Initial spin fluctuations as a probe of cluster spin structure in $^{16}\mathrm{O}$ and $^{20}\mathrm{Ne}$ nuclei

Ben-Wei Zhang; Jun-Qi Tao; Xiang Fan; Ze-Fang Jiang

arxiv: 2512.24079 · v2 · submitted 2025-12-30 · ⚛️ nucl-th · hep-ph

Initial spin fluctuations as a probe of cluster spin structure in ¹⁶O and ²⁰Ne nuclei

Xiang Fan , Jun-Qi Tao , Ze-Fang Jiang , Ben-Wei Zhang This is my paper

Pith reviewed 2026-05-16 19:25 UTC · model grok-4.3

classification ⚛️ nucl-th hep-ph

keywords alpha clusteringspin fluctuationsheavy-ion collisionsnuclear structureLambda hyperonsGlauber modellight nucleispin polarization

0 comments

The pith

Alpha clustering suppresses initial spin fluctuations in oxygen and neon collisions compared to uncorrelated models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how the alpha-cluster structure of oxygen-16 and neon-20 nuclei imprints on initial spin fluctuations during their high-energy collisions. Strong short-range spin-isospin correlations inside the clusters reduce the event-by-event variance of net spin polarization relative to a smooth spherical distribution with random spins. A scaled version of the fluctuation measure removes trivial size effects and displays a non-monotonic pattern that depends on collision centrality and cluster geometry. The ratio of this scaled quantity between the neon and oxygen systems is presented as a stable signature. The work concludes that spin correlations among produced lambda hyperons can therefore constrain the ground-state spin arrangement of these light nuclei.

Core claim

In relativistic 16O+16O and 20Ne+20Ne collisions, Monte-Carlo Glauber calculations with ab initio clustered configurations from Nuclear Lattice Effective Field Theory show that the initial net spin polarization variance is suppressed by the short-range correlations characteristic of alpha clusters, unlike the higher variance obtained from uncorrelated Woods-Saxon baselines. The suppression exhibits non-monotonic centrality dependence once finite-size effects are scaled out, and the ratio of scaled fluctuations between the two systems is identified as a robust observable that deviates from the baseline by distinct percent-level amounts.

What carries the argument

Event-by-event variance of initial net spin polarization computed in the Monte-Carlo Glauber framework, using alpha-cluster nuclear configurations versus spherical uncorrelated baselines.

If this is right

Suppression of spin fluctuations follows directly from the short-range spin-isospin correlations inside alpha clusters.
The scaled fluctuation observable varies non-monotonically with collision centrality according to cluster geometry.
The ratio of scaled fluctuations between 20Ne and 16O systems remains robust against overall normalization uncertainties.
Final-state Lambda-hyperon spin correlations can serve as a probe of the initial fluctuations with only percent-level dilution.
Distinct percent-level deviations from the uncorrelated baseline are expected for both nuclei.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same ratio observable could be applied to collisions of other light nuclei whose clustering properties are known from theory.
If the percent-level mapping holds, existing heavy-ion datasets at the LHC could already test nuclear spin structure models.
Refined hydrodynamic simulations would be required to verify that dilution stays at the percent level across centrality bins.
Analogous fluctuation ratios might be constructed for other spin-sensitive final-state particles.

Load-bearing premise

The initial net spin polarization variance maps directly onto measurable final-state Lambda-hyperon spin correlations with only percent-level dilution from hydrodynamic evolution and hadronization.

What would settle it

A collider measurement of the ratio of scaled spin fluctuations between 20Ne+20Ne and 16O+16O collisions at 5.36 TeV that shows no percent-level deviation from the uncorrelated baseline, or that exhibits dilution far larger than a few percent, would falsify the predicted imprint of cluster structure.

Figures

Figures reproduced from arXiv: 2512.24079 by Ben-Wei Zhang, Jun-Qi Tao, Xiang Fan, Ze-Fang Jiang.

**Figure 2.** Figure 2: FIG. 2. Schematic illustration of the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. (Color online) Standard deviation of the polarization param [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (Color online) Centrality dependence of the scaled standard [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. (Color online) Centrality dependence of the ratio [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

read the original abstract

We investigate the imprint of $\alpha$ clustering on initial spin fluctuations in relativistic $^{16}\mathrm{O}+{}^{16}\mathrm{O}$ and $^{20}\mathrm{Ne}+{}^{20}\mathrm{Ne}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.36$~TeV. Utilizing \textit{ab initio} configurations from Nuclear Lattice Effective Field Theory (NLEFT) and phenomenological $\alpha$-cluster models within a Monte-Carlo Glauber framework, we compute the event-by-event variance of the initial net spin polarization. We find that the strong short-range spin--isospin correlations characteristic of $\alpha$ clusters lead to a significant suppression of spin fluctuations compared to a spherical Woods--Saxon baseline with uncorrelated spins. By constructing a scaled fluctuation observable that accounts for trivial finite-size effects, we demonstrate that this suppression exhibits a non-monotonic centrality dependence sensitive to the detailed cluster geometry. Furthermore, we propose the ratio of scaled spin fluctuations between $^{20}\mathrm{Ne}$ and $^{16}\mathrm{O}$ systems as a robust probe. Our results predict distinct percent-level deviations from the baseline for clustered nuclei, suggesting that measurements of final-state $\Lambda$-hyperon spin correlations can provide novel constraints on the ground-state spin structure of light nuclei.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper proposes a scaled spin-fluctuation ratio between 20Ne and 16O collisions as a probe of alpha clustering, grounded in NLEFT inputs, but the direct mapping to measurable Lambda correlations rests on an untested low-dilution assumption.

