pith. sign in

arxiv: 1907.10948 · v1 · pith:A7KGLWNKnew · submitted 2019-07-25 · ⚛️ nucl-th · hep-ph· nucl-ex

Primordial fluctuations in heavy-ion collisions

Fran\c{c}ois Gelis , Giuliano Giacalone , Pablo Guerrero-Rodr\'iguez , Cyrille Marquet , Jean-Yves Ollitrault This is my paper

Pith reviewed 2026-05-24 16:10 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phnucl-ex
keywords heavy-ion collisionsinitial conditionsenergy density fluctuationscolor glass condensateeccentricity fluctuationselliptic flowtriangular flow
0
0 comments X

The pith

Energy density in heavy-ion collisions is the sum of 1/r² peaks from point charges on a smooth nucleus, reproducing CGC statistics and simultaneous elliptic-triangular flow trends.

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

The paper constructs a minimal model for the initial energy density deposited in a nucleus-nucleus collision. Each localized charge in one nucleus interacts with the smooth density of the other, depositing a sharply peaked source that falls as the two-dimensional Coulomb field 1/r². The superposition of these independent sources is shown to match both the average energy density and its two-point correlations computed in the color glass condensate framework at leading logarithmic accuracy. When the resulting fluctuating density is used to compute initial eccentricities, the model accounts for the observed centrality dependence of both elliptic and triangular flow at the same time.

Core claim

The energy density profile is obtained by superposing the two-dimensional Coulomb fields produced when each localized color charge in one nucleus collides with the smooth transverse density of the other nucleus. This construction reproduces the one-point and two-point functions of the energy-density field from the color glass condensate effective theory to leading logarithmic accuracy and thereby generates eccentricity fluctuations whose centrality dependence matches that of both elliptic and triangular flow.

What carries the argument

Superposition of independent 1/r² energy-density sources, each generated by the collision of a localized charge with a smooth nucleus.

If this is right

  • Initial conditions for hydrodynamic evolution are generated from a single, parameter-light superposition that already encodes the correct fluctuation statistics.
  • The same density field produces eccentricity fluctuations whose centrality dependence simultaneously describes both v2 and v3 without separate tuning.
  • The model supplies a concrete microscopic picture for the origin of the long-range correlations observed in the energy-density field.
  • Eccentricity moments can be computed analytically from the charge-density distribution of the incoming nuclei.

Where Pith is reading between the lines

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

  • If the 1/r² form is preserved at higher orders, the model may yield closed-form expressions for higher-order eccentricity cumulants.
  • The construction suggests a direct route to embed the same fluctuating sources into event generators used for other observables such as multiplicity fluctuations.
  • Because each source is tied to an individual color charge, the framework could be extended to study the effect of nuclear structure modifications on flow harmonics.

Load-bearing premise

The total energy density is exactly the sum of independent contributions, each falling off as the two-dimensional Coulomb field of a point charge.

What would settle it

A direct computation showing that the two-point correlation function of the energy density deviates from the leading-log color glass condensate result by an amount that cannot be absorbed into the overall normalization when the sources are summed as described.

Figures

Figures reproduced from arXiv: 1907.10948 by Cyrille Marquet, Fran\c{c}ois Gelis, Giuliano Giacalone, Jean-Yves Ollitrault, Pablo Guerrero-Rodr\'iguez.

Figure 1
Figure 1. Figure 1: FIG. 1. The four plots on the left illustrate the decomposition of the energy density according to Eq. (5) in a central Pb+Pb [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Symbols: Experimental data on [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

We present a simple description of the energy density profile created in a nucleus-nucleus collision, motivated by high-energy QCD. The energy density is modeled as the sum of contributions coming from elementary collisions between localized charges and a smooth nucleus. Each of these interactions creates a sharply-peaked source of energy density falling off at large distances like $1/r^2$, corresponding to the two-dimensional Coulomb field of a point charge. Our model reproduces the one-point and two-point functions of the energy density field calculated in the framework of the color glass condensate effective theory, to leading logarithmic accuracy. We apply it to the description of eccentricity fluctuations. Unlike other existing models of initial conditions for heavy-ion collisions, it allows us to reproduce simultaneously the centrality dependence of elliptic and triangular flow.

