arxiv: 2605.04558 · v1 · submitted 2026-05-06 · ⚛️ nucl-th

Recognition: unknown

Effects of event-by-event hydrodynamic fluctuations on bottomonium dynamics in Pb--Pb collisions at sqrt{s_{NN}} = 5.02 TeV

Baoyi Chen, Jiamin Liu, Linyuan Wei, Yiyun Tang

Pith reviewed 2026-05-08 17:06 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords bottomoniumhydrodynamic fluctuationsnuclear modification factorelliptic flowPb-Pb collisionsheavy quarkoniumviscous hydrodynamicsevent-by-event simulation

0 comments

The pith

Event-by-event hydrodynamic fluctuations have only marginal effects on bottomonium R_AA and v2 in Pb-Pb collisions.

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

The paper simulates bottomonium evolution inside the hot medium created in lead-lead collisions at 5.02 TeV. It compares two versions of the medium: one that includes realistic event-by-event fluctuations from viscous hydrodynamics and one that uses a smooth average profile. The internal state of each bottomonium is evolved with a time-dependent Schrödinger equation that incorporates a temperature-dependent complex potential. The comparison shows that both the nuclear modification factor and the elliptic flow change only slightly when fluctuations are added. This indicates that the average medium properties largely determine the observed suppression and flow for these heavy states.

Core claim

Simulations of bottomonium dynamics in Pb-Pb collisions at 5.02 TeV using both fluctuating event-by-event viscous hydrodynamics and smooth media show that the nuclear modification factor R_AA and elliptic flow v2 for various bottomonium states are only marginally affected by the medium fluctuations.

What carries the argument

The iEBE-VISHNU event-by-event viscous hydrodynamic framework for medium evolution combined with a time-dependent Schrödinger equation using a temperature-dependent complex heavy-quark potential for bottomonium internal evolution.

Load-bearing premise

The iEBE-VISHNU hydrodynamic model and the chosen temperature-dependent complex potential fully capture the relevant physics of medium evolution and bottomonium interactions.

What would settle it

A calculation with a different hydrodynamic model or an extended potential that includes additional fluctuation-driven dissociation channels producing large shifts in R_AA or v2 would falsify the claim of only marginal effects.

Figures

Figures reproduced from arXiv: 2605.04558 by Baoyi Chen, Jiamin Liu, Linyuan Wei, Yiyun Tang.

**Figure 1.** Figure 1: FIG. 1. In-medium heavy-quark potential used in the view at source ↗

**Figure 2.** Figure 2: FIG. 2. Elliptic flow coefficient view at source ↗

**Figure 3.** Figure 3: FIG. 3. Representative temperature contour maps at the time view at source ↗

**Figure 4.** Figure 4: FIG. 4. Comparison of bottomonium view at source ↗

**Figure 5.** Figure 5: FIG. 5. Comparison of view at source ↗

read the original abstract

We investigate the effects of event-by-event hydrodynamic fluctuations on bottomonium nuclear modification factors and elliptic flow in Pb--Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. The internal evolution of the heavy quarkonium is described by a time-dependent Schr\"odinger equation with a temperature-dependent complex heavy-quark potential, while the hot QCD medium evolution is simulated using the iEBE-VISHNU event-by-event viscous hydrodynamic framework. By incorporating both fluctuating and smooth hot media, we observe that both $R_{AA}$ and $v_2$ of various bottomonium states are marginally affected by the medium fluctuations. By realistically simulating the dynamical evolution of bottomonium within a large set of event-by-event fluctuating hot QCD medium, this work provides key insights into the behavior of heavy-quarkonium observables in relativistic heavy-ion collisions.

