Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Left-right splitting of elliptic flow in heavy ion collisions: TRENTo-3D initialization and CLVisc hydrodynamic simulations

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Odd flow harmonics drive the left-right splitting of elliptic flow in heavy-ion collisions.

desk verdict Solid analytic extension and useful model scan, but the v3-dominated Δv2(pT) prediction needs event-by-event hydro before I'd bet on it. read the letter →

arxiv 2505.14637 v1 pith:MZ2VYMIN submitted 2025-05-20 nucl-th hep-ph

Ze-Fang Jiang , Xiang Fan , Duan She , Shasha Ye , Ben-Wei Zhang This is my paper · ORCID
classification nucl-thhep-ph
keywords ellipticflowsplittingleft-rightasymmetrydirectedtriangularTRENTo-3DCLVisctiltedfireballheavy-ioncollisions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish why elliptic flow differs on the left and right sides of the reaction plane in non-central heavy-ion collisions. It claims that this splitting, Δv2, is primarily controlled by odd flow harmonics: directed flow v1 dominates its rapidity dependence, while triangular flow v3 dominates its transverse-momentum dependence. Using the TRENTo-3D initial condition model coupled with CLVisc hydrodynamics, the paper makes testable predictions for the ratio Δv2/v2, including a slope of 4.4% in pseudorapidity and a zero crossing near pT ~ 1.5 GeV. A sympathetic reader would care because these predictions turn Δv2 into a probe of the three-dimensional initial geometry of the quark-gluon plasma and a constraint on sub-nucleonic structure parameters.

What carries the argument

The central object is the Fourier-mode decomposition of Δv2, Eq. (18), which expresses the left-right splitting as a rational function of v1, v2, v3, and v5 relative to the reaction plane. This identity shows that only odd harmonics contribute to the splitting and that v2 enters as a multiplicative weight, so the sign and magnitude of Δv2 are set by the competition between v1, v3, and v5. The machinery also includes the TRENTo-3D initial condition, which generates a longitudinally tilted, asymmetric energy-density profile with tunable sub-nucleonic hotspots and fragmentation regions, and the CLVisc (3+1)-dimensional viscous hydrodynamic code that evolves this profile into final-state particle anisotropies. Together, they convert the abstract harmonic formula into concrete predictions for Δv2(η) and Δv2(pT).

What would settle it

Measure Δv2/v2 as a function of pT in 5-40% Au+Au collisions at 200 GeV using the spectator plane to define left and right; if the zero crossing does not appear near pT ≈ 1.5 GeV, or if the pseudorapidity slope d(Δv2/v2)/dη differs significantly from 4.4% for |η| < 1.0, the predicted v3 dominance is ruled out. A computational falsifier would be to rerun the same TRENTo-3D + CLVisc setup event-by-event rather than with a 2000-event average and compare the resulting v3 contribution to Δv2(pT).

Watch

Extended reading notes

Core claim

The paper derives an analytic decomposition of the left-right elliptic flow splitting, Δv2, in terms of reaction-plane-correlated odd harmonics v1, v3, and v5, weighted by v2 itself. Applying this to Au+Au collisions at 200 GeV with TRENTo-3D initial conditions and (3+1)-dimensional CLVisc hydrodynamics, the authors find that the v1 term dominates Δv2(η), while the v3 term becomes the dominant contributor to Δv2(pT) in the region |η| < 1.3. They further show that Δv2(pT) is sensitive to the number of sub-nucleonic constituents nc, the transverse momentum scale kT, and fragmentation profile parameters α and β, whereas Δv2(η) responds mainly to kT through its control of the fireball's longitudinal tilt. The paper concludes with two quantitative predictions: the slope d(Δv2/v2)/dη reaches 4.4% for |η| < 1.0, and Δv2/v2 crosses zero at pT ≈ 1.5 GeV.

Load-bearing premise

The predictions assume that a single smooth initial condition, formed by averaging 2000 events, faithfully captures the reaction-plane-correlated odd harmonics (v1, v3, v5) that enter the Δv2 formula, even though the paper attributes the nc dependence of Δv2(pT) to event-by-event sub-nucleonic fluctuations that averaging suppresses.