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 / 3 minor

Summary. The manuscript proposes a model for the initial energy density profile in nucleus-nucleus collisions, constructed as a superposition of sharply peaked 1/r² sources arising from elementary collisions between localized charges and a smooth nucleus. This ansatz is shown to reproduce the one- and two-point functions of the energy density computed in the color glass condensate (CGC) framework to leading-logarithmic accuracy. The model is subsequently applied to the computation of eccentricity fluctuations, yielding a parameter-free description that simultaneously reproduces the measured centrality dependence of elliptic (v₂) and triangular (v₃) flow.

Significance. If the central matching and flow results hold, the work supplies a theoretically motivated, parameter-free initial-condition model that directly connects CGC correlators to hydrodynamic observables. The absence of adjustable parameters and the simultaneous description of v₂ and v₃ centrality trends constitute a clear strength, providing a falsifiable link between high-energy QCD and flow data.

major comments (2)
  1. [§3] The claim that the sum of 1/r² sources reproduces the CGC two-point function to leading-log accuracy is central; the explicit derivation (including the treatment of the infrared cutoff and the averaging over charge configurations) must be shown to confirm that no sub-leading terms are inadvertently retained.
  2. [§5] In the eccentricity and flow section, the statement that the model is free of parameters should be accompanied by an explicit list of all inputs (nuclear profile, charge density, etc.) and a demonstration that none are tuned to the flow data.
minor comments (3)
  1. [§2] Notation for the energy-density field and its correlators should be unified between the CGC review and the model definition to avoid ambiguity.
  2. Figure captions should explicitly state the centrality bins and the hydrodynamic code used for the v₂, v₃ comparison.
  3. [§4] A brief remark on the range of validity of the leading-log approximation (e.g., with respect to the saturation scale) would help readers assess the model's domain of applicability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the recommendation for minor revision. We address the two major comments below and will incorporate the requested clarifications in the revised manuscript.

read point-by-point responses

  1. Referee: [§3] The claim that the sum of 1/r² sources reproduces the CGC two-point function to leading-log accuracy is central; the explicit derivation (including the treatment of the infrared cutoff and the averaging over charge configurations) must be shown to confirm that no sub-leading terms are inadvertently retained.

    Authors: We agree that an explicit derivation strengthens the central claim. In the revised version we will add a dedicated appendix that derives the two-point correlator from the superposition of 1/r² sources. The calculation will explicitly treat the infrared cutoff (introduced via a finite nuclear radius or exponential regulator), perform the average over random charge configurations, and demonstrate that all retained terms are strictly leading-log while sub-leading contributions vanish in the high-energy limit. revision: yes

  2. Referee: [§5] In the eccentricity and flow section, the statement that the model is free of parameters should be accompanied by an explicit list of all inputs (nuclear profile, charge density, etc.) and a demonstration that none are tuned to the flow data.

    Authors: We will revise the text to include a concise table or paragraph listing every external input: (i) the nuclear density profile (standard Woods-Saxon parameters taken from electron-scattering data), (ii) the average color charge density per nucleon (fixed by the saturation scale matching to CGC), and (iii) the infrared regulator scale (set by the nuclear radius). We will explicitly state that none of these quantities are adjusted to reproduce v₂ or v₃; the centrality trends arise solely from the geometry of the superposition and the CGC-matched correlators. revision: yes

Circularity Check

1 steps flagged

CGC one- and two-point matching achieved by model construction; flow application independent

specific steps
  1. self definitional [Abstract]
    "The energy density is modeled as the sum of contributions coming from elementary collisions between localized charges and a smooth nucleus. Each of these interactions creates a sharply-peaked source of energy density falling off at large distances like 1/r^2... Our model reproduces the one-point and two-point functions of the energy density field calculated in the framework of the color glass condensate effective theory, to leading logarithmic accuracy."

    The functional form (sum of 1/r^2 Coulomb sources) is introduced as the model definition; the claim that this form reproduces the CGC one- and two-point functions to LL accuracy is therefore satisfied by construction once the sources are summed, rather than derived from an independent calculation.

full rationale

The paper defines the energy density explicitly as a sum of 1/r^2 sources from elementary collisions and states that this construction reproduces the CGC correlators to LL accuracy. That match is therefore by design rather than an independent derivation. The subsequent calculation of eccentricity fluctuations and their centrality dependence for v2 and v3 is presented as a separate application that tests the model against data without additional parameters.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, axioms, or invented entities are stated in the provided text. The model introduces a phenomenological source term motivated by CGC but details are absent.

pith-pipeline@v0.9.0 · 5674 in / 1232 out tokens · 32904 ms · 2026-05-24T16:10:42.471290+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

