Suppression of elliptic flow without viscosity

Adam Takacs; Denes Molnar

arxiv: 1906.12311 · v1 · pith:VBFISW2Tnew · submitted 2019-06-28 · ⚛️ nucl-th · hep-ex· hep-ph· nucl-ex

Suppression of elliptic flow without viscosity

Adam Takacs , Denes Molnar This is my paper

Pith reviewed 2026-05-25 13:15 UTC · model grok-4.3

classification ⚛️ nucl-th hep-exhep-phnucl-ex

keywords elliptic flowCooper-Fryeideal fluidviscosityheavy-ion collisionsfreeze-outv2 suppressionlocal equilibrium distributions

0 comments

The pith

Ideal fluids suppress elliptic flow at high pT when using generalized equilibrium distributions at freeze-out.

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

The paper studies particle emission from ideal fluids in the Cooper-Frye approach but replaces the usual Boltzmann distributions with more general local equilibrium distributions. It finds that this change alone reduces the elliptic flow v2 at transverse momenta above 1.5 GeV/c, even though shear stress and bulk pressure remain zero everywhere. The resulting suppression grows with pT and is weaker for heavier particles, reproducing features normally attributed to viscosity. Readers should care because elliptic flow data are the main input used to extract the shear viscosity of the quark-gluon plasma created in heavy-ion collisions.

Core claim

Even though we study ideal fluids (i.e., shear stress and bulk pressure are zero everywhere), we find a suppression of elliptic flow (v2) at high transverse momenta (pT>1.5 GeV/c), relative to results obtained with the traditional Boltzmann distributions. The non-viscous suppression shows qualitatively similar features to the well-known shear viscous suppression of v2; for example, it increases with pT, and it is smaller for heavier species as seen in self-consistent kinetic theory calculations.

What carries the argument

The Cooper-Frye freeze-out integral evaluated with generalized local equilibrium distributions that keep the underlying fluid ideal while deviating from standard Boltzmann or quantum statistics.

If this is right

Part of the v2 suppression measured in heavy-ion data may arise from the choice of distribution at freeze-out rather than from viscosity.
Shear viscosities extracted from RHIC and LHC elliptic flow data may be overestimated.
The suppression effect is expected to be larger at higher pT and smaller for heavier hadrons.
Other flow observables sensitive to the high-pT region could show analogous non-viscous suppression.

Where Pith is reading between the lines

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

Hydrodynamic models of heavy-ion collisions may need to adopt these generalized distributions to avoid misattributing all high-pT flow damping to viscosity.
Re-analysis of existing v2 data with both standard and generalized distributions could tighten bounds on the viscosity-to-entropy ratio.
The result suggests testing whether the same distributions alter other freeze-out observables such as particle spectra or azimuthal correlations.

Load-bearing premise

That the more general local equilibrium distributions are physically appropriate for converting an ideal fluid into particles at freeze-out.

What would settle it

A calculation that repeats the ideal-fluid Cooper-Frye procedure with the generalized distributions but finds no v2 suppression at pT above 1.5 GeV/c would falsify the central claim.

Figures

Figures reproduced from arXiv: 1906.12311 by Adam Takacs, Denes Molnar.

**Figure 2.** Figure 2: FIG. 2: Pressure to energy density ratio as the function of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Identified hadron spectra at midrapidity measured by [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Charged hadron differential elliptic flow at midrapid [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

read the original abstract

We investigate fluid-to-particle conversion using the usual Cooper-Frye approach but with more general local equilibrium distributions than the Boltzmann or Bose/Fermi distributions typically used. Even though we study ideal fluids (i.e., shear stress and bulk pressure are zero everywhere), we find a suppression of elliptic flow (v2) at high transverse momenta (pT>1.5 GeV/c), relative to results obtained with the traditional Boltzmann distributions. The non-viscous suppression shows qualitatively similar features to the well-known shear viscous suppression of v2; for example, it increases with pT, and it is smaller for heavier species as seen in self-consistent kinetic theory calculations. Our results question whether all of the v2 suppression seen in the data can be attributed to viscous effects, and indicate that shear viscosities extracted from RHIC and LHC elliptic flow data might be overestimated.

