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arxiv: 2510.26766 · v2 · submitted 2025-10-30 · ⚛️ nucl-ex · hep-ex

Characterizing the initial state and dynamical evolution in XeXe and PbPb collisions using multiparticle cumulants

CMS Collaboration This is my paper

Pith reviewed 2026-05-18 03:22 UTC · model grok-4.3

classification ⚛️ nucl-ex hep-ex
keywords heavy-ion collisionsflow harmonicsmultiparticle cumulantsnuclear deformationinitial-state geometryXeXe collisionsPbPb collisionsquark-gluon plasma
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The pith

Mixed-order moment correlations of flow harmonics in XeXe collisions reveal sensitivity to nuclear deformation compared to PbPb.

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

The paper measures for the first time correlations among mixed-order moments of two or three flow harmonics in xenon-xenon collisions and compares them to lead-lead results at similar energies. It uses these to probe collective behavior in the quark-gluon plasma and to show how initial-state geometry fluctuations respond to the triaxial deformation of the xenon nucleus versus the spherical lead nucleus. The work studies how results depend on the shape and size of the nuclear overlap region and highlights the roles of higher harmonics in the nonlinear hydrodynamic response. A sympathetic reader cares because the approach constrains initial-state models that govern the evolution from nuclear geometry to final particle distributions.

Core claim

For the first time, correlations among mixed-order moments of two or three flow harmonics (v_n^k, v_m^l) and (v_n^k, v_m^l, v_p^q) are measured in XeXe collisions and compared with PbPb results. These measurements compare a nearly spherical, doubly-magic 208Pb nucleus to a triaxially deformed 129Xe nucleus, emphasizing the sensitivity to initial-state geometry fluctuations arising from nuclear deformation. The dependence of these results on the shape and size of the nuclear overlap region is studied. Comparisons between v2, v3, and v4 demonstrate the importance of v3 and v4 in exploring the nonlinear hydrodynamic response of the QGP to the initial spatial anisotropy. The results constrain初始态

What carries the argument

Multiparticle mixed-harmonic cumulants up to eight particles that extract correlations between mixed-order moments of flow harmonics v_n from charged particles in |η| < 2.4 and 0.5 < p_T < 3 GeV/c.

If this is right

  • The results constrain initial-state model parameters that influence the evolution of the QGP.
  • v3 and v4 play a key role in capturing the nonlinear hydrodynamic response to initial spatial anisotropy.
  • The nuclear overlap region's shape and size directly affect the measured flow-harmonic correlations.
  • Comparisons between the two systems isolate effects from nuclear deformation in the initial geometry.

Where Pith is reading between the lines

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

  • The same mixed-cumulant technique could be applied to other deformed nuclei to map nuclear shapes more systematically.
  • These observables may help disentangle geometric fluctuations from viscous response in hydrodynamic models of the QGP.
  • Extending the analysis to lower energies or smaller systems could test whether deformation effects persist across different regimes.

Load-bearing premise

Observed differences between XeXe and PbPb mixed cumulant results are driven primarily by the triaxial deformation of the 129Xe nucleus rather than by the small differences in collision energy, system size, or other initial-state effects.

What would settle it

If the mixed-harmonic correlations measured in XeXe at 5.44 TeV match those in PbPb after correcting only for the 0.08 TeV energy difference and slight system-size variation, without needing to invoke nuclear deformation, the central sensitivity claim would be falsified.

Figures

Figures reproduced from arXiv: 2510.26766 by CMS Collaboration.

