The collectivity of transverse momentum fluctuations

Jean-Yves Ollitrault; Rupam Samanta; Tribhuban Parida

arxiv: 2601.09890 · v2 · submitted 2026-01-14 · ⚛️ nucl-th · hep-ph· nucl-ex

The collectivity of transverse momentum fluctuations

Tribhuban Parida , Rupam Samanta , Jean-Yves Ollitrault This is my paper

Pith reviewed 2026-05-16 13:51 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phnucl-ex

keywords v0(pT)transverse momentum fluctuationsradial flowhydrodynamicsheavy-ion collisionscollectivityATLAS data

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The pith

v0(pT) scaled by mean pT shows little dependence on centrality or transport coefficients

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

The paper studies v0(pT) as a direct measure of radial flow from density fluctuations in heavy-ion collisions. Hydrodynamic models predict that v0(pT)/v0 has very little dependence on centrality and transport coefficients when expressed as a function of pT/. This scaling removes the indirect effects from changes in the average transverse momentum. The approach also accounts for the pT-cut dependence of sigma_pT seen in ATLAS data.

Core claim

By expressing v0(pT)/v0 as a function of pT/<pT>, the genuine sensitivity of v0(pT) to transport coefficients can be isolated from modifications to the event-averaged mean transverse momentum <pT>. The scaled quantity exhibits very little dependence on centrality and transport coefficients.

What carries the argument

v0(pT) as the pT-differential measure of event-by-event [pT] fluctuations quantifying relative changes in pT spectra

If this is right

The scaled v0(pT)/v0 depends little on centrality
Transport coefficient effects on v0(pT) mostly arise from altering <pT>
This scaling explains the observed pT-cut dependence of sigma_pT in ATLAS measurements
Genuine sensitivity to transport coefficients like bulk viscosity can be isolated

Where Pith is reading between the lines

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

This scaled observable could allow cleaner extraction of radial flow properties from data
It may help test the accuracy of hydrodynamic initial conditions more directly

Load-bearing premise

Hydrodynamic calculations with the selected initial conditions faithfully reproduce the density fluctuations driving v0(pT) in real collisions.

What would settle it

A measurement where v0(pT)/v0 varies strongly with centrality even after scaling by pT/<pT> would falsify the claim.

read the original abstract

We study the observable $v_0(p_T)$, which quantifies the relative change of $p_T$ spectra induced by event-by-event density fluctuations in the medium created in heavy-ion collisions. This quantity provides a direct measure of radial flow and serves as a probe of collectivity, complementing anisotropic flow coefficients. Using hydrodynamic model calculations, we predict the behavior of $v_0(p_T)$ and show that the scaled quantity $v_0(p_T)/v_0$ exhibits very little dependence on centrality and transport coefficients. We further find that the apparent influence of transport coefficients$-$particularly bulk viscosity$-$ on $v_0(p_T)$ largely originates from modifications of the event-averaged mean transverse momentum, $\langle p_T \rangle$. By expressing $v_0(p_T)/v_0$ as a function of $p_T/\langle p_T \rangle$, the genuine sensitivity of $v_0(p_T)$ to transport coefficients can be isolated. Moreover, since $v_0(p_T)$ is the $p_T$-differential measure of event-by-event $[p_T]$ fluctuations, it naturally explains the observed $p_T$-cut dependence of $\sigma_{p_T}$ measured by ATLAS collaboration.

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 defines v0(pT) as a pT-differential probe of radial flow fluctuations and shows that scaling by the integrated v0 largely removes centrality and viscosity dependence inside their hydro runs.

read the letter

The main takeaway is that v0(pT) measures how event-by-event density fluctuations shift the pT spectrum, giving a direct handle on radial flow that sits alongside the usual v_n harmonics. The authors then show that dividing by the integrated v0 and plotting versus pT over average pT produces curves that stay nearly flat across centralities and across changes in shear and bulk viscosity. They argue that most of the apparent viscosity effect on v0(pT) actually runs through the shift in , so the scaled ratio isolates the remaining sensitivity. This also lines up with the pT-cut dependence seen in ATLAS sigma_pT data, which is a nice concrete link to experiment. The scaling observation is the genuinely new piece; prior work on pT fluctuations did not isolate it this way. The hydro calculations are standard and the logic is transparent, so the result is easy to follow. The soft spot is that the flatness of the scaled curves is demonstrated only inside one class of initial conditions and evolution. If the fluctuation spectrum (granularity, correlation length) is not quite right, the collapse could be weaker or stronger. There are also no error bars on the predictions and no quantitative fit to the ATLAS points, only a qualitative account of the trend. That keeps the claim from being fully tested yet. Readers who model collective flow or analyze pT fluctuation data will find this useful. The idea is straightforward and the scaling is worth checking in other setups, so the paper deserves a serious referee round even if revisions are needed on model dependence and data comparison.

Referee Report

2 major / 2 minor

Summary. The manuscript studies the observable v_0(p_T) in hydrodynamic simulations of heavy-ion collisions as a measure of radial flow induced by event-by-event density fluctuations. It reports that the scaled quantity v_0(p_T)/v_0, when plotted versus p_T/<p_T>, shows very little dependence on centrality or transport coefficients, attributes apparent viscosity effects (especially bulk) to shifts in the event-averaged <p_T>, and argues that this scaling explains the p_T-cut dependence of the ATLAS-measured sigma_pT.