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

Event-by-event fluctuations barely shift bottomonium R_AA and v2 in this setup.

read the letter

The key thing to know about this paper is that the authors find event-by-event hydrodynamic fluctuations have only a marginal impact on the nuclear modification factor and elliptic flow of bottomonium states in 5.02 TeV Pb-Pb collisions. They evolve the quarkonium using a time-dependent Schrödinger equation with a complex, temperature-dependent potential, and they do this inside both fluctuating and smooth versions of the iEBE-VISHNU hydro model. The direct comparison shows small differences in R_AA and v2 for the various states. This kind of test is straightforward but still worth doing because many groups use smooth media for simplicity when studying heavy flavors. The paper does a clean job of keeping the bottomonium dynamics identical in both cases so the only variable is the medium fluctuations. They also mention using a large set of events, which helps with the averaging. That approach lets them isolate the effect without introducing other changes. On the downside, the abstract and description don't include any numbers on how small the effect actually is, nor do they show error bars or discuss the number of events needed for convergence. Without that, it's hard to judge if the marginal difference is statistically solid or just below their resolution. The work also builds entirely on established codes and potentials, so it doesn't introduce new physics or techniques. This is the sort of paper that matters to specialists in heavy-ion phenomenology who are building models for quarkonia. It can help them decide if fluctuations are worth the effort for these observables. I would send it to peer review. The calculation is well-defined and the negative-style result could be informative for the community, even if it needs some extra quantification to be fully convincing.

Referee Report

1 major / 2 minor

Summary. The paper studies the effects of event-by-event hydrodynamic fluctuations on bottomonium R_AA and v2 in Pb-Pb collisions at 5.02 TeV. It evolves the medium with the iEBE-VISHNU viscous hydrodynamic framework and propagates bottomonium states via the time-dependent Schrödinger equation using a temperature-dependent complex heavy-quark potential. Direct comparison of fluctuating versus smooth (non-fluctuating) hydrodynamic backgrounds shows that both R_AA and v2 for various bottomonium states are only marginally affected by the fluctuations.

Significance. If the marginal-effect conclusion holds under improved statistical controls, the result would indicate that bottomonium observables are robust against hydrodynamic fluctuations, supporting the use of averaged hydrodynamic profiles in quarkonium suppression calculations and simplifying modeling of heavy-quarkonium dynamics in heavy-ion collisions.

major comments (1)

[Results] Results section (comparison of fluctuating vs. smooth media): the assertion that R_AA and v2 are 'marginally affected' is not accompanied by error bars, statistical uncertainties, or quantitative measures of the differences between the two classes of hydrodynamic evolution. Without these, it is not possible to determine whether the observed differences lie within numerical precision or represent a genuine small effect.

minor comments (2)

[Hydrodynamic framework] The definition and construction of the smooth hydrodynamic background (e.g., whether it is an event-averaged profile or a single representative profile) should be stated explicitly with a reference to the relevant equation or procedure in the iEBE-VISHNU implementation.
[Results] Figure captions and text should clarify the number of events used for the fluctuating ensemble and the statistics accumulated for each bottomonium state to allow assessment of numerical convergence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the major point below and will incorporate the requested improvements.

read point-by-point responses

Referee: [Results] Results section (comparison of fluctuating vs. smooth media): the assertion that R_AA and v2 are 'marginally affected' is not accompanied by error bars, statistical uncertainties, or quantitative measures of the differences between the two classes of hydrodynamic evolution. Without these, it is not possible to determine whether the observed differences lie within numerical precision or represent a genuine small effect.

Authors: We agree that the presentation would benefit from explicit statistical uncertainties and quantitative measures. In the revised manuscript we will add error bars to the R_AA and v_2 results, computed from the ensemble variance of the event-by-event hydrodynamic profiles. We will also report the maximum relative differences between the fluctuating and smooth cases together with their uncertainties, allowing a direct assessment that the observed effects remain within the statistical precision of the calculation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central result is obtained by explicit numerical simulation: bottomonium states are evolved via the time-dependent Schrödinger equation inside both event-by-event fluctuating iEBE-VISHNU hydrodynamic backgrounds and their smooth averaged counterparts, using the same temperature-dependent complex potential in both cases. The reported marginal impact on R_AA and v2 is a direct computational output of this side-by-side comparison across many events, not a redefinition, a fitted parameter renamed as a prediction, or a quantity forced by self-citation. All load-bearing steps (hydrodynamic evolution, potential insertion, and observable extraction) remain independent of the target observables and are externally specified by the cited frameworks and potential parametrization.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the domain-standard assumption that the chosen hydrodynamic model and complex potential capture the dominant physics; no new free parameters, axioms, or invented entities are introduced beyond those already present in the cited frameworks.