Editorial extensions

If this is right

  • If the central claim is correct, the slope of Δv2/v2 versus pseudorapidity, predicted at 4.4% for |η| < 1.0 in 5-40% Au+Au collisions at 200 GeV, is a direct experimental target.
  • The predicted zero crossing of Δv2/v2 at pT ≈ 1.5 GeV provides a sharp, falsifiable signature that distinguishes the v3-dominated regime at low pT from the v1-dominated regime at higher pT.
  • The sensitivity of Δv2(pT) to nc, kT, α, and β implies that future precision measurements of Δv2 can help constrain the sub-nucleonic structure and longitudinal fragmentation profiles of the TRENTo-3D model.
  • The relative insensitivity of Δv2(η) to nc, α, and β suggests that the rapidity dependence of Δv2 isolates the tilt of the fireball, offering a cleaner probe of initial geometry than v2 alone.
  • The explicit dependence of Δv2 on v3 and v5 implies that interpretations of elliptic flow splitting must account for triangular and higher odd harmonics, not just directed flow.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's use of a smooth, averaged initial condition (2000 events) may underestimate event-by-event fluctuations of the reaction-plane-correlated v3; if so, the predicted v3 dominance in Δv2(pT) and the exact pT of the zero crossing could shift, making event-by-event simulations a natural next check.
  • The same harmonic decomposition could be applied to other flow observables, such as left-right splitting of triangular or higher-order flow, which might provide independent tests of the three-dimensional initial geometry.
  • The sensitivity of Δv2(pT) to model parameters suggests that Δv2 could be included alongside v1 and v3 in Bayesian parameter estimation for initial-condition models, tightening the constraints on the QGP's initial state.
  • Because the decomposition expresses Δv2 in terms of reaction-plane harmonics, measurements using the RHIC Event Plane Detector (which directly estimates the reaction plane) can be compared with the model's predictions without the ambiguities of event-plane-based proxies.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This manuscript studies the left-right splitting of elliptic flow, Δv2, in 5-40% centrality Au+Au collisions at √sNN = 200 GeV, using the TRENTo-3D initial condition model coupled to (3+1)-dimensional CLVisc hydrodynamics. The authors derive an approximate analytic expression for Δv2 in terms of reaction-plane harmonics v1, v2, v3, and v5 (Eqs. (16)-(21)), and then evaluate it with a smooth initial condition obtained by averaging 2000 TRENTo-3D events. They report that v1 dominates Δv2(η), that v3 dominates Δv2(pT) in the region |η|<1.3, and that Δv2(pT) is sensitive to the sub-nucleon parameter nc, the transverse momentum scale kT, and the fragmentation profile parameters α and β. Concrete predictions are given for the slope d(Δv2/v2)/dη ≈ 4.4% for |η|<1.0 and a zero crossing of Δv2/v2 at pT ≈ 1.5 GeV.

Significance. If the predictions are correct, the paper provides a new and testable contribution to the understanding of Δv2, namely the dominant role of v3 in Δv2(pT) at mid-rapidity, which goes beyond earlier studies that considered only v1. The analytical identity for Δv2 is clearly derived and the comparison of the model's v1 with STAR data provides a nontrivial anchor. Notably, no parameter is fitted to the predicted observable, so the predictions are not circular. The sensitivity study of Δv2(pT) to nc, kT, α, and β is a useful demonstration of how this observable could constrain the TRENTo-3D model. However, the central quantitative predictions and the interpretation of the nc dependence rely on a smooth, event-averaged initial condition, and the paper does not yet demonstrate that this approximation faithfully represents the event-by-event quantities that enter actual measurements. The significance is therefore conditional on resolving that methodological point.