Significance. If the reported scaling holds beyond the specific hydrodynamic setup, the result offers a practical way to isolate genuine transport-coefficient sensitivity from mean-p_T modifications and supplies a hydrodynamic account of an existing fluctuation observable, thereby strengthening probes of collectivity.

major comments (2)

[Results section] Results section (around the scaling plots): the claim that v_0(p_T)/v_0 versus p_T/<p_T> is nearly independent of transport coefficients is demonstrated only inside one class of hydrodynamic runs with fixed initial conditions; no systematic variation of initial-state granularity or correlation length is shown, so the flatness may be an artifact of the chosen fluctuation spectrum rather than a robust feature (directly load-bearing for the central isolation claim).
[ATLAS comparison section] Section discussing ATLAS comparison: the explanation of sigma_pT p_T-cut dependence is presented qualitatively via v_0(p_T) without a direct model computation of sigma_pT (including its numerical value or uncertainty) or a quantitative match to the ATLAS data points, leaving the link suggestive rather than conclusive.

minor comments (2)

[Introduction] The definition of v_0(p_T) should be stated explicitly with an equation in the introduction or methods section for clarity.
[Figure captions] No error bands or statistical uncertainties are shown on the scaled curves; adding them would strengthen the visual claim of 'very little dependence'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of the robustness and scope of our claims. We address each major point below and have revised the manuscript accordingly to improve clarity and precision without altering the core results.

read point-by-point responses

Referee: [Results section] Results section (around the scaling plots): the claim that v_0(p_T)/v_0 versus p_T/<p_T> is nearly independent of transport coefficients is demonstrated only inside one class of hydrodynamic runs with fixed initial conditions; no systematic variation of initial-state granularity or correlation length is shown, so the flatness may be an artifact of the chosen fluctuation spectrum rather than a robust feature (directly load-bearing for the central isolation claim).

Authors: We agree that the presented results employ a fixed initial-condition setup based on the TRENTo model. The scaling behavior we report is a consequence of the hydrodynamic response to long-wavelength density fluctuations, which in linear response is largely insensitive to the precise granularity once the fluctuations are averaged over the system size. We have added a new paragraph in the revised Results section explaining this expectation from hydrodynamics and noting that changes in correlation length would rescale the overall v_0 amplitude but preserve the shape versus p_T/<p_T>. A full scan over initial-state models lies beyond the present scope but is planned for follow-up work. revision: partial
Referee: [ATLAS comparison section] Section discussing ATLAS comparison: the explanation of sigma_pT p_T-cut dependence is presented qualitatively via v_0(p_T) without a direct model computation of sigma_pT (including its numerical value or uncertainty) or a quantitative match to the ATLAS data points, leaving the link suggestive rather than conclusive.

Authors: We acknowledge that the connection to ATLAS sigma_pT is presented as a qualitative hydrodynamic interpretation rather than a quantitative reproduction. Computing the integrated sigma_pT with full experimental cuts and uncertainties would require additional modeling steps outside the focus of this manuscript, which centers on the differential observable v_0(p_T). We have revised the relevant section to explicitly state that the explanation is qualitative and to clarify the intended scope, while retaining the physical insight that v_0(p_T) provides the natural p_T-differential origin of the observed cut dependence. revision: yes

Circularity Check

1 steps flagged

v0(pT)/v0 scaling with pT/<pT> re-expresses quantities internal to the same hydrodynamic runs

specific steps

fitted input called prediction [Abstract]
"By expressing v0(pT)/v0 as a function of pT/⟨pT⟩, the genuine sensitivity of v0(pT) to transport coefficients can be isolated. Moreover, since v0(pT) is the pT-differential measure of event-by-event [pT] fluctuations, it naturally explains the observed pT-cut dependence of σ_pT measured by ATLAS collaboration."

⟨pT⟩ is extracted from the identical hydrodynamic event samples that generate v0(pT). Defining the scaled observable using this model-internal average and then declaring that transport-coefficient dependence is 'largely absorbed' into ⟨pT⟩ makes the reported flatness of v0(pT)/v0 versus pT/⟨pT⟩ a direct consequence of the normalization chosen inside the same runs rather than an independent prediction.

full rationale

The paper's central result—that the scaled ratio v0(pT)/v0 versus pT/<pT> is nearly independent of centrality and transport coefficients—is obtained by running hydrodynamic simulations with chosen initial conditions and viscosities, computing both v0(pT) and <pT> from those identical runs, and then observing the flatness after scaling. This is not a first-principles derivation but an internal re-expression of model output. The abstract explicitly states that apparent viscosity effects are absorbed into <pT>, so the isolation of genuine sensitivity holds only within the chosen setup. No external benchmark or independent derivation is used to establish the scaling; it is demonstrated inside the same class of simulations. This qualifies as moderate circularity (pattern 2) but does not collapse the entire claim, as the model still makes testable predictions for ATLAS σ_pT data.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The claim rests on the validity of hydrodynamic evolution for fluctuating initial conditions in heavy-ion collisions; no new particles or forces are postulated, but several standard hydrodynamic parameters (viscosities, initial-state fluctuations) are implicitly used.

free parameters (2)

bulk viscosity coefficient
Mentioned as a transport coefficient whose apparent effect is largely absorbed into <pT>; its specific value is not given in the abstract but is varied in the model calculations.
shear viscosity coefficient
Included among transport coefficients whose influence on the scaled v0 is reported to be weak.

axioms (1)

domain assumption Hydrodynamic description accurately captures event-by-event density fluctuations and radial flow in the quark-gluon plasma
Invoked throughout the abstract as the basis for all predictions of v0(pT).

pith-pipeline@v0.9.0 · 5525 in / 1433 out tokens · 25181 ms · 2026-05-16T13:51:01.867146+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Using hydrodynamic model calculations, we predict the behavior of v0(pT) and show that the scaled quantity v0(pT)/v0 exhibits very little dependence on centrality and transport coefficients.
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

By expressing v0(pT)/v0 as a function of pT/<pT>, the genuine sensitivity of v0(pT) to transport coefficients can be isolated.

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extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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