read the letter

The main takeaway is that alpha clustering suppresses initial net spin polarization variance relative to an uncorrelated Woods-Saxon baseline, and the authors define a scaled observable plus a 20Ne-to-16O ratio that isolates geometry effects from finite-size differences. They report percent-level deviations with non-monotonic centrality dependence in the Monte Carlo Glauber calculations using ab initio NLEFT configurations. That construction is the clearest new element; it does not appear in the cited prior work and gives a concrete, falsifiable ratio to look for in data. The modeling itself is straightforward and uses established tools, so the variance computation looks internally consistent. Credit is due for bringing realistic nuclear wave functions into the initial-state framework rather than relying solely on phenomenological cluster models. The centrality trends they extract are a useful byproduct. The soft spot is the final step to experiment. The abstract and calculations stop at the initial-state variance and simply state that the suppression should appear as percent-level signals in Lambda hyperon spin correlations after evolution. No hydrodynamic runs or dilution estimates are shown, and in these small systems viscous damping, resonance feed-down, and possible spin-orbit effects during freeze-out could easily exceed the claimed percent level. That assumption is load-bearing for the experimental claim but is not stress-tested in the paper. The work is aimed at the overlap between nuclear-structure theorists who care about clustering and heavy-ion experimentalists who can measure Lambda polarization. A reader already following spin observables or ab initio inputs to collisions would get the most out of the ratio idea and the centrality plots. It is solid enough on the initial-state side and novel enough on the observable side to deserve a serious referee, even though the dilution question will need addressing in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript examines the imprint of α-clustering on initial spin fluctuations in ¹⁶O+¹⁶O and ²⁰Ne+²⁰Ne collisions at √s_NN = 5.36 TeV. Employing ab initio Nuclear Lattice Effective Field Theory configurations and phenomenological α-cluster models within a Monte-Carlo Glauber framework, the authors compute the event-by-event variance of the initial net spin polarization. They report that short-range spin-isospin correlations in α clusters cause significant suppression relative to a spherical Woods-Saxon baseline with uncorrelated spins. A scaled fluctuation observable is constructed to isolate this effect, revealing non-monotonic centrality dependence, and the ratio of scaled fluctuations between the ²⁰Ne and ¹⁶O systems is proposed as a robust probe. The work predicts distinct percent-level deviations from the baseline, suggesting that measurements of final-state Λ-hyperon spin correlations can constrain the ground-state spin structure of light nuclei.

Significance. If the central mapping from initial-state spin variance to final-state observables holds, this study provides a new avenue to probe nuclear clustering and spin correlations using relativistic heavy-ion data. By combining ab initio inputs with standard Glauber modeling, it generates concrete, falsifiable predictions for percent-level effects in Λ spin correlations, which could offer independent constraints on nuclear structure models beyond traditional spectroscopy.

major comments (2)

[Abstract and discussion of final-state mapping] The prediction of measurable percent-level deviations in final-state Λ-hyperon spin correlations (abstract) rests on the assumption that the initial net spin polarization variance maps directly onto the observable after hydrodynamic evolution and hadronization with only percent-level dilution. In small systems, viscous damping, resonance feed-down, and possible spin-orbit coupling at freeze-out can introduce additional decorrelation whose magnitude is not quantified or tested for sensitivity.
[Results section on scaled observable] The scaled fluctuation observable is defined to remove trivial finite-size effects and is used to claim non-monotonic centrality dependence sensitive to cluster geometry, but the manuscript provides neither the explicit functional form nor robustness checks against variations in α-cluster parameters or Glauber modeling choices.

minor comments (2)

[Notation and definitions] The notation for the scaled spin fluctuation observable should be accompanied by an explicit equation to ensure reproducibility.
[Figures] Figures displaying centrality dependence would benefit from error bands reflecting statistical and model uncertainties to illustrate the claimed percent-level deviations more clearly.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading and constructive comments, which have helped clarify the scope and presentation of our work. We address the major comments point by point below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Abstract and discussion of final-state mapping] The prediction of measurable percent-level deviations in final-state Λ-hyperon spin correlations (abstract) rests on the assumption that the initial net spin polarization variance maps directly onto the observable after hydrodynamic evolution and hadronization with only percent-level dilution. In small systems, viscous damping, resonance feed-down, and possible spin-orbit coupling at freeze-out can introduce additional decorrelation whose magnitude is not quantified or tested for sensitivity.

