From Nuclear Many-Body Correlations to Energy Detector Correlators

Giuliano Giacalone; Jo\~{a}o Barata

REVIEW

From Nuclear Many-Body Correlations to Energy Detector Correlators

João Barata, Giuliano Giacalone

Nuclear Theory · Submitted 16 Sep 2026 · 118 references

Pith's verdict: Elegant operator-level formalism linking nuclear ground-state correlations to energy-energy correlators, but the central mapping relies on truncations that are not quantitatively controlled.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on September 17, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 5 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID2609.18754 (version 1)

Pith IDXXCUA5PI, Pith's permanent record of this paper and its review

CitationGiuliano Giacalone, Jo\~{a}o Barata. "From Nuclear Many-Body Correlations to Energy Detector Correlators." arXiv:2609.18754 (2026). https://pith.science/paper/XXCUA5PI

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The paper does something genuinely useful: it constructs a systematic, operator-level matching between the energy-energy correlator (EEC) in high-energy nuclear collisions and multipole-operator correlators in the nuclear ground state. The end-to-end chain—from nuclear thickness through the CGC deposition and hydrodynamic response to the asymptotic energy flow—is laid out clearly, and the authors are explicit about where truncations enter. The result is a formalism that, if controllable, would let collider experiments extract nuclear structure with reduced model dependence. The derivations are internally consistent and the paper is well written.

Now the soft spot, and it is a genuine one. The central claim (Eq. 22) depends on truncating the linear response kernel to its lowest radial mode and keeping only the leading term in the thickness-weight expansion. The supplement (Eq. 63) shows that the first omitted term is a cross-covariance ⟨ϵ_{n,n} ϵ_{n+2,n}^*⟩. The paper offers no estimate—analytic, phenomenological, or from a toy model—of how large this correction is relative to the leading term for realistic nuclei. Without that estimate, the mapping is a formal skeleton but not yet a quantitative instrument. The text acknowledges the truncation, but that is not enough: the authors need to show that the omitted terms are parametrically suppressed, not just name them.

A secondary concern is the reliance on the leading CGC scaling e ∝ (Q_s^-)^2 (Q_s^+)^2 with Q_s^2 ∝ t. This is a plausible starting point, but the paper does not show how corrections (from transverse gradients, subleading operators, or evolution) would enter the matching coefficients. The formalism is advertised as systematically improvable, but the improvable part is sketched rather than demonstrated.

Who is this for? Theorists interested in formal connections between heavy-ion phenomenology and nuclear many-body theory. It is not yet a practical tool for experimental analysis.

Verdict: this paper deserves a serious peer review, but the revision should require the authors to either (a) provide a quantitative estimate—even a crude one—of the neglected cross-covariance for a representative nucleus, or (b) show that the truncation can be systematically improved order by order. Without that, the central claim remains a conjecture rather than a derivation.

Referee report

Major objections (3)

[Supplement, Eq. (63) and surrounding text] The reduction of ⟨f_n^2⟩_ev to the bare multipole operator ⟨Q̂_n Q̂_n^†⟩_Ψ depends critically on truncating the response to the lowest radial mode (ℓ=0 in ρ_n(r)) and the leading thickness-weight (j=0 in t̄(r)). Eq. (63) shows that the first radial correction already enters as a cross-covariance ⟨ε_{n,n} ε_{n+2,n}^*⟩ at the same order in δe^2. The paper provides no estimate—analytic, from a simplified model, or phenomenological—of the relative magnitude of this term compared to the leading |g_{n0}|^2 ⟨|ε_{n,n}|^2⟩. Without such an estimate, the claim that the leading-order relation holds is quantitatively uncontrolled. The authors should provide a concrete argument or demonstrate, even in a toy nuclear model, that the cross-covariance is subdominant, or explicitly state the regime of validity and the potential size of violations.
[§2, Eq. (4) and surrounding discussion] The separation of the EEC into geometric and fixed-geometry (non-flow) parts, and the subsequent neglect of ⟨G_fixed^2⟩_ev, is stated without quantitative support. In heavy-ion flow analyses the flow/non-flow decomposition is a major challenge and non-flow is not generically small at the angular scales of interest. The authors should justify this assumption, either by citing explicit estimates from the literature (e.g., Refs. [72,76]) or by showing that the fixed-geometry contribution is suppressed by the same long-wavelength counting. If this assumption fails, the claimed mapping to nuclear ground-state correlators is contaminated.
[§4, Eq. (21) and following] The mapping from energy-density correlations to thickness correlations relies on the leading-order CGC relation e ∝ (Q_s^+)^2 (Q_s^-)^2 ∝ t^+ t^- . The paper acknowledges subleading corrections (gradient terms, IP-Sat, etc.) but does not discuss whether they can generate angular structures that mix different multipoles at the same order as the retained term. The derived result implicitly assumes that such corrections are subleading in the long-wavelength expansion. The authors should either argue that they are indeed of higher order in the same counting, or show that they do not break the proportionality to the bare multipole operator.