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

  1. Rapidity dependence of mean transverse momentum fluctuation and decorrelation in baryon-dense medium

    nucl-th 2026-02 unverdicted novelty 5.0

    Mean transverse momentum fluctuations in baryon-rich matter are driven by energy and baryon density variations, remain robust to baryon diffusion, and show splitting between protons and antiprotons.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages · cited by 1 Pith paper · 24 internal anchors

  1. [1]

    Pressure isotropization in high energy heavy ion collisions

    T. Epelbaum and F. Gelis, Phys. Rev. Lett. 111, 232301 (2013) doi:10.1103/PhysRevLett.111.232301 [arXiv:1307.2214 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.111.232301 2013

  2. [2]

    Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory

    A. Kurkela, A. Mazeliauskas, J. F. Paquet, S. Schlicht- ing and D. Teaney, Phys. Rev. Lett. 122, no. 12, 122302 (2019) doi:10.1103/PhysRevLett.122.122302 [arXiv:1805.01604 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.122.122302 2019

  3. [3]

    Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions

    P. Romatschke and U. Romatschke, arXiv:1712.05815 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  4. [4]

    C. Gale, S. Jeon and B. Schenke, Int. J. Mod. Phys. A 28, 1340011 (2013) doi:10.1142/S0217751X13400113 [arXiv:1301.5893 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x13400113 2013

  5. [5]

    Fast resonance decays in nuclear collisions

    A. Mazeliauskas, S. Floerchinger, E. Grossi and D. Teaney, Eur. Phys. J. C 79, no. 3, 284 (2019) doi:10.1140/epjc/s10052-019-6791-7 [arXiv:1809.11049 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-019-6791-7 2019

  6. [6]

    Krasnitz and R

    A. Krasnitz and R. Venugopalan, Phys. Rev. Lett. 84 (2000) 4309 doi:10.1103/PhysRevLett.84.4309 [hep- ph/9909203]

    work page doi:10.1103/physrevlett.84.4309 2000

  7. [7]

    Energy density of the Glasma

    T. Lappi, Phys. Lett. B 643, 11 (2006) doi:10.1016/j.physletb.2006.10.017 [hep-ph/0606207]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2006.10.017 2006

  8. [8]

    J. L. Albacete, P. Guerrero-Rodrguez and C. Marquet, JHEP 1901, 073 (2019) doi:10.1007/JHEP01(2019)073 [arXiv:1808.00795 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep01(2019)073 1901

  9. [9]

    Giacalone, P

    G. Giacalone, P. Guerrero-Rodrguez, M. Luzum, C. Mar- quet and J. Y. Ollitrault, arXiv:1902.07168 [nucl-th]

    work page arXiv 1902

  10. [10]

    Collision geometry fluctuations and triangular flow in heavy-ion collisions

    B. Alver and G. Roland, Phys. Rev. C 81, 054905 (2010) Erratum: [Phys. Rev. C 82, 039903 (2010)] doi:10.1103/PhysRevC.82.039903, 10.1103/Phys- RevC.81.054905 [arXiv:1003.0194 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.82.039903 2010

  11. [11]

    Relativistic viscous hydrodynamics, conformal invariance, and holography

    R. Baier, P. Romatschke, D. T. Son, A. O. Starinets and M. A. Stephanov, JHEP 0804, 100 (2008) doi:10.1088/1126-6708/2008/04/100 [arXiv:0712.2451 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2008/04/100 2008

  12. [12]

    Triangularity and Dipole Asymmetry in Heavy Ion Collisions

    D. Teaney and L. Yan, Phys. Rev. C 83, 064904 (2011) doi:10.1103/PhysRevC.83.064904 [arXiv:1010.1876 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.83.064904 2011

  13. [13]

    J. P. Blaizot, W. Broniowski and J. Y. Ol- litrault, Phys. Lett. B 738, 166 (2014) doi:10.1016/j.physletb.2014.09.028 [arXiv:1405.3572 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2014.09.028 2014

  14. [14]

    R. S. Bhalerao, M. Luzum and J. Y. Ol- litrault, Phys. Rev. C 84, 054901 (2011) doi:10.1103/PhysRevC.84.054901 [arXiv:1107.5485 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.84.054901 2011

  15. [15]

    Some Features of the Glasma

    T. Lappi and L. McLerran, Nucl. Phys. A772, 200 (2006) doi:10.1016/j.nuclphysa.2006.04.001 [hep-ph/0602189]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.nuclphysa.2006.04.001 2006

