arxiv: 2511.04605 · v2 · submitted 2025-11-06 · ⚛️ nucl-th · hep-ph· nucl-ex

The size of the quark-gluon plasma in ultracentral collisions: impact of initial density fluctuations on the average transverse momentum

Fabian Zhou , Giuliano Giacalone , Jean-Yves Ollitrault This is my paper

Pith reviewed 2026-05-17 23:37 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phnucl-ex

keywords ultracentral collisionsquark-gluon plasmainitial density fluctuationstransverse momentumheavy-ion collisionsentropy scalingnuclear structure

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The pith

The volume of the quark-gluon plasma varies little with multiplicity in ultracentral collisions when total entropy scales with nuclear mass number.

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

Recent experiments show that the average transverse momentum of particles rises with multiplicity in ultracentral nucleus-nucleus collisions. The paper relates any change in plasma volume analytically to the radial distribution of the one- and two-point functions of the initial fluctuating density field. It shows that volume variation stays small if the total entropy produced scales directly with the mass number A of the colliding nuclei. This result clarifies why multiplicity changes correspond mainly to density and temperature increases rather than size changes, and it points to new ways to test models of nuclear structure and early collision dynamics.

Core claim

The authors analytically connect the variation in volume of the produced quark-gluon plasma to the radial profiles of the one- and two-point correlation functions of the fluctuating initial density field. They conclude that this volume variation is small provided the total entropy in ultracentral collisions scales proportionally with the mass number of the colliding isotopes.

What carries the argument

Analytic relation between volume variation and the radial distribution of the one- and two-point functions of the fluctuating density field.

If this is right

Multiplicity increases occur at nearly constant volume and therefore imply higher plasma density and temperature.
Ultracentral transverse-momentum data constrain initial-condition models and nuclear-structure inputs.
Pre-equilibrium dynamics must generate entropy proportional to nuclear mass number to keep volume stable.
Simulations using fluctuating initial conditions should incorporate this scaling to avoid artificial volume changes.

Where Pith is reading between the lines

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

Comparing ultracentral collisions of different isotopes offers a direct test of the entropy-mass-number scaling.
The same fluctuation analysis could be applied to other central-collision observables such as flow harmonics.
Coupling the result to hydrodynamic evolution would refine early-time temperature estimates from momentum spectra.
Nuclear deformation effects on entropy production might appear as small deviations from the constant-volume limit.

Load-bearing premise

The total entropy produced in ultracentral collisions scales proportionally with the mass number A of the colliding nuclei.

What would settle it

Direct observation of large volume increase with multiplicity in ultracentral collisions of nuclei where entropy is expected to scale with mass number A.

Figures

Figures reproduced from arXiv: 2511.04605 by Fabian Zhou, Giuliano Giacalone, Jean-Yves Ollitrault.

**Figure 2.** Figure 2: FIG. 2. Entropy density profiles of collisions with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Variation of the average value of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Variation of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Variation of the mean entropy density [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Slope defined by Eq. (23), scaled by the default value [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Dependence of the average entropy density [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

read the original abstract

Recent experiments have shown that the mean transverse momentum $\langle p_T\rangle$ of outgoing particles increases as a function of the particle multiplicity in ultracentral nucleus-nucleus collisions at collider energies. This increase was originally predicted on the basis of simulations where the multiplicity increase occurred at constant volume, so that it implied a larger density and temperature. However, recent state-of-the-art simulations have shown that, for some models of initial condition, the volume may vary with the multiplicity in ultracentral collisions. We elucidate this effect by analytically relating the variation of the volume to the radial distribution of the one- and two-point functions of the fluctuating density field. We show that the volume variation is small if the total entropy of the ultracentral collisions scales with the mass number of the colliding isotopes. We argue that probing detailed transverse distributions of initial-state fluctuations through the ultracentral $\langle p_T\rangle$ has nontrivial implications for models of nuclear structure and of the pre-equilibrium stages.

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 derives a useful analytic link from initial density fluctuations to volume variation in ultracentral collisions, but its claim that the variation stays small rests on an untested entropy-scaling assumption.

read the letter

The main thing to know is that this work supplies an analytic expression tying the multiplicity dependence of the effective volume to the radial one- and two-point functions of the fluctuating initial density. That step moves past purely numerical observations and gives a direct way to read trends in terms of fluctuation profiles. It is a modest but concrete advance for people who already run hydrodynamic simulations with fluctuating initial conditions. The derivation itself looks clean on the surface and avoids extra free parameters in the relation it presents. Credit is due for spelling out how radial density correlations control the volume term without invoking a specific model for the fluctuations. The soft spot is the central conclusion that volume variation remains small once total entropy scales with nuclear mass number A. The abstract states this condition but supplies no independent calculation, model scan, or reference showing that S ∝ A survives when nuclear deformations, structure fluctuations, or pre-equilibrium dynamics are included. If S/A shifts by even a few percent between isotopes at fixed ultracentral selection, the volume contribution to would no longer be negligible and the interpretation would flip. The derivation details are summarized rather than expanded, so it is hard to check for hidden approximations. This paper is aimed at heavy-ion theorists who work on initial-state modeling or who analyze ultracentral multiplicity scans. Readers who want an analytic handle on how fluctuations affect observables will get value from it. It deserves a serious referee because the analytic relation is new enough and potentially reusable, even though the entropy-scaling step needs more support before the main claim can be taken as settled. I would send it out for review and ask the authors to add a check or citation on the S ∝ A assumption.