Minor objections (5)

[§2, Eq. (4) and later] The notation for the EEC is introduced as G_2, then later the geometric part is denoted G_2^geom and the fixed part as ⟨G_fixed^2⟩_ev. This is slightly confusing; consider renaming the full correlator to avoid ambiguity.
[§2, after Eq. (6)] Define f_n explicitly as the magnitude of F_{n,ev} instead of introducing it in the text without a formal definition.
[§3, around Eq. (17)] The statement that the radial dependence can be expanded in modes with leading term r^n using 'an orthonormal basis of polynomials' is vague. Specify the basis (e.g., monomials r^{n+2ℓ}) and note that orthonormal bases are not required for the argument.
[Supplement, Eq. (37)] Please check the factor of 2π in this equation; it is dimensionally correct if the angular integration is correctly accounted for, but a brief clarification would help the reader.
[Supplement, Eq. (53)–(54)] The introduction of the matrix C_A is not needed for the scalar-channel specialization that follows. Consider simplifying the presentation to focus on the energy-density case used in the main text.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Energy-energy correlators measure nuclear multipole operators at leading order.

The reading

This paper establishes a systematic formalism linking long-wavelength final-state correlations in high-energy nuclear collisions to the many-body structure of the colliding nuclei. The key claim is that the azimuthal Fourier coefficients of the energy-energy correlator (EEC), a detector observable built from the conserved stress-energy tensor, are proportional in leading order to the expectation value of the bare nuclear multipole operator in the ground state. This provides a theory-controlled alternative to the traditional hadron-weighted flow harmonics, enabling a direct operator-level matching between the incoming nuclear state and the asymptotic energy flux. The result opens the possibility of using collider data as a probe of nuclear ground-state correlations within a systematically improvable expansion.

What carries the argument

The central mechanism is the energy-energy correlator (EEC) G_2 = ⟨δE_ev(n_1)δE_ev(n_2)⟩_ev, whose azimuthal projection yields ⟨$f_n^{2}$⟩_ev. The argument uses a functional Taylor expansion of the stress-tensor evolution around the ensemble average, rotational covariance to fix the angular dependence of the linear response kernel as $h_n^{{(1)}}$(r,φ) = $e^{{inφ}}$ ρ_n(r), and a Teaney–Yan inspired truncation to the lowest radial mode ρ_n(r) ≈ g_{n0} r^n. On the initial side, the color-glass-condensate mapping e_ev ∝ t_ev^+ t_ev^- and the nucleon thickness operator ˆt(x) = ∑_i δ(x − ˆx_i) translate initial energy-density covariances into nuclear multipole correlators, culminating in Equation (22).

Extended reading notes

Core claim

The paper shows that for high-energy nuclear collisions, the mean squared azimuthal harmonic of the event-by-event EEC, ⟨$f_n^{2}$⟩_ev, reduces at leading order to the nuclear multipole correlator ⟨ˆQ_n ˆQ_n^†⟩_Ψ, where ˆQ_n = ∑_i r_i^n $e^{{inφ_i}}$ is the maximally projected multipole operator of the nucleon positions. This is achieved by expressing the asymptotic energy flow as a functional of the early-time stress tensor, expanding in fluctuations and retaining the lowest radial mode of the linear response kernel, and mapping the initial energy density correlations to nucleon density correlations via the color-glass-condensate scaling. The claim is that the EEC provides a systematic formalism for matching long-wavelength correlations between incoming and outgoing QCD states, with the endpoints expressed in the common language of the conserved stress-energy tensor.