  16. [16]

    Gelis, E

    F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venu- gopalan, Ann. Rev. Nucl. Part. Sci. 60, 463 (2010) doi:10.1146/annurev.nucl.010909.083629 [arXiv:1002.0333 [hep-ph]]

    work page doi:10.1146/annurev.nucl.010909.083629 2010

  17. [17]

    L. D. McLerran and R. Venugopalan, Phys. Rev. D 49, 2233 (1994) doi:10.1103/PhysRevD.49.2233 [hep- ph/9309289]

    work page doi:10.1103/physrevd.49.2233 1994

  18. [18]

    M. L. Miller, K. Reygers, S. J. Sanders and P. Steinberg, Ann. Rev. Nucl. Part. Sci. 57, 205 (2007) doi:10.1146/annurev.nucl.57.090506.123020 [nucl- ex/0701025]

    work page doi:10.1146/annurev.nucl.57.090506.123020 2007

  19. [19]

    Fluctuating Glasma initial conditions and flow in heavy ion collisions

    B. Schenke, P. Tribedy and R. Venu- gopalan, Phys. Rev. Lett. 108, 252301 (2012) doi:10.1103/PhysRevLett.108.252301 [arXiv:1202.6646 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.108.252301 2012

  20. [20]

    Aaboud et al

    M. Aaboud et al. [ATLAS Collaboration], [arXiv:1904.04808 [nucl-ex]]

    work page arXiv 1904

  21. [21]

    Flow fluctuations and long-range correlations: elliptic flow and beyond

    M. Luzum, J. Phys. G 38, 124026 (2011) doi:10.1088/0954-3899/38/12/124026 [arXiv:1107.0592 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0954-3899/38/12/124026 2011

  22. [22]

    F. G. Gardim, F. Grassi, M. Luzum and J. Y. Ollitrault, Phys. Rev. C 85, 024908 (2012) doi:10.1103/PhysRevC.85.024908 [arXiv:1111.6538 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.85.024908 2012

  23. [23]

    Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions

    H. Niemi, G. S. Denicol, H. Holopainen and P. Huovi- nen, Phys. Rev. C 87, no. 5, 054901 (2013) doi:10.1103/PhysRevC.87.054901 [arXiv:1212.1008 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.87.054901 2013

  24. [24]

    F. G. Gardim, J. Noronha-Hostler, M. Luzum and F. Grassi, Phys. Rev. C 91, no. 3, 034902 (2015) doi:10.1103/PhysRevC.91.034902 [arXiv:1411.2574 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.91.034902 2015

  25. [25]

    Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs

    Z. Qiu and U. W. Heinz, Phys. Rev. C 84, 024911 (2011) doi:10.1103/PhysRevC.84.024911 [arXiv:1104.0650 [nucl-th]]. 6

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.84.024911 2011

  26. [26]

    Linear and cubic response to the initial eccentricity in heavy-ion collisions

    J. Noronha-Hostler, L. Yan, F. G. Gardim and J. Y. Ollitrault, Phys. Rev. C 93, no. 1, 014909 (2016) doi:10.1103/PhysRevC.93.014909 [arXiv:1511.03896 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.93.014909 2016

  27. [27]

    Flow analysis from multiparticle azimuthal correlations

    N. Borghini, P. M. Dinh and J. Y. Ollitrault, Phys. Rev. C 64, 054901 (2001) doi:10.1103/PhysRevC.64.054901 [nucl-th/0105040]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.64.054901 2001

  28. [28]

    Energy dependence and fluctuations of anisotropic flow in Pb-Pb collisions at $\mathbf{\sqrt{{\textit s}_\text{NN}}} = \mathbf{5.02}$ and $\mathbf{2.76}$ TeV

    S. Acharya et al. [ALICE Collaboration], JHEP 1807, 103 (2018) doi:10.1007/JHEP07(2018)103 [arXiv:1804.02944 [nucl-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep07(2018)103 2018

  29. [29]

    Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV

    S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. C 89, no. 4, 044906 (2014) doi:10.1103/PhysRevC.89.044906 [arXiv:1310.8651 [nucl-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.89.044906 2014

  30. [30]

    P. Alba, V. Mantovani Sarti, J. Noronha, J. Noronha- Hostler, P. Parotto, I. Portillo Vazquez and C. Ratti, Phys. Rev. C 98, no. 3, 034909 (2018) doi:10.1103/PhysRevC.98.034909 [arXiv:1711.05207 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.98.034909 2018