major comments (4)
  1. [Section II.B, Fig. 1, and Eqs. (16)-(21)] The initial conditions are obtained by averaging 2000 TRENTo-3D events into a single smooth profile that is then evolved hydrodynamically. This is not equivalent to averaging final-state harmonics event by event because Eq. (18) is nonlinear in v1, v2, v3, and v5; in general, the event average of the right-hand side is not equal to the right-hand side evaluated at the averaged harmonics. The paper must either run event-by-event hydrodynamic simulations, provide a quantitative estimate of the bias introduced by the one-shot averaging, or present a specific argument why the smooth profile captures the reaction-plane-correlated odd harmonics v1, v3^RP, and v5^RP that enter Eq. (18). Without such a justification, the predicted v3 dominance in Δv2(pT) and the pT≈1.5 GeV zero crossing in Fig. 8 are not firmly established.
  2. [Section III, Fig. 4 (lower panel)] The text attributes the nc dependence of Δv2(pT) to enhanced 'hotspot' fluctuations at larger nc, but the calculation uses a smooth initial condition averaged over 2000 events, which the same text acknowledges suppresses sub-nucleonic fluctuations in the case of Δv2(η). This is internally inconsistent: if fluctuations are averaged out, they cannot be the mechanism for the nc sensitivity seen in the lower panel of Fig. 4. The authors should recompute the nc dependence with event-by-event initial conditions, or alternatively explain how nc affects the averaged initial geometry (for example through the effective source size or the Gaussian smearing width) and revise the interpretation accordingly.
  3. [Section II.C, Eq. (14)] The azimuthal distribution in Eq. (14) contains both cosine and sine terms through the coefficients vn and sn, but the derivation of Eqs. (16)-(21) keeps only the cosine harmonics. The paper should either justify that the sn terms vanish or are negligible for the reaction-plane definition used here, or include them in the algebra. As written, the approximate expression for Δv2 is an uncontrolled truncation of the full Fourier expansion.
  4. [Section III, Fig. 8] The quantitative predictions—d(Δv2/v2)/dη = 4.4% and Δv2/v2 crossing zero at pT ≈ 1.5 GeV—are given as central values without any statistical or systematic uncertainty. Since these are presented as testable predictions, the authors should propagate at least the posterior parameter uncertainties from the Bayesian calibration of Ref. [42], or demonstrate robustness to reasonable variations in the model parameters. Without such an uncertainty estimate, the predictions are difficult to falsify experimentally.
minor comments (5)
  1. [Abstract and Introduction] There are grammatical errors, e.g., 'are primarily depend' in the abstract and 'our results demonstrate' should be 'our results demonstrate that'. Please edit for clarity.
  2. [Fig. 1 caption] The caption contains 'somth' which appears to be a typo for 'smooth'. Also, Fig. 4 caption contains 'samller' which should be 'smaller'.
  3. [Section II.C] The sentence 'the v3 and v5 does not represent the usual flow coefficient' has a subject-verb agreement error; it should be 'v3 and v5 do not represent the usual flow coefficients'.
  4. [References] Ref. [42] is an arXiv preprint (arXiv:2306.08665). If a peer-reviewed version is now available, it should be cited instead of or in addition to the preprint.
  5. [Figures] Several figures (especially Figs. 2-4) have axis labels that appear corrupted or missing in the extracted text; the authors should ensure that all axis labels and legends are legible in the final PDF, since the current rendering may hinder reproduction.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Δv2 predictions are genuine outputs of an externally calibrated initial-condition and hydrodynamic framework, not refits of the target observable.

full rationale

The paper's derivation chain is self-contained and non-circular. The TRENTo-3D model parameters in Table I are taken from the Bayesian calibration of Ref. [42] to dNch/dη distributions, and the paper states these parameters 'successfully reproduces the dNch/dη distributions'; no parameter is fitted to Δv2. The central formula, Eq. (18) and its truncated forms Eqs. (19)-(21), is derived as a mathematical identity from the Fourier expansion of dN/dφ (Eq. (14)), not imposed by construction. The harmonic coefficients v1, v2, v3, and v5 that enter Eq. (21) are outputs of the TRENTo-3D+CLVisc simulation, with v1 checked against STAR data in Fig. 2. The claims that v1 dominates Δv2(η) and v3 dominates Δv2(pT) are therefore quantitative model results, not consequences of how the observables are defined. The only self-citations (CLVisc code Refs. [34,35] and earlier hydro studies Refs. [30,31]) are tool and background citations with external usage; they are not load-bearing for the Δv2 derivation. The use of a 2000-event-averaged one-shot initial condition is a modeling approximation that could affect numerical precision, but it does not make the prediction equivalent to an input or to a fitted quantity, so it is a correctness caveat rather than circularity.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central claim depends entirely on parameters fitted in prior work (Ref [42]) and on modeling choices (smooth initial condition, no afterburner, freeze-out energy density). The paper itself introduces no new free parameters or entities.