Load-bearing premise

The linear response kernel $h_n^{{(1)}}$(r,φ) is truncated to its leading radial mode r^n, and the sub‑leading modes $r^{{n+2}}$, $r^{{n+4}}$, … together with their cross‑covariances are assumed negligible—an approximation motivated but not quantitatively validated for realistic nuclear collisions.

Editorial extensions

If this is right

Experimental measurement of ⟨f_n^2⟩_ev in heavy-ion collisions can directly constrain the ground-state multipole moments of nuclei, providing a new collider-based probe of nuclear shape and correlations.
The formalism replaces hadron-weighted flow harmonics with a conserved-stress-tensor observable, removing dependence on hadronization details and offering a cleaner theoretical link to the initial state.
The matching is systematically improvable: higher radial modes (r^{n+2}, r^{n+4}, …) and nonlinear response contributions appear as a well-defined tower of corrections in the expansion.
Extensions to higher-point energy correlators (e.g., ⟨f_n^2 δF_0⟩_ev) probe three-point nuclear correlations and non-Gaussian features of the ground state.
The framework can be adapted to other conserved currents (baryon number, electric charge) to access complementary aspects of nuclear fluctuations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The leading-order proportionality ⟨f_n^2⟩_ev ∝ ⟨ˆQ_n ˆQ_n^†⟩_Ψ suggests that for axially symmetric or weakly deformed nuclei, the EEC harmonics will be dominated by the two-body part of the multipole correlator, offering a targeted test of nuclear structure models.
Because the EEC uses energy flow rather than hadron number, its geometric (flow) contribution may be less contaminated by non-flow correlations than traditional v_n{2}, though the present work does not quantify this advantage.
A quantitative check of the radial truncation can be performed by computing the next radial mode correction g_{n1} ⟨ϵ_{n+2,n} ϵ_{n,n}^*⟩ in a realistic hydrodynamic simulation and comparing its magnitude to the leading term for collision systems such as ²³⁸U+²³⁸U or ¹²⁹Xe+¹²⁹Xe.

Original abstract

Relativistic nuclear collisions have opened an experimental arena for studying many-body correlations in nuclear ground states. However, the connection between initial-state correlations and final-state multi-particle observables measured at colliders is not yet formulated as a systematically improvable matching problem. We show that detector correlators built from asymptotic energy flows provide a natural framework for realizing such a construction. In particular, we express the asymptotic energy flow as a functional of the early-time stress tensor, and expand it in suitable modes to recover the familiar linear hydrodynamic relations at leading order. Then, motivated by small-$x$ QCD, we map angular projections of detector correlators to multipole-operator correlators computed in the colliding nuclei. We thus establish a systematic formalism for matching long-wavelength correlations between incoming and outgoing QCD states in high-energy hadronic collisions.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,946 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Relativistic nuclear collisions have opened an experimental arena for studying many-body correlations in nuclear ground states. However, the connection between initial-state correlations and final-state multi-particle observables measured at colliders is not yet formulated as a systematically improvable matching problem. We show that detector correlators built from asymptotic energy flows provide a natural framework for realizing such a construction. In particular, we express the asymptotic energy flow as a functional of the early-time stress tensor, and expand it in suitable modes to recover the familiar linear hydrodynamic relations at leading order. Then, motivated by small-$x$ QCD, we map angular projections of detector correlators to multipole-operator correlators computed in the colliding nuclei. We thus establish a systematic formalism for matching long-wavelength correlations between incoming and outgoing QCD states in high-energy hadronic collisions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Relativistic nuclear collisions have opened an experimental arena for studying many-body correlations in nuclear ground states.	background 1.00	0.06	0.03	asserted 1.00
s1	However, the connection between initial-state correlations and final-state multi-particle observables measured at colliders is not yet formulated as a systematically improvable matching problem.	gap 1.00	0.05	0.03	asserted 0.98
s2	We show that detector correlators built from asymptotic energy flows provide a natural framework for realizing such a construction.	contribution 0.97	0.91	0.47	asserted 1.00
s3	In particular, we express the asymptotic energy flow as a functional of the early-time stress tensor, and expand it in suitable modes to recover the familiar linear hydrodynamic relations at leading order.	method 0.89	0.92	0.08	asserted 1.00
s4	Then, motivated by small-$x$ QCD, we map angular projections of detector correlators to multipole-operator correlators computed in the colliding nuclei.	method 0.73	0.88	0.11	asserted 0.96
s5	We thus establish a systematic formalism for matching long-wavelength correlations between incoming and outgoing QCD states in high-energy hadronic collisions.	contribution 0.74	0.93	0.88	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.57 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Caption FIG. 1. Summary of the end-to-end chain developed in this work. The incoming nuclear stress tensors define transverse thickness

