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arxiv: 2605.30710 · v2 · pith:SXNUZO4Unew · submitted 2026-05-29 · ✦ hep-ph · nucl-th

Canonical statistical hadronization with local baryon conservation for higher-order cumulants

Mario Ciacco , Sourav Kundu , Volodymyr A. Kuznietsov , Maximiliano Puccio , Volodymyr Vovchenko This is my paper

Pith reviewed 2026-06-28 22:20 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords canonical ensemblelocal baryon conservationcumulantsheavy-ion collisionsnet-protonLHChadronization
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The pith

Local baryon conservation alone can drive κ6/κ2 to small or negative values in restricted acceptance at the LHC.

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

The paper studies higher-order cumulants of baryon number in the canonical ensemble with local baryon conservation for heavy-ion collisions at the LHC. It generalizes the density correlations method to include Gaussian local conservation in spatial rapidity space and computes cumulants up to sixth order. The resulting predictions for net-proton cumulants in O-O and Pb-Pb collisions serve as an ideal hadron gas baseline. Local conservation effects can produce small or negative κ6/κ2 ratios in limited acceptance windows, matching the diffusion master equation exactly.

Core claim

In the canonical ensemble with Gaussian local baryon conservation in spatial rapidity space, the ratio of sixth to second order cumulants of net baryon number can reach small or negative values within limited rapidity acceptances, a behavior often linked to chiral criticality, and this establishes the ideal hadron gas baseline for LHC net-proton measurements in O-O and Pb-Pb collisions.

What carries the argument

The Gaussian local conservation of baryon number in spatial rapidity space, which generalizes the density correlations approach to compute cumulants up to sixth order.

If this is right

  • Gaussian local conservation produces predictions comparable to the V_c approach at midrapidity but with marked differences at larger rapidity acceptances.
  • Coordinate-space results agree exactly with the diffusion master equation for all cumulant ratios up to κ6/κ2.
  • Blast-wave model predictions provide net-proton cumulant baselines for O-O and Pb-Pb collisions at the LHC.
  • The conservation baseline must be accounted for when interpreting upcoming LHC measurements that might signal chiral criticality.

Where Pith is reading between the lines

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

  • Negative cumulant ratios observed in data may arise from conservation laws rather than critical phenomena.
  • The Gaussian rapidity model could be tested against full hydrodynamic simulations of the collision evolution.
  • Extending the same local conservation treatment to electric charge or strangeness would yield additional baselines for multi-charge cumulants.

Load-bearing premise

Local baryon conservation is modeled as taking a Gaussian form in spatial rapidity space.

What would settle it

An LHC measurement in which net-proton κ6/κ2 stays positive for every acceptance window would contradict the prediction that local conservation drives the ratio negative in restricted acceptances.

Figures

Figures reproduced from arXiv: 2605.30710 by Mario Ciacco, Maximiliano Puccio, Sourav Kundu, Volodymyr A. Kuznietsov, Volodymyr Vovchenko.

Figure 1
Figure 1. Figure 1: The two-point conservation kernel κ2(η1, η2) as a function of η1 at fixed η2 for ση = 2 and ηmax = 5.1. Three boundary conditions are compared: minimum-image periodic (solid blue), full periodic (dashed green), and reflecting (dash-dotted black). The vertical dashed red line indicates the position of η2. (a) η2 = 0 (centered): all three prescriptions coincide. (b) η2 = 2.9 (shifted toward the boundary): th… view at source ↗
Figure 2
Figure 2. Figure 2: Coordinate-space cumulant ratios κ2/Nacc (left), κ4/κ2 (middle), and κ6/κ2 (right) as a function of the acceptance fraction α = ηcut/ηmax for the ideal gas at µB = 0, where Nacc ≡ ⟨B+B¯⟩acc. Solid lines correspond to the Gaussian local￾conservation kernel with widths ση = 2.02, 1.20, 0.78, 0.40, and the global conservation limit (solid black). Dashed lines show the equivalent Vc approach of Ref. [29] with … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the Gaussian local-conservation approach (black dashed/dash-dotted lines, with [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Momentum-space net-proton cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Centrality dependence of second-order proton cumulants in O–O collisions at [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Centrality dependence of the net-proton cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Predictions for net-proton cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Net-proton cumulant ratios κ2(p−p¯)/⟨p+¯p⟩ (left), κ4(p−p¯)/κ2(p−p¯) (middle), and κ6(p−p¯)/κ2(p−p¯) (right) in 0–5% central Pb–Pb collisions at √ sNN = 5.02 TeV, for local conservation with ση = 0.78, shown as a function of ∆˜η up to the projected ALICE 3 coverage [37, 38]. Three momentum windows are compared: the current ALICE acceptance 0.6 < p < 1.5 GeV/c (solid blue), the high-p extension 1.5 < p < 10… view at source ↗
read the original abstract

We study higher-order cumulants of the conserved baryon number at the LHC within the canonical ensemble with local baryon conservation. We generalize the density correlations approach of [Phys. Rev. C 110, L061902 (2024)] to incorporate the effect of Gaussian local conservation in spatial rapidity space in cumulants up to 6th order. Gaussian local conservation improves upon the commonly employed $V_c$ approach, yielding comparable predictions at midrapidity, but marked differences for larger rapidity acceptances. Our coordinate-space results are in exact agreement with the diffusion master equation approach for all cumulant ratios up to $\kappa_6/\kappa_2$. Using the blast-wave model to apply kinematic cuts, we obtain predictions for net-proton cumulants in O--O and Pb--Pb collisions at the LHC that establish an ideal hadron gas baseline. We find that local baryon conservation alone can drive $\kappa_6/\kappa_2$ to small or even negative values in restricted acceptance, a behavior often associated with chiral criticality. The conservation baseline must therefore be carefully accounted for when interpreting upcoming LHC measurements.