axioms (2)

domain assumption The iEBE-VISHNU viscous hydrodynamic framework with event-by-event fluctuations accurately models the hot QCD medium evolution in Pb-Pb collisions.
Invoked to generate both fluctuating and smooth media for the comparison.
domain assumption The temperature-dependent complex heavy-quark potential correctly describes the internal evolution of bottomonium states in the medium.
Used inside the time-dependent Schrödinger equation.

pith-pipeline@v0.9.0 · 5466 in / 1337 out tokens · 64638 ms · 2026-05-08T17:06:31.760435+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

38 extracted references · 34 canonical work pages · 1 internal anchor

[1]

Bazavovet al., Phys

A. Bazavovet al., Phys. Rev. D85, 054503 (2012), arXiv:1111.1710 [hep-lat]

work page arXiv 2012
[2]

Matsui and H

T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986)

1986
[3]

Andronicet al., Eur

A. Andronicet al., Eur. Phys. J. C76, 107 (2016), arXiv:1506.03981 [nucl-ex]

work page arXiv 2016
[4]

Rothkopf, Phys

A. Rothkopf, Phys. Rept.858, 1 (2020), arXiv:1912.02253 [hep-ph]

work page arXiv 2020
[5]

J. Zhao, K. Zhou, S. Chen, and P. Zhuang, Prog. Part. Nucl. Phys.114, 103801 (2020), arXiv:2005.08277 [nucl- th]

work page arXiv 2020
[6]

M. He, H. van Hees, and R. Rapp, Prog. Part. Nucl. Phys. 130, 104020 (2023), arXiv:2204.09299 [hep-ph]

work page arXiv 2023
[7]

Brambilla, A

N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Nucl. Phys. B566, 275 (2000), arXiv:hep-ph/9907240

work page arXiv 2000
[8]

Brambilla, M

N. Brambilla, M. A. Escobedo, J. Soto, and A. Vairo, Phys. Rev. D96, 034021 (2017), arXiv:1612.07248 [hep- ph]

work page arXiv 2017
[9]

Margotta, K

M. Margotta, K. McCarty, C. McGahan, M. Strick- land, and D. Yager-Elorriaga, Phys. Rev. D83, 105019 (2011), [Erratum: Phys.Rev.D 84, 069902 (2011)], arXiv:1101.4651 [hep-ph]

work page arXiv 2011
[10]

Brambilla, M

N. Brambilla, M. ´A. Escobedo, M. Strickland, A. Vairo, 6 /uni00000013/uni00000018/uni00000014/uni00000013/uni00000014/uni00000018/uni00000015/uni00000013 /uni00000053/uni00000037(GeV//uni00000046) /uni00000013/uni00000011/uni00000013 /uni00000013/uni00000011/uni00000015 /uni00000013/uni00000011/uni00000017 /uni00000013/uni00000011/uni00000019 /uni0000001...

work page arXiv 2012
[11]

Wen and B

L. Wen and B. Chen, Phys. Lett. B839, 137774 (2023), arXiv:2208.10050 [nucl-th]

work page arXiv 2023
[12]

Schenke, S

B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C82, 014903 (2010), arXiv:1004.1408 [hep-ph]

work page arXiv 2010
[13]

H. Song, S. A. Bass, U. Heinz, T. Hirano, and C. Shen, Phys. Rev. Lett.106, 192301 (2011), [Erratum: Phys.Rev.Lett. 109, 139904 (2012)], arXiv:1011.2783 [nucl-th]

work page arXiv 2011
[14]

Collective flow and viscosity in relativistic heavy-ion collisions,

U. Heinz and R. Snellings, Ann. Rev. Nucl. Part. Sci.63, 123 (2013), arXiv:1301.2826 [nucl-th]

work page arXiv 2013
[15]

L. Pang, Q. Wang, and X.-N. Wang, Phys. Rev. C86, 024911 (2012), arXiv:1205.5019 [nucl-th]

work page arXiv 2012
[16]

Alver and G

B. Alver and G. Roland, Phys. Rev. C81, 054905 (2010), [Erratum: Phys.Rev.C 82, 039903 (2010)], arXiv:1003.0194 [nucl-th]

work page arXiv 2010
[17]