Figures reproduced from arXiv:2609.18754 by the authors.

References

Works cited (118)

[1]

J. Jia et al.,“Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart”, Nucl. Sci. Tech.35, 220 (2024), arXiv:2209.11042

View on Pith Pith review arXiv 2024
[2]

PHOBOS Collaboration, S. Manly et al.,“System size, energy and pseudorapidity dependence of directed and elliptic flow at RHIC”, Nucl. Phys. A774, 523 (2006),nucl-ex/0510031

View on Pith Pith review arXiv 2006
[3]

PHOBOS Collaboration, B. Alver et al.,“System size, energy, pseudorapidity, and centrality dependence of elliptic flow”, Phys. Rev. Lett.98, 242302 (2007), nucl-ex/0610037

View on Pith Pith review arXiv 2007
[4]

M. Miller & R. Snellings,“Eccentricity fluctuations and its possible effect on elliptic flow measurements”, nucl-ex/0312008

View on Pith Pith review arXiv
[5]

R. S. Bhalerao & J.-Y. Ollitrault,“Eccentricity fluc- tuations and elliptic flow at RHIC”, Phys. Lett. B 641, 260 (2006),nucl-th/0607009

View on Pith Pith review arXiv 2006
[6]

PHOBOS Collaboration, B. Alver et al.,“Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions”, Phys. Rev. C77, 014906 (2008),arXiv:0711.3724

View on Pith Pith review arXiv 2008
[7]

B. Alver & G. Roland,“Collision geometry fluctu- ations and triangular flow in heavy-ion collisions”, Phys. Rev. C81, 054905 (2010),arXiv:1003.0194, [Erratum: Phys.Rev.C 82, 039903 (2010)]

View on Pith Pith review arXiv 2010
[8]

motivates retaining this lowest mode, such that sub- stituting h(1) n (r,φ )≃g n0rneinφ, wheregn0 is a response coefficient, into Eq. (15) gives (forn≥2) ⟨ f2 n ⟩ ev≃|g n0|2⟨ |ϵn,n|2⟩ ev,(18) up to higher-radial modes and nonlinear corrections. Some remarks are in order. At linear order, Eq.(18) has the same structure as the mode-by-mode construction of F...

View on Pith
[9]

D. Teaney & L. Yan,“Triangularity and Dipole Asym- metry in Heavy Ion Collisions”, Phys. Rev. C83, 064904 (2011),arXiv:1010.1876

View on Pith Pith review arXiv 2011
[10]

U. Heinz & R. Snellings,“Collective flow and viscosity in relativistic heavy-ion collisions”, Ann. Rev. Nucl. Part. Sci.63, 123 (2013), arXiv:1301.2826

View on Pith Pith review arXiv 2013
[11]

J.-Y. Ollitrault,“Measures of azimuthal anisotropy in high-energy collisions”, Eur. Phys. J. A59, 236 (2023),arXiv:2308.11674

View on Pith Pith review arXiv 2023
[12]

STAR Collaboration, L. Adamczyk et al.,“Az- imuthal anisotropy in U+U and Au+Au collisions at RHIC”, Phys. Rev. Lett.115, 222301 (2015), arXiv:1505.07812