Authors: We appreciate the referee highlighting this important caveat. Our manuscript focuses on the initial-state spin fluctuations computed in the Monte-Carlo Glauber framework; the percent-level deviations quoted in the abstract refer specifically to differences in the initial net spin polarization variance between the clustered configurations and the uncorrelated Woods-Saxon baseline. We agree that mapping these initial fluctuations to final-state Λ-hyperon spin correlations involves additional effects (viscous damping, resonance feed-down, spin-orbit coupling) whose magnitude is not quantified here. In the revised manuscript we will (i) rephrase the abstract to make clear that the quoted deviations are at the initial-state level and (ii) add a dedicated paragraph in the discussion section that explicitly lists these potential sources of decorrelation and states that a full quantitative mapping would require spin-transport hydrodynamic simulations, which lie beyond the present scope. revision: yes
Referee: [Results section on scaled observable] The scaled fluctuation observable is defined to remove trivial finite-size effects and is used to claim non-monotonic centrality dependence sensitive to cluster geometry, but the manuscript provides neither the explicit functional form nor robustness checks against variations in α-cluster parameters or Glauber modeling choices.

Authors: We apologize for the omission of the explicit definition. The scaled fluctuation observable is constructed as the event-by-event variance of the net spin polarization normalized by the square of the number of participants (σ_S² / ⟨N_part⟩²) to remove the leading finite-size scaling; the precise functional form will be inserted into the revised results section. Regarding robustness, the non-monotonic centrality dependence appears consistently for both the NLEFT and phenomenological α-cluster inputs, but we acknowledge that systematic variations were not shown. In the revision we will add an appendix presenting checks in which the α-cluster radius is varied by ±10 % around the nominal value and the Glauber nucleon width and nucleon-nucleon cross section are changed within their uncertainties. These additional calculations confirm that the non-monotonic shape and the proposed ²⁰Ne/¹⁶O ratio remain qualitatively stable. revision: yes

standing simulated objections not resolved

Full quantitative evaluation of the dilution between initial-state spin variance and final-state Λ spin correlations, which would require dedicated hydrodynamic simulations with spin transport and is outside the scope of the present initial-state study.

Circularity Check

0 steps flagged

No significant circularity; direct computation from external NLEFT inputs

full rationale

The paper computes the event-by-event variance of initial net spin polarization directly from ab initio NLEFT configurations and phenomenological alpha-cluster models inside the Monte-Carlo Glauber framework. The scaled fluctuation observable is constructed from this computed variance solely to remove trivial finite-size effects, and the ratio between the 20Ne and 16O systems is proposed as a probe on that basis. No parameter is fitted to the target suppression result, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The mapping to final-state Lambda correlations is presented as an assumption with stated percent-level dilution rather than a derived equality, so the central claim does not reduce to its inputs by construction. External NLEFT configurations supply independent input, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim depends on the validity of the Monte-Carlo Glauber initial-condition model for spin polarization and on the input nuclear configurations from NLEFT and phenomenological alpha-cluster models; no new entities are postulated.

free parameters (1)

alpha-cluster geometry parameters
Chosen in the phenomenological models to reproduce ground-state properties of 16O and 20Ne.

axioms (2)

domain assumption Strong short-range spin-isospin correlations inside alpha clusters
Taken from standard nuclear structure input used in both NLEFT and cluster models.
domain assumption Glauber framework accurately captures initial net spin polarization variance
Standard assumption in relativistic heavy-ion initial-condition modeling.

pith-pipeline@v0.9.0 · 5546 in / 1396 out tokens · 24302 ms · 2026-05-16T19:25:38.503691+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

strong short-range spin–isospin correlations characteristic of α clusters lead to a significant suppression of spin fluctuations compared to a spherical Woods–Saxon baseline
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

scaled fluctuation observable that accounts for trivial finite-size effects

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Reference graph

Works this paper leans on

73 extracted references · 73 canonical work pages · 6 internal anchors

[1]

K. t. P. C. Adcox, Nucl. Phys. A757, 184 (2005)

work page 2005
[2]

M ¨uller, J

B. M ¨uller, J. Schukraft, and B. Wyslouch, Ann. Rev. Nucl. Part. Sci.62, 361 (2012)

work page 2012
[3]

L. t. S. C. Adamczyk, Nature548, 62 (2017)

work page 2017
[4]

S. t. A. C. Acharya, Phys. Rev. C101, 044611 (2020)

work page 2020
[5]

Liang and X.-N

Z.-T. Liang and X.-N. Wang, Phys. Rev. Lett.94, 102301 (2005)

work page 2005
[6]

Becattini, F

F. Becattini, F. Piccinini, and J. Rizzo, Phys. Rev. C77, 024906 (2008)

work page 2008
[7]

Becattini, I

F. Becattini, I. Karpenko, M. A. Lisa, I. Upsal, and S. V oloshin, Phys. Rev. C95, 054902 (2017)

work page 2017
[8]

Y . Xie, D. Wang, and L. P. Csernai, Phys. Rev. C95, 031901 (2017)

work page 2017
[9]

Li, X.-L

H. Li, X.-L. Xia, X.-G. Huang, and H.-Z. Huang, Phys. Lett. B 820, 136597 (2021), arXiv:2106.09443 [nucl-th]

work page arXiv 2021
[10]

J. t. S. C. Adam, Phys. Rev. Lett.123, 132301 (2019)

work page 2019
[11]

Becattini and I

F. Becattini and I. Karpenko, Phys. Rev. Lett.120, 012302 (2018)

work page 2018
[12]

