

Key Results

$\Xi$ - $K$ Interaction:
- The correlation function shows a clear deviation from unity at low relative momenta, indicating a strong interaction.
- The fit yields a scattering length with a real part $\Re f_0 = -0.61 \pm 0.02(\text{stat}) \pm 0.07(\text{syst})$ fm and an imaginary part $\Im f_0 = 0.41 \pm 0.04(\text{stat}) \pm 0.01(\text{syst})$ fm.
- The negative real part indicates a repulsive strong interaction. The large imaginary part reflects significant inelastic channels.
- Theoretical predictions from the unitarized ChPT (BCN model) and the Dynamical Coupled-Channels (ANL-Osaka) approach fail to fully describe the data, particularly the magnitude of the repulsion and the behavior at low relative momenta. The BCN model predicts a weaker anticorrelation than observed.
$\Xi$ - $\pi$ Interaction and Resonances:
- The correlation function lies above unity at low $k^*$ , indicating an overall attractive interaction.
- The extracted scattering length is $\Re f_0 = 0.070 \pm 0.004(\text{stat}) \pm 0.011(\text{syst})$ fm and $\Im f_0 = 0.002 \pm 0.003(\text{stat}) \pm 0.010(\text{syst})$ fm (compatible with zero). This confirms a shallow attractive strong interaction.
- The analysis successfully identifies and determines the properties of two excited states:
  - $\Xi(1620)$ : Mass $M = 1608.16 \pm 1.56$ MeV/ $c^2$ , Width $\Gamma = 47.12 \pm 5.63$ MeV.
  - $\Xi(1690)$ : Mass $M = 1680.72 \pm 3.27$ MeV/ $c^2$ , Width $\Gamma = 26.41 \pm 13.86$ MeV.
- The measured mass and width for $\Xi(1690)$ are consistent with PDG values and previous measurements by LHCb and Belle. The $\Xi(1620)$ mass is consistent with the Belle measurement in the same channel, while the width is narrower, consistent with $\Lambda$ - $K^-$ correlation results.
- A structure at $k^* \approx 850-950$ MeV/ $c$ is attributed to the decay of $\Xi_c^0 \to \Xi \pi$ , rather than the poorly known $\Xi(2500)$ state.

Significance and Claims
The paper claims to present the first high-precision femtoscopic data on $\Xi$ - $K$ and $\Xi$ - $\pi$ interactions at small relative momenta.

For $\Xi$ - $K$ : The results provide crucial experimental constraints for the $S=-1$ meson-baryon interaction, specifically the isospin-triplet component. The observed repulsion is not fully captured by current theoretical models (BCN and ANL-Osaka), suggesting a need for further refinement in describing coupled-channel dynamics and the influence of the $\Lambda\pi$ channel.
For $\Xi$ - $\pi$ : The data confirm a shallow attractive interaction and provide precise determinations of the $\Xi(1620)$ and $\Xi(1690)$ properties. These measurements offer a complementary approach to spectroscopy, investigating the interaction between constituents of molecular candidates.
Theoretical Impact: The high-precision data are intended to help refine the understanding of resonant states, provide stronger constraints for chirally motivated potentials (particularly for NLO calculations), and address the challenge of describing coupled-channel dynamics that may lead to molecular configurations.

The author notes that while the LL model provides an indication of the interaction character, it has limitations regarding small source sizes and rich coupled-channel dynamics. Future work within LHC Run 3 and 4 is suggested to involve correlations of $\Sigma K$ pairs to access heavier $\Xi^*$ states and better understand the coupled-channel dynamics in the $S=-2$ sector.

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