free parameters (8)
  • n_c (constituent partons per nucleon) = 16.4 (varied to 3, 10, 20)
    From Bayesian calibration in Ref [42]; controls sub-nucleonic hotspot density and affects v3 and thus Δv2(pT) in this paper.
  • k_T (parton transverse momentum scale) = 0.33 GeV (varied in sensitivity study)
    From Ref [42]; sets the longitudinal tilt geometry and η_max; the paper finds Δv2(η) strongly sensitive to it.
  • alpha (fragmentation profile exponent) = 4.6 (varied to 1, 3, 4.6)
    From Ref [42]; controls the fragmentation region profile; affects Δv2(pT) non-monotonically.
  • beta (fragmentation profile exponent) = 0.19 (varied to 0.1, 0.2, 0.5)
    From Ref [42]; controls longitudinal shape; larger beta flattens distribution and reduces Δv2(pT).
  • w (source size) = 1.3 fm
    From Ref [42]; sets initial source size; not varied in this study.
  • chi (correlation length ratio) = 0.5
    From Ref [42]; tunes sub-nucleon correlation length; not varied.
  • f (central fireball profile exponent) = 1.0
    From Ref [42]; controls central fireball rapidity profile; not varied.
  • e_frz (freeze-out energy density) = 0.4 GeV/fm^3
    Chosen in this paper for Cooper-Frye freeze-out; affects pT spectra and flow harmonics; no uncertainty given.
assumptions (5)
  • domain assumption TRENTo-3D parameters calibrated to dNch/dη in Ref [42] transfer to Δv2 predictions at 200 GeV without re-calibration.
    The paper inherits all model parameters from the prior Bayesian fit and does not validate the new observable against data.
  • domain assumption The reaction-plane angle ψ_RP used in the model is experimentally accessible via the first-order spectator plane (STAR Event Plane Detector).
    Section II.C; the Δv2 definition and the comparison strategy depend on this proxy.
  • ad hoc to paper A smooth, event-averaged initial condition (2000 events per centrality) captures the reaction-plane-correlated odd harmonics v3^RP and v5^RP.
    Section II.B and Fig. 1; the one-shot averaging suppresses event-by-event fluctuations that generate v3, yet the paper claims sensitivity to nc via v3.
  • domain assumption Neglecting hadronic rescattering after freeze-out and bulk viscosity does not change Δv2 qualitatively.
    Section II.B explicitly states these omissions; low-pT flow harmonics are typically modified by an afterburner.
  • standard math Truncating the Fourier decomposition at n=5 is sufficient for Δv2.
    Eqs. (14)-(21); higher harmonics are assumed negligible in the integrals.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Left-right splitting of elliptic flow in heavy ion collisions: TRENTo-3D initialization and CLVisc hydrodynamic simulations." pith.science (2026). https://pith.science/paper/MZ2VYMIN

@misc{pith2026250514637,
  author       = {Pith},
  title        = {Pith review of: Left-right splitting of elliptic flow in heavy ion collisions: TRENTo-3D initialization and CLVisc hydrodynamic simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MZ2VYMIN}},
  note         = {Machine review of arXiv:2505.14637}
}
abstract

Using the TRENTo-3D initial condition model coupled with (3+1)-dimensional CLVisc hydrodynamic simulations, we systematically investigate the left-right splitting of elliptic flow ($\Delta v_{2}$) for soft particles in relativistic heavy-ion collisions. Our study reveals that the final distribution characteristics of $\Delta v_{2}$ are primarily depend on the odd flow harmonics and $v_{2}$ itself. We find that the parton transverse momentum scale $k_\mathrm{T}$ not only determines the geometric tilt of the QGP fireball but also significantly affects the rapidity dependence of both $v_1$ and $\Delta v_{2}$, providing new insights into the splitting mechanism of $\Delta v_{2}$. Furthermore, our results demonstrate that $\Delta v_{2} (p_\mathrm{T})$ exhibits significant sensitivity to influences such as the sub-nucleonic degrees of freedom (or `hotspots'), transverse momentum scale, and fragmentation region profile. By analyzing the $\Delta v_{2}$ and $\Delta v_{2}/v_{2}$ ratio, our findings provide new constraints on the uncertainties of the QGP initial state and provide additional constraints for refining model parameters.