X.-L. Xia, H. Li, X.-G. Huang, and H.-Z. Huang, Phys. Rev. C 100, 014913 (2019)

work page 2019
[13]

A New Twist on Top Quark Spin Correlations

M. Baumgart and B. Tweedie, JHEP03, 117, arXiv:1212.4888 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv
[14]

Fucilla and Y

M. Fucilla and Y . Hatta, (2025), arXiv:2509.05267 [hep-ph]

work page arXiv 2025
[15]

Y . Afik, Y . Kats, J. R. M. de Nova, A. Soffer, and D. Uzan, Phys. 10 Rev. D111, L111902 (2025), arXiv:2406.04402 [hep-ph]

work page arXiv 2025
[16]

T. Han, M. Low, N. McGinnis, and S. Su, JHEP05, 081, arXiv:2412.21158 [hep-ph]

work page arXiv
[17]

Giacalone and E

G. Giacalone and E. Speranza, (2025), arXiv:2502.13102 [nucl-th]

work page arXiv 2025
[18]

L.-G. Pang, H. Petersen, Q. Wang, and X.-N. Wang, Phys. Rev. Lett.117, 192301 (2016)

work page 2016
[19]

V . L. Lyuboshitz and V . V . Lyuboshitz, Phys. Part. Nucl. Lett. 7, 370 (2010)

work page 2010
[20]

Ellis and D

J. Ellis and D. S. Hwang, JHEP1011, 026

work page
[21]

Lin, L.-G

S.-J. Lin, L.-G. Pang, and X.-N. Wang, JHEP In press

work page
[22]

M. t. S. C. Abdallah, arXiv:2307.07373 [nucl-ex] (2023)

work page arXiv 2023
[23]

M. I. Abdulhamidet al.(STAR), Nature635, 67 (2024), arXiv:2401.06625 [nucl-ex]

work page arXiv 2024
[24]

Jia, Rept

J. Jia, Rept. Prog. Phys.88, 092301 (2025), arXiv:2501.16071 [nucl-th]

work page arXiv 2025
[25]

Giacalone, G

G. Giacalone, G. Nijs, and W. van der Schee, Phys. Rev. Lett. 131, 202302 (2023)

work page 2023
[26]

Bally, G

B. Bally, G. Giacalone, and M. Bender, Phys. Rev. Lett.128, 082301 (2022)

work page 2022
[28]

Liu, H.-C

L.-M. Liu, H.-C. Wang, S.-J. Li, C. Zhang, J. Xu, Z.-Z. Ren, J. Jia, and X.-G. Huang, arXiv e-prints , arXiv:2502.08057 (2025), arXiv:2502.08057 [nucl-th]

work page arXiv 2025
[29]

Ding, L.-G

C. Ding, L.-G. Pang, S. Zhang,et al., Chin. Phys. C47, 024105 (2023)

work page 2023
[30]

Zhang, J

C. Zhang, J. Chen, G. Giacalone, S. Huang, J. Jia, and Y .-G. Ma, Phys. Lett. B862, 139322 (2025), arXiv:2404.08385 [nucl-th]

work page arXiv 2025
[31]

L. R. Hafstad and E. Teller, Phys. Rev.54, 681 (1938)

work page 1938
[32]

Ikeda, N

K. Ikeda, N. Takigawa, and H. Horiuchi, Prog. Theor. Phys. Suppl.68, 464 (1968)

work page 1968
[33]

Freer, H

M. Freer, H. Horiuchi, P. Schuck, and E. Tursunov, Rev. Mod. Phys.90, 035004 (2018)

work page 2018
[34]

Carlson, S

J. Carlson, S. Gandolfi, F. Pederiva, S. C. Pieper, R. Schiavilla, K. E. Schmidt, and R. B. Wiringa, Rev. Mod. Phys.87, 1067 (2015)

work page 2015
[35]

B. R. Barrett, P. Navr´atil, and J. P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)

work page 2013
[36]

Lee, Prog

D. Lee, Prog. Part. Nucl. Phys.63, 117 (2009)

work page 2009
[37]

Epelbaum, H

E. Epelbaum, H. Krebs, D. Lee, and U.-G. Meißner, Phys. Rev. Lett.106, 192501 (2011)

work page 2011
[38]

J. M. Yao, B. Bally, J. Engel, R. Wirth, T. R. Roth, and H. Herg- ert, Phys. Rev. Lett.124, 232501 (2020)

work page 2020
[39]

Brewer, A

J. Brewer, A. Mazeliauskas, and W. van der Schee, Phys. Rev. Lett.127, 242301 (2021)

work page 2021
[40]

Acharyaet al.(ALICE Collaboration), (2025), see also related results from ATLAS and CMS Collaborations, arXiv:2509.06428 [nucl-ex]

S. Acharyaet al.(ALICE Collaboration), (2025), see also related results from ATLAS and CMS Collaborations, arXiv:2509.06428 [nucl-ex]

work page arXiv 2025
[41]

Florkowski, A

W. Florkowski, A. Kumar, and R. Ryblewski, Progress in Parti- cle and Nuclear Physics108, 103709 (2019), arXiv:1811.04409 [nucl-th]

work page arXiv 2019
[42]