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

The paper claims v2 suppression at high pT from generalized distributions in ideal-fluid Cooper-Frye, but provides no explicit forms or moment checks to confirm zero shear and bulk pressure.

read the letter

The main thing to know is that the abstract reports elliptic flow suppression at pT > 1.5 GeV/c even for ideal fluids when the usual Boltzmann distributions are replaced by more general local equilibrium forms at freeze-out. The effect is said to grow with pT and be smaller for heavier particles, resembling viscous suppression but without any shear or bulk pressure in the fluid. This is presented as new and as a reason to question whether all observed v2 suppression comes from viscosity, which would mean extracted eta/s values from RHIC and LHC data are too high. That is the central claim and the only quantitative hint given. The work is straightforward in its setup: it keeps the fluid ideal everywhere and isolates the change to the distribution function in the Cooper-Frye conversion. That isolation is useful and worth checking. The soft spot is exactly the one in the stress-test note. No explicit construction of the generalized distributions appears in the abstract, nor any demonstration that the integrals over them recover the ideal-fluid T^mu nu and N^mu with vanishing dissipative currents. Standard local equilibrium is fixed by T, u^mu, and mu; any departure has to satisfy the same moments or it effectively adds dissipation at the hypersurface. Without that check shown, it is impossible to tell whether the reported suppression is independent of viscosity or an artifact of an inconsistent freeze-out step. The citation pattern is thin because the abstract alone is all that is supplied. This is for people who already work on hydrodynamic freeze-out modeling and want to see alternative sources of high-pT v2 damping. A reader who cares about whether the standard viscous interpretation is unique would find the question worth following up. The paper deserves a serious referee once the full text supplies the missing distribution forms and the moment verification; the idea is simple enough that a referee can check it quickly.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates fluid-to-particle conversion in ideal hydrodynamic simulations of heavy-ion collisions via the Cooper-Frye prescription, but employing more general local-equilibrium distributions than the standard Boltzmann (or Bose/Fermi) forms. It reports that these distributions produce a suppression of elliptic flow v2 at high transverse momentum (pT > 1.5 GeV/c) even though shear stress and bulk pressure remain identically zero, with the suppression increasing with pT and decreasing for heavier particles in a manner qualitatively similar to viscous effects. The authors conclude that not all observed v2 suppression need be attributed to viscosity and that extracted shear-viscosity values may therefore be overestimated.

Significance. If the generalized distributions can be shown to be fully consistent with the ideal-fluid energy-momentum tensor and particle current on the freeze-out hypersurface, the result would directly affect the extraction of QGP transport coefficients from RHIC and LHC data. The reported mass and pT dependence, obtained from a numerical study of ideal fluids, constitutes a concrete, falsifiable observation that merits careful scrutiny.

major comments (2)

[section describing the generalized local-equilibrium distributions] The central claim requires that the generalized distributions recover exactly the ideal-fluid T^{μν} and N^μ (zero shear and bulk) when integrated over the Cooper-Frye hypersurface. No explicit construction or verification of these moment conditions is visible in the provided description of the distributions; without it the reported v2 suppression cannot be unambiguously attributed to the choice of distribution rather than an implicit mismatch in the freeze-out step.
[results section on v2(pT) and species dependence] The abstract states that the non-viscous suppression is 'qualitatively similar' to shear-viscous suppression and exhibits the expected mass ordering. Quantitative plots or tables comparing the magnitude of the effect to viscous calculations at the same ideal-fluid background are needed to establish whether the two mechanisms are distinguishable in practice.

minor comments (2)

Clarify the precise functional form of the generalized distributions (including any additional parameters) and state the equation of state used for the ideal fluid.
Specify the freeze-out temperature and the range of pT over which the suppression is observed in the figures.

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 comment below.

read point-by-point responses

Referee: [section describing the generalized local-equilibrium distributions] The central claim requires that the generalized distributions recover exactly the ideal-fluid T^{μν} and N^μ (zero shear and bulk) when integrated over the Cooper-Frye hypersurface. No explicit construction or verification of these moment conditions is visible in the provided description of the distributions; without it the reported v2 suppression cannot be unambiguously attributed to the choice of distribution rather than an implicit mismatch in the freeze-out step.

Authors: The generalized distributions are constructed by design to reproduce the hydrodynamic energy density, pressure, and flow velocity exactly, thereby ensuring that their moments yield the ideal-fluid T^{μν} and N^μ with vanishing shear stress and bulk pressure. We will add an explicit analytic derivation of the moment conditions together with a numerical verification on the freeze-out hypersurface in a new appendix of the revised manuscript. revision: yes
Referee: [results section on v2(pT) and species dependence] The abstract states that the non-viscous suppression is 'qualitatively similar' to shear-viscous suppression and exhibits the expected mass ordering. Quantitative plots or tables comparing the magnitude of the effect to viscous calculations at the same ideal-fluid background are needed to establish whether the two mechanisms are distinguishable in practice.

