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arxiv: 2604.21971 · v1 · submitted 2026-04-23 · ✦ hep-ph · hep-ex· nucl-th

Recognition: unknown

Hydrodynamics and Energy Correlators

Jo\~ao Barata , Matvey V. Kuzmin , Ian Moult , Andrey V. Sadofyev , Jo\~ao M. Silva
Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:07 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-th
keywords energy-energy correlatorsheavy-ion collisionshydrodynamicsQCD matterGubser flowangular structurecollective modes
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The pith

Energy-energy correlators in heavy-ion collisions follow collective flow scaling at large angles before crossing to hydrodynamic mode control at smaller angles.

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

The paper maps the angular dependence of energy-energy correlators produced in heavy-ion collisions by dividing the small-angle regime into successive dynamical regimes. At the largest angles inside that regime the observable is set by disconnected contributions whose scaling is fixed by the collective hydrodynamic flow of the expanding medium. At intermediate angles connected contributions take over and the angular pattern is governed by the same collective hydrodynamic modes that appear in certain conformal field theory states. These regimes are then expected to connect smoothly to the light-ray operator product expansion and finally to the behavior of dilute hadronic matter. The resulting picture supplies concrete analytic expressions for the angular shape and identifies new observables that can report on the properties of the produced QCD medium.

Core claim

In the collinear limit the energy-energy correlator of hadrons from a boost-invariant Gubser hydrodynamic medium is dominated at the largest angles by a disconnected piece whose angular dependence is fixed analytically by the collective flow velocity field; at smaller angles the connected piece becomes important and the correlator is controlled by collective hydrodynamic modes whose angular behavior matches that found in heavy and large-charge states of conformal field theories.

What carries the argument

Energy-energy correlator angular distribution in the collinear limit, decomposed into disconnected contributions fixed by Gubser flow and connected contributions governed by collective hydrodynamic modes.

If this is right

  • An explicit analytic formula for the angular dependence of the EEC arising from boost-invariant Gubser flow.
  • Azimuthal perturbations to the flow produce measurable modulations in the EEC that can be used to constrain initial-state anisotropies.
  • The intermediate-angle regime of the EEC is predicted to exhibit the same angular scaling previously identified in heavy and large-charge CFT states.
  • A continuous crossover from the hydrodynamic-mode regime to the light-ray OPE structure occurs at still smaller angles before the correlator finally matches the dilute hadronic limit.

Where Pith is reading between the lines

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

  • The same hydrodynamic-mode regime may appear in other high-multiplicity hadronic collisions if collective flow develops.
  • Energy-energy correlators could serve as a new experimental handle on the shear viscosity and other transport coefficients of the quark-gluon plasma.
  • The sequence of regimes provides a template for testing whether hydrodynamic descriptions remain valid down to the smallest resolved angles in current collider data.

Load-bearing premise

The assumption that at smaller angular separations the energy-energy correlator is controlled by collective hydrodynamic modes whose angular dependence matches the pattern seen in conformal field theory states.

What would settle it

A precision measurement of the angular shape of the energy-energy correlator in heavy-ion data that deviates from the analytic form derived for Gubser flow at the largest angles inside the collinear regime.

Figures

Figures reproduced from arXiv: 2604.21971 by Andrey V. Sadofyev, Ian Moult, Jo\~ao Barata, Jo\~ao M. Silva, Matvey V. Kuzmin.

