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Effects of sub-nucleonic fluctuations on the longitudinal structure of heavy-ion collisions

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Sub-nucleonic fluctuations reshape longitudinal flow and baryon stopping in heavy-ion collisions.

desk verdict Solid new McDipper+CLVisc machinery with an honest but unproven central claim, confounded by per-scenario K_g re-tuning. read the letter →

arxiv 2501.14872 v2 pith:XGH7Z5GT submitted 2025-01-24 nucl-th hep-ph

Oscar Garcia-Montero , Sören Schlichting , Jie Zhu This is my paper · ORCID
classification nucl-thhep-ph PACS 25.75.-q24.10.Nz
keywords sub-nucleonicfluctuationsheavy-ioncollisionslongitudinaldecorrelationbaryonstoppinganisotropicflowColorGlassCondensate3+1DviscoushydrodynamicsPb-Pbat2.76TeV
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 asks whether the lumpy, sub-nucleonic structure of colliding nuclei changes how energy and baryon number are deposited along the collision axis, and whether that structure leaves a measurable imprint on final flow patterns. It builds a complete simulation chain in which the Color Glass Condensate based McDipper initial state, extended with hotspot and thickness fluctuations inside each nucleon, feeds the 3+1 dimensional viscous hydrodynamic code CLVisc. The authors find that sub-nucleonic fluctuations reduce baryon stopping and enhance anisotropic flow and longitudinal decorrelation, with the strongest effects in central collisions. Comparing against CMS and ALICE data, the model describes central-collision decorrelation but underpredicts it in mid-central and peripheral collisions, which the authors interpret as evidence that quark-sector fluctuations are still missing.

What carries the argument

The working machinery is the 3D resolved McDipper initial-state model, a kT-factorized Color Glass Condensate formulation in which gluon production comes from dipole amplitudes and quark production from valence-quark stopping, extended with sub-nucleonic fluctuations: each nucleon is a weighted superposition of Gaussian hotspots whose weights carry log-normal thickness fluctuations. These energy and net-baryon densities are matched onto the 3+1D viscous hydrodynamics code CLVisc, which evolves the fireball including baryon diffusion, and the longitudinal decorrelation observable rn is computed from the forward/backward ratio of flow vectors. The hotspot granularity is the ingredient that breaks the fireball into steeper density gradients, while thickness fluctuations add event-by-event weight variations; together they shape the rapidity dependence of vn and the decorrelation rate.

What would settle it

Run the same McDipper+CLVisc setup with event-by-event fluctuating valence and sea quark distributions, as in the prescription of Ref. [87], and recompute r2 in 30-50% central Pb-Pb collisions; if the longitudinal decorrelation still falls short of the CMS data, the missing-fluctuations-in-the-quark-sector explanation is ruled out.

Watch

Extended reading notes

Core claim

The central claim, stated in Sec. IV, is that sub-nucleonic fluctuations in the initial state measurably change the longitudinal structure of heavy-ion collisions: including three hotspots and log-normal thickness fluctuations per nucleon suppresses baryon stopping, increases anisotropic flow, and strengthens longitudinal decorrelation, especially in central collisions. The paper further claims that the residual underprediction of the longitudinal decorrelation ratio r2 in mid-central and peripheral collisions points to a missing source of fluctuations in the quark sector, because at forward rapidity a growing share of the deposited energy comes from quark stopping and the current implementation uses only averaged collinear quark parton distributions.

Load-bearing premise

The paper's interpretation rests on the assumption that the longitudinal structure of the initial state is faithfully described by the kT-factorized CGC formulas with smooth, averaged collinear quark parton distributions, and that the omitted pre-equilibrium evolution and hadronic afterburner do not account for the remaining decorrelation deficit.

Editorial extensions

If this is right

  • Sub-nucleonic fluctuations must be included in initial-state models if rapidity-dependent observables such as v2(η), v3(η), and r2 are to be described quantitatively.
  • Baryon stopping is sensitive to the granularity of the initial state, so baryon-number transport measurements can constrain the number and width of hotspots.
  • Because sub-nucleonic fluctuations mostly enhance flow in central collisions and suppress it in peripheral ones, the centrality dependence of vn serves as a clean diagnostic of initial-state granularity.
  • The underprediction of r2 in mid-central and peripheral collisions motivates a statistical treatment of quark parton distributions in saturation-based initial conditions.
  • Longitudinal decorrelation at large rapidity receives a growing contribution from quark stopping, so forward measurements and mid-rapidity references are needed to disentangle gluon and quark deposition mechanisms.

