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arxiv: 2508.20995 · v2 · submitted 2025-08-28 · ⚛️ nucl-th

Bottomonium transport in a strongly coupled quark-gluon plasma

Biaogang Wu , Ralf Rapp This is my paper

Pith reviewed 2026-05-18 20:20 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords bottomonium transportquark-gluon plasmaheavy-ion collisionsT-matrix interactionsregenerationsuppressionLHC Pb-Pb datahydrodynamic evolution
0
0 comments X p. Extension

The pith

A semiclassical transport model with lattice-based reaction rates reproduces the centrality dependence of bottomonium yields in LHC 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 develops a transport framework for bottomonium in the quark-gluon plasma that uses nonperturbative rates derived from lattice QCD T-matrix interactions combined with hydrodynamic evolution of the medium. Suppression is calculated along particle trajectories while regeneration uses an extended rate equation accounting for spatial gradients. With significantly larger reaction rates than before, the model requires careful treatment of bottom quark distributions and equilibrium limits. It successfully accounts for the observed centrality dependence of bottomonium production in lead-lead collisions at 5.02 TeV, though it shows differences at high transverse momenta.

Core claim

Within current uncertainties our approach can describe the centrality dependence of bottomonium yields measured in Pb-Pb (√s_NN=5.02 TeV) collisions at the LHC, while discrepancies are found at large transverse momenta. This is achieved by setting up a semiclassical transport approach that combines nonperturbative reaction rates rooted in lattice-constrained T-matrix interactions with a viscous hydrodynamic medium evolution, computing suppression along trajectories and regeneration via a rate equation extended to a medium with spatial gradients.

What carries the argument

Semiclassical transport approach combining nonperturbative reaction rates from lattice-constrained T-matrix interactions with viscous hydrodynamic evolution, using trajectory-based suppression and a rate equation extended to media with spatial gradients.

If this is right

  • The substantially higher reaction rates enhance both dissociation and regeneration processes compared to earlier calculations.
  • A reliable assessment of bottomonium equilibrium limits becomes necessary because of the increased rates.
  • Non-thermal momentum distributions of bottom quarks must be tracked through the expanding medium.
  • The framework accounts for centrality dependence of yields within current uncertainties.

Where Pith is reading between the lines

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

  • The same transport setup could be applied to other quarkonium states or different collision energies to test consistency.
  • Discrepancies at large transverse momenta may point to additional high-momentum mechanisms not captured by the current rates.
  • If valid, the approach would strengthen heavy quarkonia as quantitative probes of transport properties in the strongly coupled plasma.

Load-bearing premise

The non-thermal distributions of bottom quarks transported through the expanding medium and the reliable assessment of bottomonium equilibrium limits remain valid when the much larger reaction rates are used.

What would settle it

Precise measurements of bottomonium yields versus transverse momentum at high pT in Pb-Pb collisions that either match the model's predictions closely or deviate from them would test whether the enhanced rates and equilibrium treatment hold.

Figures

Figures reproduced from arXiv: 2508.20995 by Biaogang Wu, Ralf Rapp.

Figure 1
Figure 1. Figure 1: Time evolution of temperature along Y trajectories in viscous hy￾drodynamics for Pb-Pb collisions at √ sNN = 5.02 TeV in a rapidity window |y| < 0.9. Top panel: for individual trajectories (gray lines) and their average (thick orange curve) in central collisions (b = 0 fm). Bottom panel: averages for different centralities (for impact parameters from 0 to 14.4 fm). The hori￾zontal dashed line indicates Tf=… view at source ↗
Figure 2
Figure 2. Figure 2: Time evolution of entropy and volume in hydrodynamics in Pb-Pb [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: RAA of Υ(1S ) (left), Υ(2S ) (middle), and Υ(3S ) (right) as a function of the number of participants at mid-rapidity (upper) and forward rapidity (lower) compared to the CMS data [35, 36], ATLAS data [37], and ALICE data [38, 39]. The bands represent our results with a shadowing of 20%–30% (mid-rapidity) and of 25%–35% (forward-rapidity) together with the uncertainties from the bottomonium formation time,… view at source ↗
Figure 4
Figure 4. Figure 4: Minimum-bias pT-spectra of the total (blue), primordial (orange) and regenerated (red) Υ(1S ) (left), Υ(2S ) (middle), and Υ(3S ) (right) at mid-rapidity in Pb-Pb (5.02 TeV) collisions. The bands represent a 20-30% shadowing range, added in quadrature with the uncertainties from the bottomonium formation times. the end time, τ(Tf). The ICM results are combined with the pT￾dependent suppressed primordial co… view at source ↗
read the original abstract