Bhadury, W

S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ry- blewski, European Physical Journal Special Topics230, 655 (2021), arXiv:2101.11964 [nucl-th]

work page arXiv 2021
[43]

Speranza and N

E. Speranza and N. Weickgenannt, European Physical Journal A57, 155 (2021), arXiv:2007.00138 [nucl-th]

work page arXiv 2021
[44]

Huang, Nuclear Science and Techniques36, 208 (2025), arXiv:2411.11753 [nucl-th]

X.-G. Huang, Nuclear Science and Techniques36, 208 (2025), arXiv:2411.11753 [nucl-th]

work page arXiv 2025
[45]

Wigner, Phys

E. Wigner, Phys. Rev.51, 106 (1937)

work page 1937
[46]

T. Sogo, G. Ropke, and P. Schuck, Phys. Rev. C79, 051301 (2009), arXiv:0901.0675 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[47]

Tohsaki, H

A. Tohsaki, H. Horiuchi, P. Schuck, and G. R ¨opke, Phys. Rev. Lett.87, 192501 (2001)

work page 2001
[48]

J. S. Moreland, J. E. Bernhard, and S. A. Bass, Phys. Rev. C92, 011901 (2015), arXiv:1412.4708 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[49]

J. S. Moreland, J. E. Bernhard, and S. A. Bass, Phys. Rev. C 101, 024911 (2020), arXiv:1808.02106 [nucl-th]

work page arXiv 2020
[50]

Soeder, W

D. Soeder, W. Ke, J. F. Paquet, and S. A. Bass, (2023), arXiv:2306.08665 [nucl-th]

work page arXiv 2023
[51]

M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, Ann. Rev. Nucl. Part. Sci.57, 205 (2007), arXiv:nucl-ex/0701025 [nucl-ex]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[52]

The Importance of Correlations and Fluctuations on the Initial Source Eccentricity in High-Energy Nucleus-Nucleus Collisions

B. Alveret al., Phys. Rev. C77, 014906 (2008), arXiv:0711.3724 [nucl-ex]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[53]

Navaset al.(Particle Data Group), Phys

S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

work page 2024
[54]

G. e. a. A. C. Aad, Phys. Rev. Lett.123, 042001 (2019), arXiv:1903.07570 [hep-ex]

work page arXiv 2019
[55]

A. M. e. a. C. C. Sirunyan, Nature622, 71 (2023), arXiv:2303.06046 [hep-ex]

work page arXiv 2023
[56]

Becattini and M

F. Becattini and M. A. Lisa, Annual Review of Nuclear and Particle Science70, 395 (2020)

work page 2020
[57]

Weickgenannt, E

N. Weickgenannt, E. Speranza, D. Wagner, Q. Wang, and D. H. Rischke, Physical Review D105, 116026 (2022), arXiv:2203.04766 [hep-ph]

work page arXiv 2022
[58]

Hongo, X.-G

M. Hongo, X.-G. Huang, M. Kaminski, M. Stephanov, and H.-U. Yee, Journal of High Energy Physics11, 150 (2021), arXiv:2107.14231 [hep-th]

work page arXiv 2021
[59]

T. A. L ¨ahde and U.-G. Meißner,Nuclear Lattice Effective Field Theory: An Introduction, Lecture Notes in Physics, V ol. 957 (Springer, 2019)

work page 2019
[60]

Giacalone et al

G. Giacaloneet al., Phys. Rev. Lett.135, 012302 (2025), arXiv:2402.05995 [nucl-th]

work page arXiv 2025
[61]

Summerfield, B.-N

N. Summerfield, B.-N. Lu, C. Plumberg, D. Lee, J. Noronha- Hostler, and A. Timmins, Phys. Rev. C104, L041901 (2021), arXiv:2103.03345 [nucl-th]

work page arXiv 2021
[62]

Yamaguchi, W

Y . Yamaguchi, W. Horiuchi, and N. Itagaki, Phys. Rev. C108, 014322 (2023), arXiv:2301.09839 [nucl-th]

work page arXiv 2023
[63]

Bijker and F

R. Bijker and F. Iachello, Nucl. Phys. A1006, 122077 (2021), arXiv:2011.01976 [nucl-th]

work page arXiv 2021
[64]

Mehrabpour, [arXiv:2506.12673 [nucl-th]]

H. Mehrabpour, arXiv preprint (2025), arXiv:2506.12673 [nucl-th]

work page arXiv 2025
[65]

Yamaguchi, W

Y . Yamaguchi, W. Horiuchi, and N. Itagaki, Phys. Rev. C108, 014322 (2023), arXiv:2305.09182 [nucl-th]

work page arXiv 2023
[66]

Li, W.-X

W. Li, W.-X. Zhou, and Y .-G. Ma, arXiv preprint (2025), arXiv:2504.04688 [nucl-th]

work page arXiv 2025
[67]

H. D. Vries, C. W. D. Jager, and C. D. Vries, At. Data Nucl. Data Tables36, 495 (1987)

work page 1987
[68]

Adachi and Y

S. Adachi and Y . Kanada-En’yo, Phys. Lett. B818, 136344 (2021), arXiv:2010.12484 [nucl-th]

work page arXiv 2021
[69]