Figure 1
Figure 1. Figure 1: Schematic angular structure of the EEC measured on a bulk matter state for angu [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Absolute value of the connected part of ⟨E(n1)E(n2)⟩ divided by its dimensionful pre-factor N = wT2R4/(6π 2 ) for the toy model with infinite static thermal matter, hadronizing at a later time. The blue line corresponds to the full result in Eq. (12), while the red dashed line corresponds to the 1/(T R) ≪ χ ≪ 1 envelope, i.e. the ∼ 1/χ2 scaling in Eq. (13) without the cos(·). This quantity depends only on … view at source ↗
Figure 3
Figure 3. Figure 3: Absolute value of the connected part of ⟨E(n1)E(n2)⟩ divided by its dimensionful pre-factor N = wτT2 r 4 in/(36π 2 ) for the toy model with a finite hadronizing shell as a function of χ. The blue line corresponds to the full result in Eq. (18), while the red dashed line corresponds to the 1/(T rin) ≪ χ ≪ 1 envelope, i.e. the ∼ 1/χ2 scaling in Eq. (19) without the cos(·). This quantity depends only on two d… view at source ↗
Figure 4
Figure 4. Figure 4: F defined in Eq. (45), for zero viscosity flow, divided by its dimensionful pre-factor and as a function of the dimensionless parameter R 1/4 ϵ = ϵh/  qTˆ 0  . The range corresponds to q −1 ∈ (4, 10) fm, Tˆ 0 ≃ 5.5 and ϵh ≃ 0.83 GeV/fm3 . 0.00 0.05 0.10 0.15 0.20 H¯ 0 0.5 0.6 0.7 0.8 0.9 1.0 Fvisc./ Finv. q−1 = 4 fm q−1 = 6 fm q−1 = 8 fm q−1 = 10 fm 1.00 1.25 1.50 1.75 2.00 2.25 2.50 R 1/4  0.5 0.6 0.7 … view at source ↗
Figure 5
Figure 5. Figure 5: Ratio between F for viscous and inviscid cases, computed numerically from Eq. (45), as a function of normalized viscosity H¯ 0 = H0/Tˆ 0 (left panel), for q −1 ∈ (4, 10) fm and of R 1/4 ϵ = ϵh/  qTˆ 0  (right panel), for H0 ∈ (0.05, 1). We have set Tˆ 0 ≃ 5.5 and ϵh ≃ 0.83 GeV/fm3 . unperturbed quantity. The perturbations then read [105] δϵ = −4  1 + H0g 2/3 2Tˆ 0  ϵnAn(x⊥) cos nϕ , δuτ = 0 , (46) δu⊥ … view at source ↗
Figure 6
Figure 6. Figure 6: Ratio Fn/F0 for viscous Gubser flow as a function of harmonic number n, for multiple values of transverse size q −1 ∈ (4, 10) fm for fixed H0 = 0.5 (left panel) and of viscosity H0 ∈ (0.05, 1) for fixed q −1 = 4 fm (right panel). with An(x⊥) =  2qx⊥ 1+(qx⊥) 2 n , and ϵn encodes the initial magnitude of the perturbation modes. The leading contributions to first order in ϵn are presented in appendix. There… view at source ↗
read the original abstract

We study energy-energy correlators (EECs) in many-body quantum states, focusing on the matter produced in the aftermath of heavy-ion collisions. We analyze the angular structure of EECs in the collinear limit and identify a sequence of dynamical regimes. At the largest angular separations within the small-angle regime, the observable is dominated by disconnected contributions, leading to a classical scaling determined by the collective flow of the medium. We explicitly construct this contribution for hadrons produced from a hydrodynamic medium described by boost-invariant Gubser flow, obtaining the angular dependence of the EEC analytically. We further consider azimuthal perturbations to this flow, illustrating how EECs can be used to probe anisotropies in the initial state. At smaller angular separations, connected contributions become increasingly important. We argue that in this regime the EEC is controlled by collective hydrodynamic modes. The resulting angular behavior is similar to the one identified in the EECs of heavy and large-charge states of conformal field theories. At even smaller angles, this regime is expected to match onto the structure determined by the light-ray operator product expansion, before eventually crossing over to the smallest-angle behavior characteristic of dilute hadronic matter. Altogether, these results provide a unified picture of the angular structure of EECs in many-body QCD states and suggest new observables sensitive to the properties of matter in 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.