Quarkonium production in high-energy heavy-ion collisions remains a key probe of the quark-gluon plasma formed in these reactions, but the development of a fully integrated nonperturbative approach remains a challenge. Toward this end, we set up a semiclassical transport approach that combines nonperturbative reaction rates rooted in lattice-constrained $T$-matrix interactions with a viscous hydrodynamic medium evolution. Bottomonium suppression is computed along trajectories in the hydrodynamic evolution while regeneration is evaluated via a rate equation extended to a medium with spatial gradients. The much larger reaction rates compared to previous calculations markedly enhance both dissociation and regeneration processes. This, in particular, requires a reliable assessment of bottomonium equilibrium limits and of the non-thermal distributions of the bottom quarks transported through the expanding medium. Within current uncertainties our approach can describe the centrality dependence of bottomonium yields measured in Pb-Pb ($\sqrt{s_{_{\rm NN}}}$=5.02\,TeV) collisions at the LHC, while discrepancies are found at large transverse momenta.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript develops a semiclassical transport approach for bottomonium in a strongly coupled QGP. It combines nonperturbative reaction rates from lattice-constrained T-matrix interactions with viscous hydrodynamic medium evolution. Suppression is computed along trajectories in the expanding medium, while regeneration is evaluated using a rate equation extended to media with spatial gradients. The authors emphasize that the much larger T-matrix rates enhance both dissociation and regeneration, requiring careful treatment of bottomonium equilibrium limits and non-thermal bottom-quark distributions. They claim that, within current uncertainties, the model describes the centrality dependence of bottomonium yields in Pb-Pb collisions at √s_NN=5.02 TeV, while discrepancies appear at large transverse momenta.

Significance. If the non-thermal bottom-quark distributions and equilibrium-limit assessments remain valid under the scaled-up rates in the presence of hydrodynamic gradients, the work offers a more consistent nonperturbative framework for quarkonium transport. This could strengthen comparisons to LHC data on centrality dependence and highlight the role of strong coupling in regeneration processes.

major comments (2)
  1. [Abstract (paragraph on rate-equation extension and non-thermal distributions)] The central claim that the model describes centrality dependence within uncertainties rests on the rate-equation extension to spatially inhomogeneous media and the trajectory-based suppression calculation. These steps require that bottom quarks remain non-thermal and that equilibrium limits can be reliably assessed even with the much larger reaction rates. No explicit comparison of thermalization timescales to the hydrodynamic expansion time is reported, which directly affects the reliability of the pT-dependent yields where discrepancies are noted.
  2. [Abstract (centrality-dependence claim)] The statement that the approach 'can describe the centrality dependence ... within current uncertainties' is presented without quantitative error bands on the theoretical yields or an explicit overlay of data points with uncertainties. This makes it difficult to assess whether the agreement is robust or sensitive to the choice of equilibrium limits and bottom-quark distributions.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the specific uncertainties (e.g., hydrodynamic parameters, T-matrix variations) that are folded into the 'within current uncertainties' assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to improve clarity and strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract (paragraph on rate-equation extension and non-thermal distributions)] The central claim that the model describes centrality dependence within uncertainties rests on the rate-equation extension to spatially inhomogeneous media and the trajectory-based suppression calculation. These steps require that bottom quarks remain non-thermal and that equilibrium limits can be reliably assessed even with the much larger reaction rates. No explicit comparison of thermalization timescales to the hydrodynamic expansion time is reported, which directly affects the reliability of the pT-dependent yields where discrepancies are noted.