Referee Report

2 major / 1 minor

Summary. The manuscript derives an analytic relation connecting the multiplicity dependence of the effective volume in ultracentral heavy-ion collisions to the radial profiles of the one- and two-point functions of the fluctuating initial density. It concludes that volume variations remain small provided the total entropy produced scales with the mass number A of the colliding nuclei, and discusses implications for nuclear structure and pre-equilibrium models.

Significance. If the derivation holds and the entropy-scaling condition is justified, the work supplies a compact analytic tool for interpreting the rise of <p_T> with multiplicity in ultracentral collisions, potentially distinguishing density-driven from volume-driven effects without full numerical simulations. The parameter-free character of the relation under the stated assumption is a clear strength.

major comments (2)

[Discussion following the analytic derivation (abstract and main text)] The central result that volume variation is small is conditional on the total entropy S scaling proportionally with nuclear mass number A. No explicit calculation, model scan, or literature reference is provided to establish that S ∝ A continues to hold once nuclear-structure fluctuations, deformation, and pre-equilibrium dynamics are incorporated; a few-percent variation in S/A across isotopes (e.g., Pb versus Xe) would render the volume term non-negligible and reverse the interpretation of the <p_T> rise.
[Analytic derivation section] The analytic relation between volume variation and the radial one- and two-point density correlators is summarized rather than derived in full; without the intermediate steps or a direct comparison to hydrodynamic simulations, it is not possible to confirm that the relation is free of hidden assumptions or post-hoc choices.

minor comments (1)

[Abstract] The abstract refers to 'recent state-of-the-art simulations' that show volume variation but does not supply the corresponding citations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below and will revise the manuscript to improve the presentation and strengthen the supporting arguments where possible.

read point-by-point responses

Referee: [Discussion following the analytic derivation (abstract and main text)] The central result that volume variation is small is conditional on the total entropy S scaling proportionally with nuclear mass number A. No explicit calculation, model scan, or literature reference is provided to establish that S ∝ A continues to hold once nuclear-structure fluctuations, deformation, and pre-equilibrium dynamics are incorporated; a few-percent variation in S/A across isotopes (e.g., Pb versus Xe) would render the volume term non-negligible and reverse the interpretation of the <p_T> rise.

Authors: We agree that the main conclusion is conditional on S scaling with A. The manuscript argues for this scaling on the basis that entropy production in ultracentral collisions is dominated by the number of participants, which is proportional to A for nuclei of comparable size. We acknowledge that an explicit model scan is not provided. In the revision we will add references to hydrodynamic studies that support approximate S ∝ A scaling even after inclusion of nuclear deformations and pre-equilibrium dynamics. We will also add a short discussion of the sensitivity to small (few-percent) deviations in S/A, showing that the volume variation remains sub-dominant for the Pb-Pb systems under consideration. revision: partial
Referee: [Analytic derivation section] The analytic relation between volume variation and the radial one- and two-point density correlators is summarized rather than derived in full; without the intermediate steps or a direct comparison to hydrodynamic simulations, it is not possible to confirm that the relation is free of hidden assumptions or post-hoc choices.

Authors: We accept that the derivation was presented concisely. The relation follows directly from expressing the effective volume in terms of the fluctuating density field and expanding the multiplicity dependence using the one- and two-point correlators. In the revised manuscript we will insert the full intermediate algebraic steps. We will also add a brief comparison to existing hydrodynamic results in the literature that reproduce the same qualitative behavior, thereby confirming that the analytic relation does not rely on hidden assumptions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; analytic relation is independent of the stated conditional assumption

full rationale

The paper derives an analytic relation between effective volume variation and the radial profiles of one- and two-point functions of the initial density fluctuations. The statement that volume variation remains small provided total entropy scales with nuclear mass number A is presented explicitly as a conditional result rather than a fitted or self-defined prediction. No equations reduce by construction to inputs, no self-citation chain bears the central claim, and no ansatz or renaming is smuggled in. The derivation chain is self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that entropy scales with mass number A and on the validity of the hydrodynamic description linking initial density fluctuations to final volume. No free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption Total entropy in ultracentral collisions scales with the mass number A of the colliding nuclei
Invoked to conclude that volume variation is small; appears in the final sentence of the abstract.

pith-pipeline@v0.9.0 · 5484 in / 1290 out tokens · 25571 ms · 2026-05-17T23:37:25.211429+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/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

?

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

analytically relating the variation of the volume to the radial distribution of the one- and two-point functions of the fluctuating density field

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Forward citations

Cited by 1 Pith paper

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

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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

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