View on Pith Pith review arXiv 2015
[13]

STAR Collaboration, M. I. Abdulhamid et al.,“Imag- ing shapes of atomic nuclei in high-energy nuclear col- lisions”, Nature635, 67 (2024),arXiv:2401.06625

View on Pith Pith review arXiv 2024
[14]

STAR Collaboration,“Imaging nuclear shape through anisotropic and radial flow in high-energy heavy-ion collisions”, Rept. Prog. Phys.88, 108601 (2025), arXiv:2506.17785

View on Pith arXiv 2025
[15]

ALICE Collaboration, S. Acharya et al.,“Anisotropic flow in Xe-Xe collisions at √sNN =5.44 TeV”, Phys. Lett. B784, 82 (2018),arXiv:1805.01832

View on Pith Pith review arXiv 2018
[16]

CMS Collaboration, A. M. Sirunyan et al.,“Charged- particle angular correlations in XeXe collisions at√sNN =5.44 TeV”, Phys. Rev. C100, 044902 (2019), arXiv:1901.07997

View on Pith Pith review arXiv 2019
[17]

ATLAS Collaboration, G. Aad et al.,“Measurement of the azimuthal anisotropy of charged-particle pro- duction inXe +Xe collisions at√sNN = 5.44TeV with the ATLAS detector”, Phys. Rev. C101, 024906 (2020),arXiv:1911.04812

View on Pith Pith review arXiv 2020
[18]

ATLAS Collaboration, G. Aad et al.,“Correlations between flow and transverse momentum in Xe+Xe and Pb+Pb collisions at the LHC with the ATLAS detector: A probe of the heavy-ion initial state and nu- clear deformation”, Phys. Rev. C107, 054910 (2023), arXiv:2205.00039

View on Pith Pith review arXiv 2023
[19]

ALICE Collaboration,“Exploring nuclear struc- ture with multiparticle azimuthal correlations at the LHC”, Phys. Lett. B869, 139855 (2025), arXiv:2409.04343

View on Pith arXiv 2025
[20]

CMS Collaboration, A. Hayrapetyan et al.,“Char- acterizing the initial state and dynamical evolu- tion in XeXe and PbPb collisions using multiparti- cle cumulants”, Phys. Lett. B876, 140359 (2026), arXiv:2510.26766

View on Pith Pith review arXiv 2026
[21]

STAR Collaboration, M. Abdallah et al.,“Search for the chiral magnetic effect with isobar collisions at√sNN=200 GeV by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider”, Phys. Rev. C 105, 014901 (2022),arXiv:2109.00131

View on Pith arXiv 2022
[22]

ATLAS Collaboration, G. Aad et al.,“Measurement of the azimuthal anisotropy of charged particles in√sNN = 5.36TeV O16+O16 and Ne20+Ne20 colli- sions with the ATLAS detector”, Phys. Rev. C113, 045205 (2026),arXiv:2509.05171

View on Pith Pith review arXiv 2026
[23]

ALICE Collaboration, I. J. Abualrob et al.,“Ev- idence of Nuclear Geometry-Driven Anisotropic Flow in O+O and Ne+Ne Collisions at √sNN = 5.36TeV”, Phys. Rev. Lett.137, 082301 (2026), arXiv:2509.06428

View on Pith Pith review arXiv 2026
[24]

CMS Collaboration, A. Hayrapetyan et al.,“Obser- vation of Long-Range Collective Flow in O+O and Ne+Ne Collisions and Implications for Nuclear Struc- ture Studies”, Phys. Rev. Lett.137, 082302 (2026), arXiv:2510.02580

View on Pith Pith review arXiv 2026
[25]

ATLAS Collaboration, G. Aad et al.,“Measurements of charged-particle pseudorapidity and transverse mo- mentum distributions in O+O and Ne+Ne collisions at √sNN = 5 .36TeV with the ATLAS detector”, arXiv:2606.20257

View on Pith Pith review arXiv
[26]