Reading between the lines

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

  • If quark-sector fluctuations do close the r2 gap, the same mechanism should also affect net-proton cumulants and charge-balance observables at forward rapidity, giving independent tests beyond flow decorrelations.
  • The hotspot prescription could be tested by varying the number of hotspots Nq and their width Bq separately to see whether r2 constrains them individually or only in combination.
  • A quantitative match to the CMS data will likely require adding pre-equilibrium dynamics and a hadronic afterburner, so the attribution of the deficit to quark fluctuations should be revisited once those stages are included.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper couples the 3D resolved McDipper initial-state model, extended with sub-nucleonic fluctuations (hotspots and thickness fluctuations), to the 3+1D viscous hydrodynamics code CLVisc, and studies Pb+Pb collisions at sqrt(s_NN)=2.76 TeV. The authors compare five initial-state scenarios (smooth nucleons, hotspots, nucleon thickness fluctuations, and hotspot plus thickness fluctuations with two fluctuation strengths) and present results for charged-hadron and net-proton rapidity distributions, pT spectra, directed flow v1, elliptic and triangular flow v2/v3, and the longitudinal decorrelation observable r2 across centrality classes. Their central finding is that sub-nucleonic fluctuations reduce baryon stopping and enhance anisotropic flow and longitudinal decorrelation, especially in central collisions, while the model still underestimates decorrelation in mid-central and peripheral collisions, which they attribute to missing quark-sector fluctuations.

Significance. If the central claim holds, the paper provides a valuable step toward a more complete 3D description of heavy-ion collisions, showing that sub-nucleonic degrees of freedom leave an imprint on rapidity-dependent observables and should be included in initial-state models. The main strengths are the first coupling of the resolved McDipper initial state to 3+1D viscous hydrodynamics, the breadth of observables compared with ALICE and CMS data, and the public availability of the McDipper code (Ref. [55]). The paper is also honest about its limitations, explicitly noting the absence of a hadronic afterburner, the lack of a 3+1D pre-equilibrium stage, and the need for further tuning. However, the causal interpretation is weakened by the scenario-dependent re-tuning of K_g, which changes the quark/gluon energy partition and is therefore entangled with the geometric effects that the paper aims to isolate.

major comments (3)
  1. [Sec. II D and Sec. III A] The central scenario comparisons are not at fixed physics content because K_g is re-tuned for each scenario (Sec. II D: K_g = 2.23, 2.34, 2.61, 2.71, 3.20). Since K_g multiplies only the gluon term in Eq. (1), increasing K_g does more than change the overall normalization: it increases the gluon energy share and decreases the quark energy share. The authors themselves note in Sec. III A that the energy carried by gluons increases due to the increase of K_g and tends to concentrate at mid-rapidity while the quark energy decreases. Consequently, the reported reduction of baryon stopping and the enhanced v2(eta), v3(eta), and r2 in the hotspot runs could be driven by the altered quark/gluon partition rather than by the geometric non-overlap of hotspots. A control calculation at fixed K_g, or a decomposition separating geometry effects from energy-sharing effects, is needed before the causal statements in Sec. IV can be supported.
  2. [Sec. III E and Sec. IV] The attribution of the remaining longitudinal-decorrelation deficit to missing quark-sector fluctuations is an interpretation, not a demonstrated result. The same deficit could receive significant contributions from the neglected 3+1D pre-equilibrium evolution (which the authors flag as desirable in Secs. III E and IV), from the omitted hadronic afterburner (whose absence they already connect to the too-hard pT spectra and overestimated flow in Secs. III B and III D), or from hydrodynamic thermal fluctuations, which they cite in Sec. III E as essential (Refs. [88, 89]). Since quark fluctuations are nowhere implemented in the model (Eq. (4) uses averaged collinear quark PDFs), the statement that the disagreement 'should be attributed to missing sources of fluctuations in the initial condition, most likely in the quark sector' goes beyond the evidence presented in this work. Please rephrase this as one candidate explanation among several, or perform a dedicated test that isolates the quark sector (e.g., sampling quark positions according to the local PDF density).
  3. [Sec. III D and Figs. 9-12] The model overestimates the magnitudes of v2 and v3 in several centrality classes, and the authors attribute this to the too-hard pT spectra. Because the longitudinal decorrelation r2 is defined through ratios of flow vectors, the quantitative agreement with the CMS r2 data is affected by this same model deficiency. The claim that the inclusion of sub-nucleonic fluctuations 'brings the shape of the rapidity dependence of elliptic flow closer to experimental data' is therefore only qualitative; the paper would benefit from a quantitative goodness-of-fit comparison, or from an explicit statement that the r2 comparison is illustrative rather than a quantitative validation of the missing-fluctuation hypothesis.
minor comments (5)
  1. [Abstract and Sec. II A] In the abstract and Sec. II A, 'resolvedMcDipper' should be written as 'resolved McDipper' with a space.
  2. [Fig. 2 and Sec. II B] The p+p multiplicity comparison in Fig. 2 uses K_g values tuned to Pb+Pb collisions and parameters in Eq. (12) from 5.02 TeV pp data, while the ALICE data shown are at 7 TeV; the authors acknowledge this, but the caption should state it explicitly to avoid misleading readers.
  3. [Eq. (12)] The function a_J in Eq. (12) is not defined; please define it or provide a reference.
  4. [Sec. III D] In the text below Fig. 9, 'the integrated McDipper+CLVisc model generally works well at low pT' is too strong given that the v2{2} and v2{4} curves visibly overshoot the data; consider using 'gives a reasonable description' or similar.
  5. [Ref. [55]] The GitHub reference for McDipper is cited without a version tag or commit identifier; since the paper describes 'McDipper v1.2', please provide a versioned DOI or a specific release tag to ensure reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central observables are genuine forward predictions, and the scenario-dependent K_g tuning is a modeling confound rather than a reduction by construction.