Shafi and S

K. Shafi and S. Chatterjee, (2025), arXiv:2505.11713 [nucl-th]

work page arXiv 2025
[70]

Y . Wang, S. Zhao, B. Cao, H.-j. Xu, and H. Song, Phys. Rev. C 109, L051904 (2024), arXiv:2401.15723 [nucl-th]

work page arXiv 2024
[71]

Drogosz, W

Z. Drogosz, W. Florkowski, and M. Hontarenko, Phys. Rev. D 110, 096018 (2024), arXiv:2408.03106 [hep-ph]

work page arXiv 2024
[72]

Ke, (2025), arXiv:2509.09549 [nucl-th]

W. Ke, (2025), arXiv:2509.09549 [nucl-th]

work page arXiv 2025
[73]

Zhang and J

C. Zhang and J. Jia, Phys. Rev. Lett.128, 022301 (2022)

work page 2022
[74]

Relativistic fluid dynamics with spin

W. Florkowski, B. Friman, A. Jaiswal, R. Ryblewski, and E. Speranza, Physical Review C97, 041901 (2018), arXiv:1705.00587 [nucl-th]. 11 Appendix A: Derivation of the spin–correlation observable In this appendix, we outline the derivation of the relation between theΛ-pair spin-correlation observablev 2 Λ and the event-by-event polarization variance⟨P 2⟩, f...

work page internal anchor Pith review Pith/arXiv arXiv 2018

[1] [1]

K. t. P. C. Adcox, Nucl. Phys. A757, 184 (2005)

work page 2005

[2] [2]

M ¨uller, J

B. M ¨uller, J. Schukraft, and B. Wyslouch, Ann. Rev. Nucl. Part. Sci.62, 361 (2012)

work page 2012

[3] [3]

L. t. S. C. Adamczyk, Nature548, 62 (2017)

work page 2017

[4] [4]

S. t. A. C. Acharya, Phys. Rev. C101, 044611 (2020)

work page 2020

[5] [5]

Liang and X.-N

Z.-T. Liang and X.-N. Wang, Phys. Rev. Lett.94, 102301 (2005)

work page 2005

[6] [6]

Becattini, F

F. Becattini, F. Piccinini, and J. Rizzo, Phys. Rev. C77, 024906 (2008)

work page 2008

[7] [7]

Becattini, I

F. Becattini, I. Karpenko, M. A. Lisa, I. Upsal, and S. V oloshin, Phys. Rev. C95, 054902 (2017)

work page 2017

[8] [8]

Y . Xie, D. Wang, and L. P. Csernai, Phys. Rev. C95, 031901 (2017)

work page 2017

[9] [9]

Li, X.-L

H. Li, X.-L. Xia, X.-G. Huang, and H.-Z. Huang, Phys. Lett. B 820, 136597 (2021), arXiv:2106.09443 [nucl-th]

work page arXiv 2021

[10] [10]

J. t. S. C. Adam, Phys. Rev. Lett.123, 132301 (2019)

work page 2019

[11] [11]

Becattini and I

F. Becattini and I. Karpenko, Phys. Rev. Lett.120, 012302 (2018)

work page 2018

[12] [12]

X.-L. Xia, H. Li, X.-G. Huang, and H.-Z. Huang, Phys. Rev. C 100, 014913 (2019)

work page 2019

[13] [13]

A New Twist on Top Quark Spin Correlations

M. Baumgart and B. Tweedie, JHEP03, 117, arXiv:1212.4888 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv

[14] [14]

Fucilla and Y

M. Fucilla and Y . Hatta, (2025), arXiv:2509.05267 [hep-ph]

work page arXiv 2025

[15] [15]

Y . Afik, Y . Kats, J. R. M. de Nova, A. Soffer, and D. Uzan, Phys. 10 Rev. D111, L111902 (2025), arXiv:2406.04402 [hep-ph]

work page arXiv 2025

[16] [16]

T. Han, M. Low, N. McGinnis, and S. Su, JHEP05, 081, arXiv:2412.21158 [hep-ph]

work page arXiv

[17] [17]

Giacalone and E

G. Giacalone and E. Speranza, (2025), arXiv:2502.13102 [nucl-th]

work page arXiv 2025

[18] [18]

L.-G. Pang, H. Petersen, Q. Wang, and X.-N. Wang, Phys. Rev. Lett.117, 192301 (2016)

work page 2016

[19] [19]

V . L. Lyuboshitz and V . V . Lyuboshitz, Phys. Part. Nucl. Lett. 7, 370 (2010)

work page 2010

[20] [20]

Ellis and D

J. Ellis and D. S. Hwang, JHEP1011, 026

work page

[21] [21]

Lin, L.-G

S.-J. Lin, L.-G. Pang, and X.-N. Wang, JHEP In press

work page

[22] [22]

M. t. S. C. Abdallah, arXiv:2307.07373 [nucl-ex] (2023)

work page arXiv 2023

[23] [23]

M. I. Abdulhamidet al.(STAR), Nature635, 67 (2024), arXiv:2401.06625 [nucl-ex]

work page arXiv 2024

[24] [24]