Referee Report

1 major / 0 minor

Summary. The manuscript examines energy-energy correlators (EECs) in many-body states relevant to heavy-ion collisions. It identifies a sequence of dynamical regimes in the collinear limit: at large angles within the small-angle regime, disconnected contributions dominate with classical scaling from collective flow, explicitly constructed for boost-invariant Gubser hydrodynamic flow; at intermediate angles, connected contributions are argued to be controlled by collective hydrodynamic modes with angular scaling akin to that in conformal field theory heavy and large-charge states; at smaller angles, it transitions to light-ray OPE behavior before crossing to dilute hadronic matter. The work proposes EECs as new observables for probing matter properties in heavy-ion collisions, including sensitivity to initial-state anisotropies via azimuthal perturbations.

Significance. If the results hold, the paper offers a unified description of the angular structure of EECs in QCD many-body states and highlights their potential as probes for hydrodynamic properties and initial conditions in heavy-ion collisions. A notable strength is the analytic construction of the disconnected contribution for Gubser flow, which provides explicit angular dependence. This could open avenues for using EECs to study collective effects beyond traditional flow observables.

major comments (1)
  1. [Abstract and intermediate-regime discussion] The claim that at smaller angular separations the connected EEC is controlled by collective hydrodynamic modes whose angular behavior matches the CFT heavy/large-charge result is asserted by analogy rather than derived via explicit mode decomposition, linearization of the hydrodynamic equations around the Gubser background, or direct computation of the connected stress-tensor correlators. This is load-bearing for the central unified picture of three sequential regimes (Abstract).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We appreciate the positive assessment of the work's significance, particularly the analytic construction for Gubser flow. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract and intermediate-regime discussion] The claim that at smaller angular separations the connected EEC is controlled by collective hydrodynamic modes whose angular behavior matches the CFT heavy/large-charge result is asserted by analogy rather than derived via explicit mode decomposition, linearization of the hydrodynamic equations around the Gubser background, or direct computation of the connected stress-tensor correlators. This is load-bearing for the central unified picture of three sequential regimes (Abstract).

    Authors: We agree that the intermediate-regime discussion relies on an argument by analogy rather than an explicit derivation. The manuscript already phrases this as 'We argue that in this regime the EEC is controlled by collective hydrodynamic modes. The resulting angular behavior is similar to the one identified in the EECs of heavy and large-charge states of conformal field theories,' reflecting that both the heavy-ion hydrodynamic medium and CFT heavy/large-charge states are governed by the same long-wavelength hydrodynamic effective theory, yielding comparable angular scaling from collective modes. We do not perform mode decomposition or linearization around the Gubser background in this work, as the focus is on the explicit disconnected contribution and identifying the overall sequence of regimes. We acknowledge that a direct computation would strengthen the claim and will revise the abstract and relevant sections to emphasize more clearly that this part of the unified picture is supported by scaling arguments and analogy to known hydrodynamic and CFT results, rather than a complete derivation. We will also note the value of future explicit calculations in this direction. revision: partial

Circularity Check

0 steps flagged

No significant circularity; explicit constructions and arguments by analogy remain independent of target results

full rationale

The paper explicitly constructs the disconnected large-angle EEC contribution from boost-invariant Gubser hydrodynamic flow and derives its angular dependence analytically without reference to the EEC data itself. The intermediate-angle regime is introduced via an argument that the connected piece is controlled by collective modes whose scaling resembles prior CFT results, rather than through a fitted parameter, self-definition, or derivation that reduces to the observable by construction. No load-bearing self-citations, uniqueness theorems imported from the authors' prior work, or ansatze smuggled via citation are required for the central claims. The overall sequence of regimes combines established hydrodynamic models with reasoned extensions and is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The work relies on standard assumptions from heavy-ion hydrodynamics.

axioms (1)
  • domain assumption The medium produced in heavy-ion collisions can be described by boost-invariant Gubser flow for constructing the disconnected contribution
    Invoked explicitly to obtain the analytical angular dependence of the EEC.

pith-pipeline@v0.9.0 · 5557 in / 1256 out tokens · 54977 ms · 2026-05-09T21:07:05.913623+00:00 · methodology

discussion (0)

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