Figures

Figures reproduced from arXiv: 2505.14637 by the authors.

Figure 1
Figure 1. FIG. 1: (Color online) The energy density evolution in the reaction plane ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (Color online) Upper panel: the rapidity dependence of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (Color online) Upper panel: Predicted [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 8
Figure 8. Figure 8: FIG. 8: (Color online) [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Study the Longitudinal Entropy Deposition using d+Au Collision

    nucl-th 2026-07 conditional novelty 5.0 of 10

    A 3D entropy deposition model with β≈0.35 and n_BC-dependent rapidity loss, plus ab initio deuteron sampling, reproduces d+Au dNch/dη, spectra, and vn and transfers to p+Au, 3He+Au, and Au+Au.

Reference graph

Works this paper leans on

53 extracted references · 47 canonical work pages · cited by 1 Pith paper

  1. [42]

    Derek Soeder, Weiyao Ke, J. F. Paquet, and Steffen A. Bass. Bayesian parameter estimation with a new three-dimensional initial-conditions model for ultrarelativistic heavy-ion colli- sions.arXiv: 2306.08665, 6 2023

    arXiv 2023

  2. [1]

    Heinz and R

    U. Heinz and R. Snellings. Collective flow and viscosity in rela- tivistic heavy-ion collisions.Ann. Rev. Nucl. Part. Sci., 63:123– 151, 2013

    work page 2013

  3. [2]

    Heavy Ion Collisions: The Big Picture, and the Big Questions.Ann

    Wit Busza, Krishna Rajagopal, and Wilke van der Schee. Heavy Ion Collisions: The Big Picture, and the Big Questions.Ann. Rev. Nucl. Part. Sci., 68:339–376, 2018

    work page 2018

  4. [3]

    Huichao Song and U. W. Heinz. Suppression of elliptic flow in a minimally viscous quark-gluon plasma.Phys. Lett. B, 658:279– 283, 2008

    work page 2008

  5. [4]

    Bass, and Berndt Muller

    Hannah Petersen, Guang-You Qin, Steffen A. Bass, and Berndt Muller. Triangular flow in event-by-event ideal hydrodynamics in Au+Au collisions at √sNN = 200AGeV.Phys. Rev. C, 82:041901, 2010

    work page 2010

  6. [5]

    Adams et al

    J. Adams et al. Particle type dependence of azimuthal anisotropy and nuclear modification of particle production in Au + Au collisions at s(NN)**(1/2) = 200-GeV.Phys. Rev. Lett., 92:052302, 2004

    work page 2004

  7. [6]

    Adamczyk et al

    L. Adamczyk et al. Beam-Energy Dependence of the Directed Flow of Protons, Antiprotons, and Pions in Au+Au Collisions. Phys. Rev. Lett., 112(16):162301, 2014

    work page 2014

  8. [7]

    Adamczyk et al

    L. Adamczyk et al. Third Harmonic Flow of Charged Particles in Au+Au Collisions at sqrtsNN = 200 GeV.Phys. Rev. C, 88(1):014904, 2013

    work page 2013

Show all 53 references
  1. [8]

    Globally polarized quark-gluon plasma in non-central A+A collisions.Phys

    Zuo-Tang Liang and Xin-Nian Wang. Globally polarized quark-gluon plasma in non-central A+A collisions.Phys. Rev. Lett., 94:102301, 2005. [Erratum: Phys.Rev.Lett. 96, 039901 (2006)]

    2006

  2. [9]

    Adamczyk et al

    L. Adamczyk et al. GlobalΛhyperon polarization in nuclear collisions: evidence for the most vortical fluid.Nature, 548:62– 65, 2017

    2017

  3. [10]

    Polarization ofΛ( ¯Λ) hyperons along the beam direction in Au+Au collisions at√sN N= 200 GeV.Phys

    Jaroslav Adam et al. Polarization ofΛ( ¯Λ) hyperons along the beam direction in Au+Au collisions at√sN N= 200 GeV.Phys. Rev. Lett., 123(13):132301, 2019

    2019

  4. [11]

    Kharzeev, and Harmen J

    Kenji Fukushima, Dmitri E. Kharzeev, and Harmen J. Warringa. The Chiral Magnetic Effect.Phys. Rev. D, 78:074033, 2008