Fluctuating Glasma initial conditions and flow in heavy ion collisions

B. Schenke, P. Tribedy, and R. Venugopalan, Phys. Rev. Lett.108, 252301 (2012), arXiv:1202.6646 [nucl-th]

work page Pith review arXiv 2012
[18]

F. G. Gardim, F. Grassi, M. Luzum, and J.-Y. Ollitrault, Phys. Rev. C85, 024908 (2012), arXiv:1111.6538 [nucl- th]

work page arXiv 2012
[19]

Qiu and U

Z. Qiu and U. W. Heinz, Phys. Rev. C84, 024911 (2011), arXiv:1104.0650 [nucl-th]

work page arXiv 2011
[20]

T. Song, K. C. Han, and C. M. Ko, Nucl. Phys. A897, 141 (2013)

2013
[21]

Islam and M

A. Islam and M. Strickland, JHEP03, 235, arXiv:2010.05457 [hep-ph]. 7

work page arXiv 2010
[22]

Alalawi, J

H. Alalawi, J. Boyd, C. Shen, and M. Strickland, Phys. Rev. C107, L031901 (2023), arXiv:2211.06363 [hep-ph]

work page arXiv 2023
[23]

H. Satz, J. Phys. G32, R25 (2006), arXiv:hep- ph/0512217

work page arXiv 2006
[24]

J. Liu, K. Zhou, and B. Chen, arXiv e-prints (2026), arXiv:2604.09198 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2026
[25]

Zheng, B

S. Zheng, B. Chen, X. Du, and S. Shi, Phys. Rev. C (2026)

2026
[26]

S. Shi, K. Zhou, J. Zhao, S. Mukherjee, and P. Zhuang, Phys. Rev. D105, 014017 (2022), arXiv:2105.07862 [hep- ph]

work page arXiv 2022
[27]

Burnier and A

Y. Burnier and A. Rothkopf, Phys. Rev. D95, 054511 (2017), arXiv:1607.04049 [hep-lat]

work page arXiv 2017
[28]

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

work page arXiv 2007
[29]

A. M. Sirunyanet al.(CMS), Phys. Lett. B790, 270 (2019), arXiv:1805.09215 [hep-ex]

work page arXiv 2019
[30]

Lansberg, Phys

J.-P. Lansberg, Phys. Rept.889, 1 (2020), arXiv:1903.09185 [hep-ph]

work page arXiv 2020
[31]

Chatrchyanet al.(CMS), Phys

S. Chatrchyanet al.(CMS), Phys. Lett. B727, 101 (2013), arXiv:1303.5900 [hep-ex]

work page arXiv 2013
[32]

C. Shen, Z. Qiu, H. Song, J. Bernhard, S. Bass, and U. Heinz, Comput. Phys. Commun.199, 61 (2016), arXiv:1409.8164 [nucl-th]

work page arXiv 2016
[33]

Adamet al.(ALICE), Phys

J. Adamet al.(ALICE), Phys. Rev. Lett.116, 222302 (2016), arXiv:1512.06104 [nucl-ex]

work page arXiv 2016
[34]

G. S. Denicol, H. Niemi, E. Molnar, and D. H. Rischke, Phys. Rev. D85, 114047 (2012), [Erratum: Phys.Rev.D 91, 039902 (2015)], arXiv:1202.4551 [nucl-th]

work page Pith review arXiv 2012
[35]

Huovinen and P

P. Huovinen and P. Petreczky, Nucl. Phys. A837, 26 (2010), arXiv:0912.2541 [hep-ph]

work page arXiv 2010
[36]

Cooper and G

F. Cooper and G. Frye, Phys. Rev. D10, 186 (1974)

1974
[37]

Acharyaet al.(ALICE), JHEP09, 006, arXiv:1805.04390 [nucl-ex]

S. Acharyaet al.(ALICE), JHEP09, 006, arXiv:1805.04390 [nucl-ex]

work page arXiv
[38]

Acharyaet al.(ALICE), Phys

S. Acharyaet al.(ALICE), Phys. Lett. B822, 136579 (2021), arXiv:2011.05758 [nucl-ex]

work page arXiv 2021