⚛️ nuclear theory

Global polarization of $\Lambda$ , $\Xi^{-}$ , and $\Omega^{-}$ hyperons in Au+Au collisions at RHIC BES-II energies

This paper investigates the global spin polarization of $\Lambda$ , $\Xi^{-}$ , and $\Omega^{-}$ hyperons in Au+Au collisions at RHIC BES-II energies using a viscous hydrodynamic framework, revealing that while $\Omega^{-}$ polarization is systematically larger due to its spin, it remains below experimental measurements, suggesting potential contributions from additional mechanisms like intra-quark spin correlations.

Original authors: Gen-Hui Li, Cong Yi, Xiang-Yu Wu, Shi Pu, Guang-You Qin

Published 2026-10-22

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CC BY 4.0

Original authors: Gen-Hui Li, Cong Yi, Xiang-Yu Wu, Shi Pu, Guang-You Qin

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 a particle accelerator, when two heavy atomic nuclei smash together at nearly the speed of light, they create a fleeting, super-hot soup of free-floating quarks and gluons known as the quark-gluon plasma. This state of matter existed only microseconds after the Big Bang, and recreating it allows physicists to study the fundamental forces that hold the universe together. One of the most striking features of this plasma is that it spins with incredible intensity, like a whirlpool in a bathtub, but on a scale where the rotation is so violent it can influence the very orientation of the tiny particles that emerge from the collision. As these particles cool and solidify into stable matter, they carry a memory of this spin, a phenomenon called global polarization. Scientists have long measured this effect in simple particles, but a new study turns its attention to more complex, multi-strange particles to see if the rules change when the ingredients become more exotic.

A team of researchers has now mapped out how this spin alignment behaves for three specific types of heavy particles—known as Lambda, Xi, and Omega hyperons—produced in collisions of gold nuclei at the Relativistic Heavy Ion Collider. By running sophisticated computer simulations that mimic the entire lifecycle of these collisions, from the initial impact to the final freeze-out of particles, the team calculated how the swirling motion of the plasma imprints itself on these particles. They focused on a wide range of collision energies, specifically between 7.7 and 27 giga-electron volts, a region where the plasma is dense with matter and the physics of spin becomes particularly intricate. The researchers did not just look at the particles directly created in the crash; they also carefully accounted for the fact that many of the particles they observe are actually the decay products of heavier, short-lived parents. This "feed-down" effect is crucial, as the way a parent particle breaks apart can alter the spin direction of its children, much like how a spinning top might wobble differently depending on how it was launched.

The results reveal a clear pattern: as the energy of the collision drops, the spin alignment of all three types of hyperons becomes stronger. This happens because lower-energy collisions produce a denser environment where the initial spin of the colliding nuclei is more effectively transferred to the plasma, and fewer particles are created to dilute this effect. The study also confirmed that the alignment grows stronger in more peripheral collisions, where the nuclei only graze each other, creating a larger velocity difference across the fireball and thus a more intense spin. When looking at the specific particles, the Omega hyperon, which carries the most spin of the three, showed a systematically higher alignment than the lighter Lambda and Xi particles, a result that matches theoretical expectations based on their mass and spin properties. However, a significant puzzle remains. While the simulations predicted an increase in Omega alignment, the calculated values still fall noticeably short of the actual measurements recorded by the STAR experiment at the same facility.

This gap between the simulation and the real-world data suggests that the current models are missing a piece of the puzzle. The researchers propose that the discrepancy might be caused by hidden connections between the strange quarks inside the Omega particle itself. Just as individual dancers might move in sync not just because of the music but because they are holding hands, the strange quarks inside the Omega might be influencing each other's spin in ways that standard fluid dynamics cannot yet capture. Additionally, the study found a distinct difference between matter and antimatter versions of these particles. The antimatter hyperons consistently showed a stronger spin alignment than their matter counterparts, a split that grows larger at lower energies. This separation appears to be driven primarily by the gradient of the chemical potential, a force related to how the density of particles changes across the collision zone, acting alongside other known effects to shape the final spin of the emerging particles.

By providing a detailed theoretical baseline for these multi-strange particles across the energy range explored by the Beam Energy Scan II, this work offers a crucial reference point for future experiments. It confirms that the general behavior of spin in the quark-gluon plasma is well understood, yet it highlights that the internal structure of the most complex particles may hold new secrets. The fact that the Omega particle's spin is not fully explained by current models points toward a richer, more interconnected world of quantum spin correlations waiting to be discovered. As experimentalists gather more precise data, this study serves as a guide, showing exactly where the current understanding holds firm and where the next great leap in knowledge is likely to occur.

Technical Summary: Global Polarization of $\Lambda$ , $\Xi^-$ , and $\Omega^-$ Hyperons in Au+Au Collisions at RHIC BES-II Energies

Problem Statement
Relativistic heavy-ion collisions generate a quark-gluon plasma (QGP) with immense orbital angular momentum, resulting in extreme vorticity that polarizes the spins of final-state hadrons. While the global polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons has been extensively measured and theoretically modeled, several critical issues remain unresolved, particularly within the context of the RHIC Beam Energy Scan II (BES-II) ( $\sqrt{s_{NN}} = 7.7\text{--}27$ GeV). These open questions include:

The dependence of global polarization on rapidity, centrality, and transverse momentum ( $p_T$ ), which requires further investigation for future experimental comparisons.
The quantitative contribution of shear-induced polarization and spin Hall effects (driven by the thermal shear tensor and baryon chemical potential gradient) to the total global polarization.
The polarization behavior of multi-strange hyperons ( $\Xi^-$ and $\Omega^-$ ), specifically whether spin correlations among strange quarks inside these particles affect observed polarization.
The origin of the polarization splitting between hyperons and anti-hyperons, distinguishing between contributions from electromagnetic fields and chemical potential gradients.