Figure 1
Figure 1. Figure 1: The upper row shows vn{2, |∆η| > 2} for elliptic (n = 2, left) and triangular (n = 3, right) flow, as a function of centrality in XeXe and PbPb collisions, calculated using the 2- particle correlation method. The vertical bars (mostly smaller than the marker size) and the open boxes represent the statistical and systematic uncertainties, respectively. The middle row compares various theoretical predictions… view at source ↗
Figure 2
Figure 2. Figure 2: The upper plots show vn{4}/vn{2, |∆η| > 2} for elliptic (n = 2, left) and triangular (n = 3, right) flow, calculated from multiparticle cumulants, as a function of centrality in XeXe and PbPb collisions. The vertical bars (mostly smaller than the marker size) on the dots and the open boxes represent the statistical and systematic uncertainties in the data, respectively. The red and blue solid lines show th… view at source ↗
Figure 3
Figure 3. Figure 3: The upper plots show the normalized symmetric cumulants NSC(2, 3) (left) and [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A selection of six-particle three-harmonic SC and NSC cumulants as functions of [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Six-particle normalized mixed harmonic cumulants (nMHC) as functions of cen [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Eight-particle normalized mixed harmonic cumulants (nMHC) as functions of cen [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

For the first time, correlations among mixed-order moments of two or three flow harmonics$-$($v_{n}^{k},v_{m}^{l}$) and ($v_{n}^{k},v_{m}^{l}, v_{p}^{q}$), with $k$, $l$, and $q$ denoting the respective orders$-$are measured in xenon-xenon (XeXe) collisions and compared with lead-lead (PbPb) results, providing a novel probe of collective behavior in heavy ion collisions. These measurements compare a nearly spherical, doubly-magic ${}^{208}$Pb nucleus to a triaxially deformed ${}^{129}$Xe nucleus, emphasizing the sensitivity to initial-state geometry fluctuations arising from nuclear deformation. The dependence of these results ($v_{n}$, $n$ = 2, 3, 4) on the shape and size of the nuclear overlap region is studied. Comparisons between $v_{2}$, $v_{3}$, and $v_{4}$ demonstrate the importance of $v_{3}$ and $v_{4}$ in exploring the nonlinear hydrodynamic response of the quark-gluon plasma (QGP) to the initial spatial anisotropy. The results constrain initial-state model parameters that influence the evolution of the QGP. The CMS detector was used to collect XeXe and PbPb data at nucleon-nucleon center-of-mass energies of $\sqrt{s_\mathrm{NN}}$ = 5.44 and 5.36 TeV, respectively. Correlations are extracted using multiparticle mixed-harmonic cumulants (up to eight-particle cumulants) with charged particles in the pseudorapidity range $\lvert\eta\rvert$ $\lt$ 2.4 and transverse momentum range 0.5 $\lt$ $p_\mathrm{T}$ $\lt$ 3 GeV/$c$.

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 / 2 minor

Summary. The manuscript reports the first measurements of correlations among mixed-order moments of two or three flow harmonics, (v_n^k, v_m^l) and (v_n^k, v_m^l, v_p^q), extracted via multiparticle cumulants (up to eight-particle) in XeXe collisions at √s_NN = 5.44 TeV. These are compared to existing PbPb results at 5.36 TeV to probe collective behavior, with emphasis on sensitivity to initial-state geometry fluctuations from the triaxial deformation of 129Xe versus the nearly spherical 208Pb. The dependence of v2, v3, and v4 on nuclear overlap shape and size is studied, and the importance of v3 and v4 for nonlinear hydrodynamic response is highlighted. Data are from CMS with charged particles in |η| < 2.4 and 0.5 < p_T < 3 GeV/c.

Significance. If the central results hold after addressing potential confounders, the work supplies a new experimental handle on initial-state fluctuations and QGP response through mixed cumulants, which can tighten constraints on nuclear deformation parameters and hydrodynamic modeling. The multiparticle approach and direct XeXe-PbPb comparison add value beyond single-harmonic measurements.