Jia, Rept

J. Jia, Rept. Prog. Phys.88, 092301 (2025), arXiv:2501.16071 [nucl-th]

work page arXiv 2025

[25] [25]

Giacalone, G

G. Giacalone, G. Nijs, and W. van der Schee, Phys. Rev. Lett. 131, 202302 (2023)

work page 2023

[26] [26]

Bally, G

B. Bally, G. Giacalone, and M. Bender, Phys. Rev. Lett.128, 082301 (2022)

work page 2022

[27] [28]

Liu, H.-C

L.-M. Liu, H.-C. Wang, S.-J. Li, C. Zhang, J. Xu, Z.-Z. Ren, J. Jia, and X.-G. Huang, arXiv e-prints , arXiv:2502.08057 (2025), arXiv:2502.08057 [nucl-th]

work page arXiv 2025

[28] [29]

Ding, L.-G

C. Ding, L.-G. Pang, S. Zhang,et al., Chin. Phys. C47, 024105 (2023)

work page 2023

[29] [30]

Zhang, J

C. Zhang, J. Chen, G. Giacalone, S. Huang, J. Jia, and Y .-G. Ma, Phys. Lett. B862, 139322 (2025), arXiv:2404.08385 [nucl-th]

work page arXiv 2025

[30] [31]

L. R. Hafstad and E. Teller, Phys. Rev.54, 681 (1938)

work page 1938

[31] [32]

Ikeda, N

K. Ikeda, N. Takigawa, and H. Horiuchi, Prog. Theor. Phys. Suppl.68, 464 (1968)

work page 1968

[32] [33]

Freer, H

M. Freer, H. Horiuchi, P. Schuck, and E. Tursunov, Rev. Mod. Phys.90, 035004 (2018)

work page 2018

[33] [34]

Carlson, S

J. Carlson, S. Gandolfi, F. Pederiva, S. C. Pieper, R. Schiavilla, K. E. Schmidt, and R. B. Wiringa, Rev. Mod. Phys.87, 1067 (2015)

work page 2015

[34] [35]

B. R. Barrett, P. Navr´atil, and J. P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)

work page 2013

[35] [36]

Lee, Prog

D. Lee, Prog. Part. Nucl. Phys.63, 117 (2009)

work page 2009

[36] [37]

Epelbaum, H

E. Epelbaum, H. Krebs, D. Lee, and U.-G. Meißner, Phys. Rev. Lett.106, 192501 (2011)

work page 2011

[37] [38]

J. M. Yao, B. Bally, J. Engel, R. Wirth, T. R. Roth, and H. Herg- ert, Phys. Rev. Lett.124, 232501 (2020)

work page 2020

[38] [39]

Brewer, A

J. Brewer, A. Mazeliauskas, and W. van der Schee, Phys. Rev. Lett.127, 242301 (2021)

work page 2021

[39] [40]

Acharyaet al.(ALICE Collaboration), (2025), see also related results from ATLAS and CMS Collaborations, arXiv:2509.06428 [nucl-ex]

S. Acharyaet al.(ALICE Collaboration), (2025), see also related results from ATLAS and CMS Collaborations, arXiv:2509.06428 [nucl-ex]

work page arXiv 2025

[40] [41]

Florkowski, A

W. Florkowski, A. Kumar, and R. Ryblewski, Progress in Parti- cle and Nuclear Physics108, 103709 (2019), arXiv:1811.04409 [nucl-th]

work page arXiv 2019

[41] [42]

Bhadury, W

S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ry- blewski, European Physical Journal Special Topics230, 655 (2021), arXiv:2101.11964 [nucl-th]

work page arXiv 2021

[42] [43]

Speranza and N

E. Speranza and N. Weickgenannt, European Physical Journal A57, 155 (2021), arXiv:2007.00138 [nucl-th]

work page arXiv 2021

[43] [44]

Huang, Nuclear Science and Techniques36, 208 (2025), arXiv:2411.11753 [nucl-th]

X.-G. Huang, Nuclear Science and Techniques36, 208 (2025), arXiv:2411.11753 [nucl-th]

work page arXiv 2025

[44] [45]

Wigner, Phys

E. Wigner, Phys. Rev.51, 106 (1937)

work page 1937

[45] [46]

T. Sogo, G. Ropke, and P. Schuck, Phys. Rev. C79, 051301 (2009), arXiv:0901.0675 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2009

[46] [47]

Tohsaki, H

A. Tohsaki, H. Horiuchi, P. Schuck, and G. R ¨opke, Phys. Rev. Lett.87, 192501 (2001)

work page 2001

[47] [48]

J. S. Moreland, J. E. Bernhard, and S. A. Bass, Phys. Rev. C92, 011901 (2015), arXiv:1412.4708 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[48] [49]

J. S. Moreland, J. E. Bernhard, and S. A. Bass, Phys. Rev. C 101, 024911 (2020), arXiv:1808.02106 [nucl-th]

work page arXiv 2020

[49] [50]

Soeder, W

D. Soeder, W. Ke, J. F. Paquet, and S. A. Bass, (2023), arXiv:2306.08665 [nucl-th]

work page arXiv 2023

[50] [51]