full rationale

The paper's central claims about baryon stopping, anisotropic flow, and longitudinal decorrelation are not derived from the fitted parameter: the only tuned quantity is the gluon normalization K_g, fixed per scenario to reproduce the mid-rapidity charged-hadron multiplicity in 0-5% central Pb+Pb collisions (Sec. II D). The observables v_2, v_3, and r_2 are computed forward through the McDipper+CLVisc chain and are never used in the tuning, so they are genuine predictions. The paper itself notes in Sec. III A that the increase of K_g with added fluctuations makes gluon energy deposition more dominant and quark-stopping energy less dominant, so the cross-scenario comparisons are not fully controlled; however, this is a model-selection confound, not a case where a predicted quantity is forced by construction. The self-citations (Refs. [34], [55], [86], [90]) point to the public McDipper model and the authors' prior work, but the hotspot ansatz comes from external references [35, 36], and no uniqueness theorem is invoked to forbid alternatives. The quark-sector-fluctuation explanation in Sec. III E is explicitly framed as a hypothesis ('We believe that this disagreement ... should be attributed to missing sources of fluctuations'), corroborated by an external reference [87], rather than presented as a derived result. Accordingly, the derivation chain is not circular, and the score is 0.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central comparisons do not introduce new entities. The main free parameters are the normalization K_g, hotspot geometry parameters, and transport inputs. The most consequential modeling premise is the smooth average treatment of quark PDFs, which the paper itself identifies as the likely missing fluctuation source.

free parameters (7)
  • K_g (gluon production normalization) = 2.23, 2.34, 2.61, 2.71, 3.20 for the five scenarios
    Tuned per scenario in Sec. II D so that charged particle multiplicity in 0-5% central Pb+Pb matches data; changes the quark/gluon energy sharing.
  • N_q (number of hotspots per nucleon) = 3
    Chosen in Sec. II B; not fitted in this paper.
  • B_q (hotspot width) = 0.04 fm^2
    Chosen in Sec. II B; controls granularity of sub-nucleonic fluctuations.
  • B_G (nucleon width) = 0.156 fm^2
    Taken from TRENTo in Sec. II B; sets the overall nucleon transverse size.
  • sigma (thickness fluctuation width) = 0.637 or 1.2
    Explored in Sec. II B; controls magnitude of log-normal participant thickness fluctuations.
  • C_eta and C_zeta (specific shear and bulk viscosity coefficients) = Temperature-dependent from Duke Bayesian analysis (Ref. [66]); C_B=0.4
    Taken from prior fits in Sec. II E; not refit here, but flow magnitudes depend on them.
  • Freeze-out energy density and initial time = epsilon_frz=0.266477 GeV/fm^3, tau0=0.6 fm
    Chosen in Secs. II E and II F; varied in Appendix C to show sensitivity.
assumptions (5)
  • domain assumption LO kT-factorization CGC formulas (Eqs. 3 and 4) adequately describe initial gluon and quark production in the longitudinal direction.
    Invoked in Sec. II A without corrections beyond the K_g normalization.
  • domain assumption IP-Sat dipole model with Gaussian local color correlations, so D_adj = D_fun^(CA/CF).
    Used in Sec. II A to obtain adjoint dipoles from fundamental dipoles.
  • ad hoc to paper Instant thermalization at tau0=0.6 fm with Landau matching and no pre-equilibrium longitudinal dynamics.
    Sec. II C connects initial state directly to hydrodynamics; the paper notes a 3+1D pre-equilibrium description is still missing.
  • domain assumption Quark stopping is described by smooth collinear PDFs without event-by-event quark fluctuations.
    Sec. II A Eq. (7) uses averaged PDFs; Sec. III E identifies the lack of quark fluctuations as the likely cause of the decorrelation deficit.
  • domain assumption Transport coefficients and equation of state from prior Bayesian analyses apply unchanged to this initial-state model.
    Sec. II E takes C_eta and C_zeta from Ref. [66] and uses NEOS-B; no refit is performed.