    2008

  5. [12]

    Event-by-event gener- ation of electromagnetic fields in heavy-ion collisions.Phys

    Wei-Tian Deng and Xu-Guang Huang. Event-by-event gener- ation of electromagnetic fields in heavy-ion collisions.Phys. Rev. C, 85:044907, 2012

    2012

  6. [13]

    Electromagnetic field effects on nucleon transverse momentum for heavy ion collisions

    Xian-Gai Deng and Yu-Gang Ma. Electromagnetic field effects on nucleon transverse momentum for heavy ion collisions. . . . Nucl. Sci. Tech., 28(12):182, 2017

    2017

  7. [14]

    Electromagnetic fields in ultra-peripheral relativistic heavy-ion collisions.Nucl

    Jie Zhao, Jin-Hui Chen, Xu-Guang Huang, and Yu-Gang Ma. Electromagnetic fields in ultra-peripheral relativistic heavy-ion collisions.Nucl. Sci. Tech., 35(2):20, 2024

    2024

  8. [15]

    Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV.Phys

    K Aamodt et al. Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV.Phys. Rev. Lett., 105:252302, 2010

    2010

  9. [16]

    Measurement of the centrality and pseudo- rapidity dependence of the integrated elliptic flow in lead-lead collisions at √sNN = 2.76TeV with the ATLAS detector.Eur

    Georges Aad et al. Measurement of the centrality and pseudo- rapidity dependence of the integrated elliptic flow in lead-lead collisions at √sNN = 2.76TeV with the ATLAS detector.Eur . Phys. J. C, 74(8):2982, 2014

    2014

  10. [17]

    Measurement of the Elliptic Anisotropy of Charged Particles Produced in PbPb Collisions at √sN N=2.76 TeV.Phys

    Serguei Chatrchyan et al. Measurement of the Elliptic Anisotropy of Charged Particles Produced in PbPb Collisions at √sN N=2.76 TeV.Phys. Rev. C, 87(1):014902, 2013

    2013

  11. [18]

    V oloshin, Arthur M

    Sergei A. V oloshin, Arthur M. Poskanzer, and Raimond Snellings. Collective phenomena in non-central nuclear col- lisions.Landolt-Bornstein, 23:293–333, 2010

    2010

  12. [19]

    Flow analysis with cumulants: Direct calculations.Phys

    Ante Bilandzic, Raimond Snellings, and Sergei V oloshin. Flow analysis with cumulants: Direct calculations.Phys. Rev. C, 83:044913, 2011

    2011

  13. [20]

    Aidala et al

    C. Aidala et al. Creation of quark–gluon plasma droplets with three distinct geometries.Nature Phys., 15(3):214–220, 2019

    2019

  14. [21]

    M. I. Abdulhamid et al. Measurements of the Elliptic and Triangular Azimuthal Anisotropies in Central He3+Au, d+Au and p+Au Collisions at sNN=200 GeV.Phys. Rev. Lett., 130(24):242301, 2023

    2023

  15. [22]

    Multiplicity and Transverse Momen- tum Dependence of Two- and Four-Particle Correlations in pPb and PbPb Collisions.Phys

    Serguei Chatrchyan et al. Multiplicity and Transverse Momen- tum Dependence of Two- and Four-Particle Correlations in pPb and PbPb Collisions.Phys. Lett. B, 724:213–240, 2013

    2013

  16. [23]

    Probing the Partonic Degrees of Freedom in High-Multiplicityp−P bcollisions at√sN N= 5.02 TeV.Phys

    Wenbin Zhao, Che Ming Ko, Yu-Xin Liu, Guang-You Qin, and Huichao Song. Probing the Partonic Degrees of Freedom in High-Multiplicityp−P bcollisions at√sN N= 5.02 TeV.Phys. Rev. Lett., 125(7):072301, 2020

    2020

  17. [24]

    Investigating the elliptic anisotropy of identified particles in p–Pb collisions with a multi-phase transport model.Nucl

    Si-Yu Tang, Liang Zheng, Xiao-Ming Zhang, and Ren-Zhuo Wan. Investigating the elliptic anisotropy of identified particles in p–Pb collisions with a multi-phase transport model.Nucl. Sci. Tech., 35(2):32, 2024