Methodology
The authors employ a (3+1)-dimensional viscous hydrodynamic framework, CLVisc, coupled with SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) for initial conditions. The simulation covers Au+Au collisions in the 20–50% centrality range across $\sqrt{s_{NN}} = 7.7\text{--}27$ GeV.

Key methodological components include:

Polarization Calculation: The mean spin-polarization vector is computed using a modified Cooper–Frye formula derived from quantum statistical models and kinetic theory. The polarization vector $P^\mu$ $P^{μ}$ is decomposed into three contributions:
- Thermal vorticity ( $\varpi_{\alpha\beta}$ ).
- Thermal shear tensor ( $\xi_{\alpha\beta}$ ).
- Gradient of the baryon chemical potential ( $\nabla(\mu/T)$ ).
Feed-Down Corrections: The study explicitly incorporates feed-down effects from the decays of heavier hyperons (e.g., $\Sigma^0$ , $\Sigma(1385)$ , $\Xi(1530)$ , $\Lambda(1405)$ ). The authors utilize linear-order polarization-transfer formulas and Wigner rotations to map the polarization from the parent rest frame to the laboratory-defined daughter rest frame. This includes handling weak decays (e.g., $\Xi_Q \to \Lambda \pi_Q$ ) with specific decay asymmetry parameters ( $\alpha, \beta, \gamma$ ).
Numerical Setup: The hydrodynamic evolution uses the NEOS-BQS equation of state. Initial conditions are generated via SMASH with Gaussian smearing. Parameters (smearing widths, normalization factor, specific shear viscosity) are tuned to reproduce soft-particle yields and transverse-momentum spectra at specific energies. Bulk viscosity is neglected, and baryon diffusion is set to zero for simplicity.

Key Contributions

Systematic Multi-Strange Analysis: This work provides the first systematic theoretical investigation of the global polarization of $\Xi^-$ and $\Omega^-$ hyperons alongside $\Lambda$ hyperons across the full RHIC BES-II energy range, including comprehensive feed-down corrections.
Decomposition of Mechanisms: The study quantifies the relative contributions of thermal vorticity, thermal shear, and chemical potential gradients, specifically isolating the role of the chemical potential gradient in hyperon-anti-hyperon splitting.
Kinematic Dependence: The paper maps the global polarization as a function of collision energy, centrality, transverse momentum, and rapidity, providing a detailed baseline for experimental comparison.

Results

Collision Energy Dependence: The global polarization ( $P_H$ ) for all three species ( $\Lambda, \Xi^-, \Omega^-$ ) increases as collision energy decreases. This trend is attributed to stronger net-baryon stopping and reduced particle multiplicity at midrapidity at lower energies.
Species Differences:
- $\Xi^-$ vs. $\Lambda$ : Feed-down effects enhance the polarization of $\Xi^-$ while reducing that of $\Lambda$ . The theoretical results for $\Xi^-$ align well with experimental data, while $\Lambda$ results are slightly lower than data at intermediate energies.
- $\Omega^-$ : Due to its larger spin quantum number ( $S=3/2$ ), the global polarization of $\Omega^-$ is systematically larger than that of $\Lambda$ and $\Xi^-$ (approximately $P_\Omega \approx 5P_\Lambda/3$ ). However, the theoretical values remain significantly below the central value of recent STAR measurements.
Hyperon-Anti-hyperon Splitting: Anti-hyperons exhibit systematically larger global polarization than their corresponding hyperons. This splitting increases toward lower collision energies and is dominated by the contribution from the chemical potential gradient, suggesting a spin Hall effect mechanism distinct from electromagnetic field contributions.
Kinematic Trends:
- Centrality: Polarization increases toward more peripheral collisions due to larger vorticity generated by stronger velocity gradients.
- Transverse Momentum ( $p_T$ ): Polarization decreases as $p_T$ increases, consistent with experimental observations.
- Rapidity ( $Y$ ): Polarization is nearly flat around midrapidity ( $|Y| \in [0, 1]$ ) and increases rapidly for $|Y| \ge 1$ .

Significance and Claims
The paper claims to provide a systematic theoretical baseline for the global polarization of multi-strange hyperons across the RHIC BES-II energy range. The authors modestly conclude that while their hydrodynamic framework successfully describes the general trends and the behavior of $\Lambda$ and $\Xi^-$ , the discrepancy between the calculated and measured global polarization of $\Omega^-$ suggests the presence of additional physical mechanisms. Specifically, they propose that short-range spin correlations (two- and three-particle spin-spin correlations) among the strange quarks inside the $\Omega^-$ may contribute to the observed polarization, identifying this as a promising direction for future theoretical and experimental investigation. Furthermore, the results clarify that the spin Hall effect (via chemical potential gradients) is a dominant factor in the observed hyperon-anti-hyperon polarization splitting.

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