M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, Ann. Rev. Nucl. Part. Sci.57, 205 (2007), arXiv:nucl-ex/0701025 [nucl-ex]

work page internal anchor Pith review Pith/arXiv arXiv 2007

[51] [52]

The Importance of Correlations and Fluctuations on the Initial Source Eccentricity in High-Energy Nucleus-Nucleus Collisions

B. Alveret al., Phys. Rev. C77, 014906 (2008), arXiv:0711.3724 [nucl-ex]

work page internal anchor Pith review Pith/arXiv arXiv 2008

[52] [53]

Navaset al.(Particle Data Group), Phys

S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

work page 2024

[53] [54]

G. e. a. A. C. Aad, Phys. Rev. Lett.123, 042001 (2019), arXiv:1903.07570 [hep-ex]

work page arXiv 2019

[54] [55]

A. M. e. a. C. C. Sirunyan, Nature622, 71 (2023), arXiv:2303.06046 [hep-ex]

work page arXiv 2023

[55] [56]

Becattini and M

F. Becattini and M. A. Lisa, Annual Review of Nuclear and Particle Science70, 395 (2020)

work page 2020

[56] [57]

Weickgenannt, E

N. Weickgenannt, E. Speranza, D. Wagner, Q. Wang, and D. H. Rischke, Physical Review D105, 116026 (2022), arXiv:2203.04766 [hep-ph]

work page arXiv 2022

[57] [58]

Hongo, X.-G

M. Hongo, X.-G. Huang, M. Kaminski, M. Stephanov, and H.-U. Yee, Journal of High Energy Physics11, 150 (2021), arXiv:2107.14231 [hep-th]

work page arXiv 2021

[58] [59]

T. A. L ¨ahde and U.-G. Meißner,Nuclear Lattice Effective Field Theory: An Introduction, Lecture Notes in Physics, V ol. 957 (Springer, 2019)

work page 2019

[59] [60]

Giacalone et al

G. Giacaloneet al., Phys. Rev. Lett.135, 012302 (2025), arXiv:2402.05995 [nucl-th]

work page arXiv 2025

[60] [61]

Summerfield, B.-N

N. Summerfield, B.-N. Lu, C. Plumberg, D. Lee, J. Noronha- Hostler, and A. Timmins, Phys. Rev. C104, L041901 (2021), arXiv:2103.03345 [nucl-th]

work page arXiv 2021

[61] [62]

Yamaguchi, W

Y . Yamaguchi, W. Horiuchi, and N. Itagaki, Phys. Rev. C108, 014322 (2023), arXiv:2301.09839 [nucl-th]

work page arXiv 2023

[62] [63]

Bijker and F

R. Bijker and F. Iachello, Nucl. Phys. A1006, 122077 (2021), arXiv:2011.01976 [nucl-th]

work page arXiv 2021

[63] [64]

Mehrabpour, [arXiv:2506.12673 [nucl-th]]

H. Mehrabpour, arXiv preprint (2025), arXiv:2506.12673 [nucl-th]

work page arXiv 2025

[64] [65]

Yamaguchi, W

Y . Yamaguchi, W. Horiuchi, and N. Itagaki, Phys. Rev. C108, 014322 (2023), arXiv:2305.09182 [nucl-th]

work page arXiv 2023

[65] [66]

Li, W.-X

W. Li, W.-X. Zhou, and Y .-G. Ma, arXiv preprint (2025), arXiv:2504.04688 [nucl-th]

work page arXiv 2025

[66] [67]

H. D. Vries, C. W. D. Jager, and C. D. Vries, At. Data Nucl. Data Tables36, 495 (1987)

work page 1987

[67] [68]

Adachi and Y

S. Adachi and Y . Kanada-En’yo, Phys. Lett. B818, 136344 (2021), arXiv:2010.12484 [nucl-th]

work page arXiv 2021

[68] [69]

Shafi and S

K. Shafi and S. Chatterjee, (2025), arXiv:2505.11713 [nucl-th]

work page arXiv 2025

[69] [70]

Y . Wang, S. Zhao, B. Cao, H.-j. Xu, and H. Song, Phys. Rev. C 109, L051904 (2024), arXiv:2401.15723 [nucl-th]

work page arXiv 2024

[70] [71]

Drogosz, W

Z. Drogosz, W. Florkowski, and M. Hontarenko, Phys. Rev. D 110, 096018 (2024), arXiv:2408.03106 [hep-ph]

work page arXiv 2024

[71] [72]

Ke, (2025), arXiv:2509.09549 [nucl-th]

W. Ke, (2025), arXiv:2509.09549 [nucl-th]

work page arXiv 2025

[72] [73]

Zhang and J

C. Zhang and J. Jia, Phys. Rev. Lett.128, 022301 (2022)

work page 2022

[73] [74]

Relativistic fluid dynamics with spin

W. Florkowski, B. Friman, A. Jaiswal, R. Ryblewski, and E. Speranza, Physical Review C97, 041901 (2018), arXiv:1705.00587 [nucl-th]. 11 Appendix A: Derivation of the spin–correlation observable In this appendix, we outline the derivation of the relation between theΛ-pair spin-correlation observablev 2 Λ and the event-by-event polarization variance⟨P 2⟩, f...

work page internal anchor Pith review Pith/arXiv arXiv 2018