    2024

  18. [25]

    Yu. B. Ivanov, V . N. Russkikh, and V . D. Toneev. Relativistic heavy-ion collisions within 3-fluid hydrodynamics: Hadronic scenario.Phys. Rev. C, 73:044904, 2006

    2006

  19. [26]

    Flow and interferometry in 3+1 dimensional vis- cous hydrodynamics.Phys

    Piotr Bozek. Flow and interferometry in 3+1 dimensional vis- cous hydrodynamics.Phys. Rev. C, 85:034901, 2012

    2012

  20. [27]

    Dynamical initial state model for relativistic heavy-ion collisions.Phys

    Chun Shen and Bj ¨orn Schenke. Dynamical initial state model for relativistic heavy-ion collisions.Phys. Rev. C, 97(2):024907, 2018

    2018

  21. [28]

    Alzhrani

    Chun Shen and S. Alzhrani. Collision-geometry-based 3D ini- tial condition for relativistic heavy-ion collisions.Phys. Rev. C, 102(1):014909, 2020

    2020

  22. [29]

    Sahr Alzhrani, Sangwook Ryu, and Chun Shen.Λspin polar- ization in event-by-event relativistic heavy-ion collisions.Phys. Rev. C, 106(1):014905, 2022

    2022

  23. [30]

    Yang, and Defu Hou

    Ze Fang Jiang, Duan She, C.B. Yang, and Defu Hou. Pertur- bation solutions of relativistic viscous hydrodynamics forlon- gitudinally expanding fireballs.Chin. Phys. C, 44(8):084107, 2020

    2020

  24. [31]

    Ze-Fang Jiang, C. B. Yang, and Qi Peng. Directed flow of charged particles within idealized viscous hydrodynamics at energies available at the BNL Relativistic Heavy Ion Col- lider and at the CERN Large Hadron Collider.Phys. Rev. C, 104(6):064903, 2021

    2021

  25. [32]

    Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart.Nucl

    Jiangyong Jia et al. Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart.Nucl. Sci. Tech., 35(12):220, 2024

    2024

  26. [33]

    Collective flow and hydrodynamics in large and small systems at the LHC

    Huichao Song, You Zhou, and Katarina Gajdosova. Collective flow and hydrodynamics in large and small systems at the LHC. Nucl. Sci. Tech., 28(7):99, 2017

    2017

  27. [34]

    Petersen, and Xin-Nian Wang

    Long-Gang Pang, H. Petersen, and Xin-Nian Wang. Pseudora- 9 pidity distribution and decorrelation of anisotropic flow within the open-computing-language implementation CLVisc hydro- dynamics.Phys. Rev. C, 97(6):064918, 2018

    2018

  28. [35]

    Xiang-Yu Wu, Guang-You Qin, Long-Gang Pang, and Xin- Nian Wang. (3+1)-D viscous hydrodynamics at finite net baryon density: Identified particle spectra, anisotropic flows, and flow fluctuations across energies relevant to the beam- energy scan at RHIC.Phys. Rev. C, 105(3):034909, 2022

    2022

  29. [36]

    Recent development of hydrodynamic modeling in heavy-ion collisions.Nucl

    Chun Shen and Li Yan. Recent development of hydrodynamic modeling in heavy-ion collisions.Nucl. Sci. Tech., 31(12):122, 10 2020

    2020

  30. [37]

    A Multi-phase transport model for relativistic heavy ion collisions.Phys

    Zi-Wei Lin, Che Ming Ko, Bao-An Li, Bin Zhang, and Subrata Pal. A Multi-phase transport model for relativistic heavy ion collisions.Phys. Rev. C, 72:064901, 2005

    2005

  31. [38]

    Further developments of a multi- phase transport model for relativistic nuclear collisions.Nucl

    Zi-Wei Lin and Liang Zheng. Further developments of a multi- phase transport model for relativistic nuclear collisions.Nucl. Sci. Tech., 32(10):113, 2021

    2021

  32. [39]

    Splitting of elliptic flow in non-central relativistic heavy-ion collisions.arXiv: 2108.12735, 8 2021