    Authors: We appreciate the referee's emphasis on this point. Our transport framework for bottom quarks incorporates a finite relaxation time derived from the same T-matrix interactions, and the resulting non-thermal distributions are used consistently in the rate equation. The observed discrepancies at high pT are in fact a direct consequence of incomplete thermalization within the hydrodynamic lifetime. To make this explicit, we will add a short discussion of the relevant timescales (bottom-quark relaxation time versus QGP expansion time) in the revised manuscript, including a brief comparison for representative pT bins. revision: partial

  2. Referee: [Abstract (centrality-dependence claim)] The statement that the approach 'can describe the centrality dependence ... within current uncertainties' is presented without quantitative error bands on the theoretical yields or an explicit overlay of data points with uncertainties. This makes it difficult to assess whether the agreement is robust or sensitive to the choice of equilibrium limits and bottom-quark distributions.

    Authors: We agree that quantitative error bands and a direct visual comparison would strengthen the presentation. In the revised manuscript we will add shaded uncertainty bands to the theoretical centrality dependence curves (reflecting variations in the T-matrix rates and hydrodynamic parameters) and include an explicit overlay figure comparing our results to the LHC data points with their experimental uncertainties. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the transport derivation chain

full rationale

The paper constructs a semiclassical transport model by combining lattice-constrained T-matrix reaction rates with viscous hydrodynamic evolution, computing bottomonium suppression along trajectories and regeneration via a rate equation extended to spatial gradients. The central claim of describing centrality dependence within uncertainties is presented as a comparison to LHC data, with explicit discrepancies noted at large pT; no equation or step is shown to reduce by construction to a fitted input or self-citation that defines the target result. The assessment of non-thermal bottom-quark distributions and equilibrium limits is required by the larger rates but is not demonstrated to be tautological with the output yields.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on lattice-constrained T-matrix interactions providing accurate nonperturbative rates, on the validity of the semiclassical transport approximation, and on the hydrodynamic medium evolution being a faithful representation of the QGP expansion. No new particles or forces are introduced.

free parameters (1)
  • bottom-quark equilibrium distributions
    Non-thermal distributions of bottom quarks are assessed and adjusted to match the enhanced regeneration rates; these are fitted or chosen to satisfy equilibrium limits.
axioms (2)
  • domain assumption Lattice QCD T-matrix interactions yield reliable reaction rates for bottomonium dissociation and regeneration at finite temperature.
    Invoked when setting up the nonperturbative reaction rates that drive both suppression and regeneration.
  • domain assumption Viscous hydrodynamic evolution accurately describes the space-time profile of the expanding medium.
    Used to define the trajectories along which suppression is computed.

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discussion (0)

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Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages · 21 internal anchors

  1. [1]

    Eichten, K

    E. Eichten, K. Gottfried, T. Kinoshita, J. B. Kogut, K. D. Lane, and T.-M. Yan, Phys. Rev. Lett. 34, 369 (1975), [Erratum: Phys.Rev.Lett. 36, 1276 (1976)]

    work page 1975

  2. [2]

    R. Rapp, D. Blaschke, and P. Crochet, Prog. Part. Nucl. Phys. 65, 209 (2010), arXiv:0807.2470 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  3. [3]

    Charmonium from Statistical Hadronization of Heavy Quarks -- a Probe for Deconfinement in the Quark-Gluon Plasma

    P. Braun-Munzinger and J. Stachel, Landolt-Bornstein 23, 424 (2010), arXiv:0901.2500 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  4. [4]

    Y . Liu, B. Chen, N. Xu, and P. Zhuang, Phys. Lett. B 697, 32 (2011), arXiv:1009.2585 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  5. [5]

    Quarkonia in the Quark Gluon Plasma

    A. Mocsy, P. Petreczky, and M. Strickland, Int. J. Mod. Phys. A 28, 1340012 (2013), arXiv:1302.2180 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  6. [6]

    E. G. Ferreiro, Phys. Lett. B 731, 57 (2014), arXiv:1210.3209 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  7. [7]