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 / 1 minor

Summary. The manuscript generalizes the density-correlations method to incorporate Gaussian local baryon conservation in spatial rapidity space, enabling calculation of baryon-number cumulants up to sixth order in the canonical ensemble. It reports exact agreement with the diffusion master equation for all ratios through κ6/κ2, applies blast-wave kinematics to obtain net-proton predictions for O-O and Pb-Pb collisions at the LHC, and concludes that local conservation alone can drive κ6/κ2 to small or negative values in restricted acceptance.

Significance. If the central results hold, the work supplies a necessary baseline for interpreting higher-order cumulant data at the LHC, demonstrating that conservation effects can produce signatures commonly associated with chiral criticality. The exact numerical agreement between two independent formalisms (density correlations and diffusion master equation) is a clear technical strength that increases in the coordinate-space predictions.

major comments (2)
  1. [Generalization of density correlations approach (abstract and § on local conservation)] The generalization beyond the V_c approximation relies on assuming a Gaussian form for the local baryon conservation correlation in spatial rapidity; this functional choice directly controls the sign and magnitude of κ6/κ2 at larger acceptances. The manuscript should test robustness against other forms (exponential or power-law tails) to establish that the reported negative values are not an artifact of the Gaussian parametrization.
  2. [Comparison with diffusion master equation] The exact agreement with the diffusion master equation is stated for all cumulant ratios up to κ6/κ2, yet the text does not clarify whether this match is independent of the Gaussian rapidity correlation or whether both methods embed the same functional assumption; this distinction is load-bearing for the claim that the result is method-independent.
minor comments (1)
  1. [Results section] Explicit numerical values for the Gaussian rapidity width and the blast-wave parameters used for the kinematic cuts should be tabulated to allow direct reproduction of the net-proton predictions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify key assumptions. We address each major comment below and will make the indicated revisions.

read point-by-point responses

  1. Referee: [Generalization of density correlations approach (abstract and § on local conservation)] The generalization beyond the V_c approximation relies on assuming a Gaussian form for the local baryon conservation correlation in spatial rapidity; this functional choice directly controls the sign and magnitude of κ6/κ2 at larger acceptances. The manuscript should test robustness against other forms (exponential or power-law tails) to establish that the reported negative values are not an artifact of the Gaussian parametrization.

    Authors: The Gaussian parametrization is physically motivated by the diffusive spreading of baryon number, which produces Gaussian correlations in rapidity. We agree that robustness checks against other forms would strengthen the work. In the revised manuscript we will add calculations using exponential and power-law correlation functions (in a new appendix) and show that, while the precise numerical values of κ6/κ2 change, the qualitative finding that local conservation can drive the ratio to small or negative values in restricted acceptance remains robust. revision: yes

  2. Referee: [Comparison with diffusion master equation] The exact agreement with the diffusion master equation is stated for all cumulant ratios up to κ6/κ2, yet the text does not clarify whether this match is independent of the Gaussian rapidity correlation or whether both methods embed the same functional assumption; this distinction is load-bearing for the claim that the result is method-independent.

    Authors: The diffusion master equation solves a stochastic diffusion process whose Green's function is Gaussian in the continuum limit; our density-correlations implementation adopts the same Gaussian local-conservation kernel. The exact numerical agreement therefore validates that the two independent mathematical frameworks (density correlations versus master equation) produce identical results when they encode the identical physical assumption of diffusive local conservation. We will add an explicit clarifying paragraph in the revised text to make this distinction clear while preserving the claim of technical consistency across formalisms. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation starts from the canonical ensemble with local baryon conservation, explicitly introduces a Gaussian correlation form in spatial rapidity as a modeling generalization of the cited density-correlations method, computes cumulant expressions up to order 6, verifies exact agreement with the independent diffusion master equation, and only then applies blast-wave kinematics for acceptance cuts. None of these steps reduce the target κ6/κ2 predictions to quantities fitted from the same data or to self-referential definitions; the Gaussian ansatz is an input assumption, not derived from or tautological with the output ratios. The central claim is therefore a model consequence rather than a logical loop.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the canonical ensemble with exact baryon conservation and the blast-wave kinematic model; the Gaussian width is an additional modeling choice whose value is not reported in the abstract.

free parameters (1)
  • Gaussian rapidity width
    Width parameter controlling the spatial extent of local baryon conservation; its specific value is not given in the abstract.
axioms (2)
  • domain assumption Canonical ensemble enforces exact global baryon-number conservation while allowing local fluctuations
    Invoked throughout the statistical hadronization framework described in the abstract.
  • domain assumption Blast-wave model accurately maps coordinate-space results to detector acceptance
    Used to obtain predictions for net-proton cumulants after kinematic cuts.

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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.

  1. Multistage dynamical modeling of heavy-ion collisions

    nucl-th 2026-06 unverdicted novelty 2.0

    The paper discusses recent progress and open issues in multistage simulations connecting bulk evolution, conserved charges, strangeness, and heavy flavor to constrain QCD matter at finite density.

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