    Zhengyu Chen, Zeyan Wang, Carsten Greiner, and Zhe Xu. Splitting of elliptic flow in non-central relativistic heavy-ion collisions.arXiv: 2108.12735, 8 2021

    2021 arXiv

  33. [40]

    Left-right splitting of elliptic flow due to directed flow in heavy ion collisions.Phys

    Chao Zhang and Zi-Wei Lin. Left-right splitting of elliptic flow due to directed flow in heavy ion collisions.Phys. Rev. C, 106(5):054910, 2022

    2022

  34. [41]

    Splitting of elliptic flow in a tilted fireball.Phys

    Tribhuban Parida and Sandeep Chatterjee. Splitting of elliptic flow in a tilted fireball.Phys. Rev. C, 106(4):044907, 2022

    2022

  35. [43]

    Denicol, Charles Gale, Sangyong Jeon, Akihiko Monnai, Bj¨orn Schenke, and Chun Shen

    Gabriel S. Denicol, Charles Gale, Sangyong Jeon, Akihiko Monnai, Bj¨orn Schenke, and Chun Shen. Net baryon diffusion in fluid dynamic simulations of relativistic heavy-ion collisions. Phys. Rev. C, 98(3):034916, 2018

    2018

  36. [44]

    Equation of state at finite densities for QCD matter in nuclear collisions

    Akihiko Monnai, Bj ¨orn Schenke, and Chun Shen. Equation of state at finite densities for QCD matter in nuclear collisions. Phys. Rev. C, 100(2):024907, 2019

    2019

  37. [45]

    QCD Equa- tion of State at Finite Chemical Potentials for Relativistic Nu- clear Collisions.Int

    Akihiko Monnai, Bj ¨orn Schenke, and Chun Shen. QCD Equa- tion of State at Finite Chemical Potentials for Relativistic Nu- clear Collisions.Int. J. Mod. Phys. A, 36(07):2130007, 2021

    2021

  38. [46]

    Splitting of proton-antiproton directed flow in rel- ativistic heavy-ion collisions.Phys

    Piotr Bozek. Splitting of proton-antiproton directed flow in rel- ativistic heavy-ion collisions.Phys. Rev. C, 106(6):L061901, 2022

    2022

  39. [47]

    Adamczyk et al

    L. Adamczyk et al. Fluctuations of charge separation perpen- dicular to the event plane and local parity violation in√sN N= 200GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider.Phys. Rev. C, 88(6):064911, 2013

    2013

  40. [48]

    Charge separation relative to the reaction plane in Pb-Pb collisions at √sN N = 2.76TeV.Phys

    Betty Abelev et al. Charge separation relative to the reaction plane in Pb-Pb collisions at √sN N = 2.76TeV.Phys. Rev. Lett., 110(1):012301, 2013

    2013

  41. [49]

    The STAR Event Plane Detector.Nucl

    Joseph Adams et al. The STAR Event Plane Detector.Nucl. Instrum. Meth. A, 968:163970, 2020

    2020

  42. [50]

    Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscos- ity*.Chin

    Jie Zhu, Xiang-Yu Wu, and Guang-You Qin. Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscos- ity*.Chin. Phys. C, 49(4):044103, 2025

    2025

  43. [51]

    Effects of sub-nucleonic fluctuations on the longitudinal structure of heavy-ion collisions.arXiv: 2501.14872, 1 2025

    Oscar Garcia-Montero, S ¨oren Schlichting, and Jie Zhu. Effects of sub-nucleonic fluctuations on the longitudinal structure of heavy-ion collisions.arXiv: 2501.14872, 1 2025

    2025 arXiv

  44. [52]

    Bass, Tetsufumi Hirano, Pasi Huovinen, Zhi Qiu, Huichao Song, and Ulrich Heinz

    Chun Shen, Steffen A. Bass, Tetsufumi Hirano, Pasi Huovinen, Zhi Qiu, Huichao Song, and Ulrich Heinz. The QGP shear viscosity: Elusive goal or just around the corner?J. Phys. G, 38:124045, 2011

    2011

  45. [53]

    Ruggieri, F

    M. Ruggieri, F. Scardina, S. Plumari, and V . Greco. Elliptic Flow from Non-equilibrium Initial Condition with a Saturation Scale.Phys. Lett. B, 727:177–181, 2013

    2013

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.