major comments (1)
  1. [Abstract and results section on XeXe-PbPb comparisons] Abstract: The central claim that the XeXe-PbPb differences emphasize sensitivity to triaxial deformation of 129Xe requires that the comparison isolates this effect from other initial-state differences. The 1.5% mismatch in √s_NN (5.44 vs 5.36 TeV) and the large difference in A (129 vs 208) alter participant density, eccentricity distributions, and hydrodynamic response independently of β and γ. The manuscript states that dependence on overlap shape and size is studied, but does not appear to include explicit model runs (deformed vs spherical initial conditions at fixed energy and matched multiplicity) that would quantify the deformation-induced shift against these confounders.
minor comments (2)
  1. [Abstract] The abstract lists the p_T and η ranges but does not specify the exact orders (k, l, q) or the precise cumulant combinations used for the mixed moments; adding this would improve clarity for readers.
  2. [Analysis or systematic uncertainties section] The manuscript would benefit from an explicit statement of how systematic uncertainties on the mixed cumulants are evaluated, particularly for the cross-system comparison.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thoughtful and detailed review of our manuscript. The major comment raises a valid concern about isolating the effects of nuclear deformation in the XeXe-PbPb comparison. We address this point directly below and have revised the manuscript to clarify the scope of our claims and acknowledge potential confounders.

read point-by-point responses

  1. Referee: [Abstract and results section on XeXe-PbPb comparisons] Abstract: The central claim that the XeXe-PbPb differences emphasize sensitivity to triaxial deformation of 129Xe requires that the comparison isolates this effect from other initial-state differences. The 1.5% mismatch in √s_NN (5.44 vs 5.36 TeV) and the large difference in A (129 vs 208) alter participant density, eccentricity distributions, and hydrodynamic response independently of β and γ. The manuscript states that dependence on overlap shape and size is studied, but does not appear to include explicit model runs (deformed vs spherical initial conditions at fixed energy and matched multiplicity) that would quantify the deformation-induced shift against these confounders.

    Authors: We agree that a fully isolated quantification of the triaxial deformation effect would benefit from dedicated hydrodynamic simulations comparing deformed versus spherical 129Xe initial conditions at fixed √s_NN and matched multiplicity. Our work is an experimental measurement focused on new multiparticle cumulant observables; we do not present new model calculations. The 1.5% energy difference is small, and the energy dependence of flow harmonics is known to be weak in this regime. To address the A difference, results are presented versus charged-particle multiplicity as a proxy for overlap size and participant number. Existing hydrodynamic calculations incorporating the measured β and γ deformation parameters for 129Xe are referenced and compared to the data. In the revised manuscript we have added a dedicated paragraph in the discussion section that explicitly lists these confounders, notes that the observed XeXe-PbPb differences are consistent with deformation expectations but cannot be attributed solely to them, and softens the abstract language to avoid overclaiming isolation of the effect. We believe this revision improves the interpretation while preserving the value of the new mixed-order cumulant measurements. revision: partial

Circularity Check

0 steps flagged

No significant circularity in experimental cumulant measurements

full rationale

The paper reports direct experimental measurements of mixed-order multiparticle cumulants extracted from XeXe and PbPb collision data collected by the CMS detector. The central results consist of observed correlations among flow harmonics v_n, v_m, v_p without any first-principles derivation chain, parameter fitting renamed as prediction, or load-bearing self-citation that reduces the reported quantities to their inputs by construction. System comparisons are presented as data-driven observations, and statements about sensitivity to nuclear deformation are interpretive rather than definitional. The analysis remains self-contained against external benchmarks because the quantities are computed from raw detector data using standard cumulant techniques, with no equations that equate outputs to fitted inputs or prior author results by tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of collective hydrodynamic behavior in heavy-ion collisions and the accuracy of nuclear deformation models for 129Xe versus 208Pb; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The quark-gluon plasma produced in these collisions behaves as a nearly perfect fluid whose expansion is governed by hydrodynamics.
    Invoked when the abstract states that the results demonstrate the importance of v3 and v4 in exploring the nonlinear hydrodynamic response.
  • domain assumption Differences in measured correlations between XeXe and PbPb are attributable to nuclear shape differences rather than other initial-state or final-state effects.
    Central to the comparison emphasized in the abstract.

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Reference graph

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