    Y . Liu, K. Zhou, and P. Zhuang, Int. J. Mod. Phys. E24, 1530015 (2015)

    work page 2015

  8. [8]

    Bottomonium Continuous Production from Unequilibrium Bottom Quarks in Ultrarelativistic Heavy Ion Collisions

    B. Chen and J. Zhao, Phys. Lett. B 772, 819 (2017), arXiv:1704.05622 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  9. [9]

    Wolschin, Int

    G. Wolschin, Int. J. Mod. Phys. A 35, 2030016 (2020), arXiv:2010.05841 [hep-ph]

    work page arXiv 2020

  10. [10]

    Brambilla, M

    N. Brambilla, M. A. Escobedo, A. Islam, M. Strickland, A. Tiwari, A. Vairo, and P. Vander Griend, Phys. Rev. D 108, L011502 (2023), arXiv:2302.11826 [hep-ph]

    work page arXiv 2023

  11. [11]

    Wu and R

    B. Wu and R. Rapp, Universe 10, 244 (2024), arXiv:2404.09881 [nucl-th]

    work page arXiv 2024

  12. [12]

    T. Song, J. Aichelin, J. Zhao, P. B. Gossiaux, and E. Bratkovskaya, EPJ Web Conf. 316, 04008 (2025), arXiv:2409.19280 [hep-ph]

    work page arXiv 2025

  13. [13]

    Daddi-Hammou, S

    A. Daddi-Hammou, S. Delorme, J.-P. Blaizot, P. B. Gossiaux, and T. Gousset, (2025), arXiv:2506.19194 [hep-ph]

    work page arXiv 2025

  14. [14]

    Andronic et al., Eur

    A. Andronic et al., Eur. Phys. J. A60, 88 (2024), arXiv:2402.04366 [nucl- th]

    work page arXiv 2024

  15. [15]

    Extraction of Heavy-Flavor Transport Coefficients in QCD Matter

    A. Beraudo et al., Nucl. Phys. A 979, 21 (2018), arXiv:1803.03824 [nucl- th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  16. [16]

    Acharya et al

    S. Acharya et al. (ALICE), JHEP 01, 174 (2022), arXiv:2110.09420 [nucl-ex]

    work page arXiv 2022

  17. [17]

    B. Wu, Z. Tang, and R. Rapp, JHEP 07, 162 (2025), arXiv:2503.10089 [nucl-th]

    work page arXiv 2025

  18. [18]

    Z. Tang, S. Mukherjee, P. Petreczky, and R. Rapp, Eur. Phys. J. A 60, 92 (2024), arXiv:2310.18864 [hep-lat]

    work page arXiv 2024

  19. [19]

    Thermalization and isotropization in heavy-ion collisions

    M. Strickland, Pramana 84, 671 (2015), arXiv:1312.2285 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  20. [20]

    Altenkort, D

    L. Altenkort, D. de la Cruz, O. Kaczmarek, R. Larsen, G. D. Moore, S. Mukherjee, P. Petreczky, H.-T. Shu, and S. Stendebach (HotQCD), Phys. Rev. Lett. 132, 051902 (2024), arXiv:2311.01525 [hep-lat]

    work page arXiv 2024

  21. [21]

    The QCD equation of state with dynamical quarks

    S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, JHEP 11, 077 (2010), arXiv:1007.2580 [hep- lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  22. [22]

    The equation of state in (2+1)-flavor QCD

    A. Bazavov et al. (HotQCD), Phys. Rev. D 90, 094503 (2014), arXiv:1407.6387 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  23. [23]

    Alqahtani and M

    M. Alqahtani and M. Strickland, Eur. Phys. J. C 81, 1022 (2021), arXiv:2008.07657 [nucl-th]

    work page arXiv 2021

  24. [24]

    X. Du, M. He, and R. Rapp, Phys. Rev. C 96, 054901 (2017), arXiv:1706.08670 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  25. [25]

    K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, Eur. Phys. J. C 82, 413 (2022), arXiv:2112.12462 [hep-ph]

    work page arXiv 2022

  26. [26]