Authors: Our central claim is the existence of a non-viscous mechanism that produces qualitatively similar features (pT dependence and mass ordering) to viscous suppression. Because the magnitude of viscous suppression depends on the specific value of η/s and on the details of the viscous hydrodynamic evolution, a direct quantitative comparison at fixed background would require additional model choices that lie outside the scope of the present work. We therefore regard the qualitative demonstration as sufficient to support the conclusion that extracted viscosities may be overestimated. If the editor and referee consider a quantitative benchmark essential, we are prepared to add a short discussion and one comparative figure in the revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; result from numerical investigation of generalized distributions

full rationale

The paper reports a numerical finding that more general local-equilibrium distributions in Cooper-Frye for strictly ideal fluids (zero shear stress and bulk pressure) produce high-pT v2 suppression relative to Boltzmann forms. No quoted equations or steps reduce this outcome to a definitional identity, a fitted parameter renamed as prediction, or a self-citation chain that bears the central claim. The abstract and description frame the suppression as an emergent numerical result under the maintained ideal-fluid moment conditions, leaving the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit information on free parameters, axioms, or invented entities; all fields left empty.

pith-pipeline@v0.9.0 · 5673 in / 1165 out tokens · 23113 ms · 2026-05-25T13:15:47.101163+00:00 · methodology

discussion (0)

Reference graph

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temper- atures

for each element to ob- tain the momentum distribution of particles. (For an an- alytic treatment with Tsallis distributions in simpliﬁed geometry, see Ref. [ 16].) For a one-component ideal ﬂuid, without conserved charges, the hydrodynamic ﬁelds are the components of the energy-momentum tensor T µν = (ε+P )uµuν −P gµν, where ε is the local energy density...

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We choose here a simple prescription where partial pressures Pi and partial en- ergy densities εi are kept the same as in the Boltzmann limit, and the matching from Eq

used with fi gives the partial contribution to the energy momentum tensor by species i, and only the total contribution T µν = ∑ i T µν i is ﬁxed by the hydro ﬁelds. We choose here a simple prescription where partial pressures Pi and partial en- ergy densities εi are kept the same as in the Boltzmann limit, and the matching from Eq. (

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This means that, in general, each species has its own temperature Λ i and normalization Ai

is performed to Pi and εi independently for each species. This means that, in general, each species has its own temperature Λ i and normalization Ai. For simplicity, we keep the exponent α the same for all species. Note that both the local pres- sure and energy density of the ideal ﬂuid are reproduced exactly, so shear stress and bulk pressure both remain...

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D. Bagchi and C. Tsallis, J. Physa. 491, 869 (2018)

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C. Tsallis, J. Stat. Phys. 52, 479 (1988)

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T. Osada and G. Wilk, Phys. Rev. C 77, 044903 (2008). Erratum: Phys. Rev. C 78, 069903 (2008)

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Luzum and P

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Cooper and G

F. Cooper and G. Frye, Phys. Rev. D 10, 186 (1974)

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Urmossy and T

K. Urmossy and T. S. Biro, Phys. Lett. B 689, 14 (2010)

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P. F. Kolb, J. Sollfrank and U. W. Heinz, Phys. Rev. C 62, 054909 (2000). P. F. Kolb and R. Rapp, Phys. Rev. C 67, 044903 (2003). P. F. Kolb and U. W. Heinz, *Hwa, R.C. (ed.) et al.: Quark gluon plasma* 634-714

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Huovinen and D

The original version 0.2 of AZHYDRO and ver- sion 0.2p2 patched by P. Huovinen and D. Molnar are available on the WWW from the Open Stan- dard Codes and Routines (OSCAR) repository at http://karman.physics.purdue.edu/OSCAR

work page

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Huovinen and P

P. Huovinen and P. Petreczky, Nucl. Phys. A 837, 26 (2010)

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S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. C 69, 034909 (2004)

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H. Song, S. A. Bass, U. Heinz, T. Hirano and C. Shen, Phys. Rev. C 83, 054910 (2011). Erratum: Phys. Rev. C 86, 059903 (2012)

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T. S. Biro and E. Molnar, Eur. Phys. J. A 48, 172 (2012)

work page 2012