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Cite this review

Pith. "Pith review of Effects of sub-nucleonic fluctuations on the longitudinal structure of heavy-ion collisions." pith.science (2026). https://pith.science/paper/XGH7Z5GT

@misc{pith2026250114872,
  author       = {Pith},
  title        = {Pith review of: Effects of sub-nucleonic fluctuations on the longitudinal structure of heavy-ion collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XGH7Z5GT}},
  note         = {Machine review of arXiv:2501.14872}
}
read the original abstract

Sub-nuclear fluctuations in the initial state of heavy-ion collisions impact not only transverse long-range correlations of small systems, but also the creation of longitudinal structures, seen in particle detectors as longitudinal decorrelation observables. In this work, we study the emergence of long-range rapidity correlations in nuclear collisions based on the 3D resolved McDIPPER initial state model, and for the first time, connect it to experimental observables using the 3+1D viscous hydrodynamics framework CLVisc. We include different sources of fluctuations at the nucleon and subnucleon level and study the effects of these additional fluctuation sources on the longitudinal structure of relevant observables, such as the flow decorrelations and directed flow.

Figures

Figures reproduced from arXiv: 2501.14872 by the authors.

Figure 1
Figure 1. The initial energy density distributions of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The effects of sub-nucleonic fluctuations on [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The energy density along the pseudo-rapidity [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: The net baryon density along the pseudo-rapidity direction for Pb+Pb √ sNN = 2.76 TeV collisions with centrality range 5-10%, 30-35%. by quarks decreases. When considering the baryon num￾ber deposition, we find that the thickness fluctuations suppress baryon stopping s…
Figure 5
Figure 5. Figure 5: Charged hadron multiplicity as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Net proton multiplicity as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: Directed flow v1(η) of charged particles from McDipper(curves)+CLVisc for Pb+Pb √ sNN =2760 GeV collisions in comparison to the experiment data from ALICE Collaboration(solid points)[77]. The shaded areas around each line represent the statistical uncertainty of the si…
Figure 9
Figure 9. Figure 9: The elliptic flow, v2{2}(red curves) and v2{4}(blue curves), for charged particles as a function of transverse momentum pT in Pb+Pb collisions at √ sNN = 2.76 TeV. The data(points) are taken from CMS [81]. The shaded areas around each line represent the statistical unc…
Figure 10
Figure 10. Figure 10: The rapidity dependence of the momentum anisotropies [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: The rapidity dependence of the momentum anisotropies [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: The rapidity dependence of the momentum anisotropies [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: The decorrelation of elliptic flow along the pseudo-rapidity direction, for Pb+Pb [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]
Figure 14
Figure 14. Figure 14: The decorrelation of elliptic flow along the pseudo-rapidity direction, for Pb+Pb [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]
Figure 15
Figure 15. Figure 15: The initial energy density distributions of [PITH_FULL_IMAGE:figures/full_fig_p016_15.png]
Figure 16
Figure 16. Figure 16: The initial net-baryon number density distributions of different classes at x=0 fm for a sampled Pb+Pb collision at √ sNN =2.76 TeV and impact parameter b=3.42 fm. desirable to include SMASH as an afterburner, since pT - differential observables in particular are expe…
Figure 17
Figure 17. Figure 17: The elliptic flow, v2{EP}(curves) calculated with event plane method, for charged particles as a function of transverse momentum pT in Pb+Pb collisions at √ sNN = 2.76 TeV. The data(points) are taken from CMS[81]. The shaded areas around each line represent the statis…
Figure 18
Figure 18. Figure 18: The rapidity dependence of the v2(η) calculated with event plane method, compared to CMS[81] data. Both data and the calculation are for 0.3<pT <3 GeV and use reference particles in (3<|η|<5). The shaded areas around each line represent the statistical uncertainty of …
Figure 19
Figure 19. Figure 19: The effects of freeze-out energy density( [PITH_FULL_IMAGE:figures/full_fig_p019_19.png]
Figure 20
Figure 20. Figure 20: The effects of freeze-out energy density( [PITH_FULL_IMAGE:figures/full_fig_p019_20.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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