    J/\Psi production, $\chi$ polarization and Color Fluctuations

    L. Gerland, L. Frankfurt, M. Strikman, H. Stoecker, and W. Greiner, Phys. Rev. Lett. 81, 762 (1998), arXiv:nucl-th/9803034

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  27. [27]

    Islam and M

    A. Islam and M. Strickland, JHEP 21, 235 (2020), arXiv:2010.05457 [hep-ph]

    work page arXiv 2020

  28. [28]

    Quarkonium In-Medium Transport Equation Derived from First Principles

    X. Yao and T. Mehen, Phys. Rev. D99, 096028 (2019), arXiv:1811.07027 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  29. [29]

    Quarkonium inside Quark-Gluon Plasma: Diffusion, Dissociation, Recombination and Energy Loss

    X. Yao and B. M ¨uller, Phys. Rev. D 100, 014008 (2019), arXiv:1811.09644 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  30. [30]

    Du and R

    X. Du and R. Rapp, Phys. Lett. B 834, 137414 (2022), arXiv:2207.00065 [nucl-th]

    work page arXiv 2022

  31. [31]

    Kaczmarek, F

    O. Kaczmarek, F. Karsch, P. Petreczky, C. Schmidt, and S. Sharma, (2025), arXiv:2505.01734 [hep-lat]

    work page arXiv 2025

  32. [32]

    In-Medium Effects on Charmonium Production in Heavy-Ion Collisions

    L. Grandchamp, R. Rapp, and G. E. Brown, Phys. Rev. Lett. 92, 212301 (2004), arXiv:hep-ph/0306077

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  33. [33]

    Grandchamp and R

    L. Grandchamp and R. Rapp, Nucl. Phys. A 709, 415 (2002), arXiv:hep- ph/0205305

    work page arXiv 2002

  34. [34]

    T. Song, K. C. Han, and C. M. Ko, Phys. Rev. C 85, 054905 (2012), arXiv:1203.2964 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  35. [35]

    A. M. Sirunyan et al. (CMS), Phys. Lett. B 790, 270 (2019), arXiv:1805.09215 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  36. [36]

    Tumasyan et al

    A. Tumasyan et al. (CMS), Phys. Rev. Lett. 133, 022302 (2024), arXiv:2303.17026 [hep-ex]

    work page arXiv 2024

  37. [37]

    Aad et al

    G. Aad et al. (ATLAS), Phys. Rev. C 107, 054912 (2023), arXiv:2205.03042 [nucl-ex]

    work page arXiv 2023

  38. [38]

    $\Upsilon$ suppression at forward rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

    S. Acharya et al. (ALICE), Phys. Lett. B 790, 89 (2019), arXiv:1805.04387 [nucl-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  39. [39]

    Acharya et al

    S. Acharya et al. (ALICE), Phys. Lett. B 822, 136579 (2021), arXiv:2011.05758 [nucl-ex]

    work page arXiv 2021

  40. [40]

    Z. Tang, B. Wu, A. Hanlon, S. Mukherjee, P. Petreczky, and R. Rapp, (2025), arXiv:2502.09044 [nucl-th]

    work page arXiv 2025

  41. [41]

    M. He, R. J. Fries, and R. Rapp, Phys. Lett. B 735, 445 (2014), arXiv:1401.3817 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  42. [42]

    Collisional and thermal dissociation of $J/\psi$ and $\Upsilon$ states at the LHC

    S. Aronson, E. Borras, B. Odegard, R. Sharma, and I. Vitev, Phys. Lett. B 778, 384 (2018), arXiv:1709.02372 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  43. [43]

    Hard probes in heavy ion collisions at the LHC: heavy flavour physics

    M. Bedjidian et al. (2004) arXiv:hep-ph/0311048

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  44. [44]

    J. P. Blaizot and J.-Y . Ollitrault, Phys. Lett. B 199, 499 (1987)

    work page 1987

  45. [45]

    M. He, B. Wu, and R. Rapp, Phys. Rev. Lett. 128, 162301 (2022), arXiv:2111.13528 [nucl-th] . 6

    work page arXiv 2022