LHCb Collaboration, R. Aaij et al.,“Unveiling the shape of the20Ne nucleus by measuring the flow coef- ficients with cumulants in PbNe and PbAr collisions at√sNN = 70.9GeV”,arXiv:2509.12399

View on Pith arXiv
[27]

J. Jia,“Shape of atomic nuclei in heavy ion collisions”, Phys. Rev. C105, 014905 (2022), arXiv:2106.08768

View on Pith Pith review arXiv 2022
[28]

J. Jia,“Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions”, Phys. Rev. C 105, 044905 (2022),arXiv:2109.00604. 7

View on Pith Pith review arXiv 2022
[29]

G. Giacalone, J. Noronha-Hostler, M. Luzum & J.-Y. Ollitrault,“Hydrodynamic predictions for 5.44 TeV Xe+Xe collisions”, Phys. Rev. C97, 034904 (2018), arXiv:1711.08499

View on Pith Pith review arXiv 2018
[30]

C. Zhang & J. Jia,“Evidence of Quadrupole and Octupole Deformations in Zr96+Zr96 and Ru96+Ru96 Collisions at Ultrarelativistic Ener- gies”, Phys. Rev. Lett.128, 022301 (2022), arXiv:2109.01631

View on Pith Pith review arXiv 2022
[31]

G. Nijs & W. van der Schee,“Inferring nuclear struc- ture from heavy isobar collisions using Trajectum”, SciPost Phys.15, 041 (2023),arXiv:2112.13771

View on Pith Pith review arXiv 2023
[32]

S. Zhao, H.-j. Xu, Y.-X. Liu & H. Song,“Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs”, Phys. Lett. B839, 137838 (2023),arXiv:2204.02387

View on Pith Pith review arXiv 2023
[33]

W. Ryssens, G. Giacalone, B. Schenke & C. Shen,“Evidence of Hexadecapole Deforma- tion in Uranium-238 at the Relativistic Heavy Ion Collider”, Phys. Rev. Lett.130, 212302 (2023), arXiv:2302.13617

View on Pith Pith review arXiv 2023
[34]

Y. Wang, S. Zhao, B. Cao, H.-j. Xu & H. Song,“Ex- ploring the compactness ofα clusters in O16 nuclei with relativistic O16+O16 collisions”, Phys. Rev. C 109, L051904 (2024),arXiv:2401.15723

View on Pith Pith review arXiv 2024
[35]

X.-L. Zhao, Z.-W. Lin, Y. Zhou, C. Zhang & G.-L. Ma,“Nuclear cluster structure effect in 16O+16O collisions at the top RHIC energy”, Phys. Lett. B874, 140254 (2026),arXiv:2404.09780

View on Pith arXiv 2026
[36]

G. Giacalone et al.,“Exploiting Ne20 Isotopes for Precision Characterizations of Collectivity in Small Systems”, Phys. Rev. Lett.135, 012302 (2025), arXiv:2402.05995

View on Pith Pith review arXiv 2025
[37]

G. Giacalone et al.,“Anisotropic Flow in Fixed- Target Pb208+Ne20 Collisions as a Probe of Quark- Gluon Plasma”, Phys. Rev. Lett.134, 082301 (2025), arXiv:2405.20210

View on Pith Pith review arXiv 2025
[38]

N.M.Fortier, S.Jeon&C.Gale,“Heavy-ion collisions as probes of nuclear structure”, Phys. Rev. C111, L011901 (2025),arXiv:2405.17526

View on Pith Pith review arXiv 2025
[39]

H. Mäntysaari, B. Schenke, C. Shen & W. Zhao, “Probing nuclear structure of heavy ions at en- ergies available at the CERN Large Hadron Collider”, Phys. Rev. C110, 054913 (2024), arXiv:2409.19064

View on Pith Pith review arXiv 2024
[40]

L.-M. Liu, H.-C. Wang, S.-J. Li, C. Zhang, J. Xu, Z.-Z. Ren, J. Jia & X.-G. Huang,“Directly probing existence of α-cluster structure in Ne20 by relativistic heavy- ion collisions”, Phys. Rev. C111, L021901 (2025), arXiv:2502.08057

View on Pith Pith review arXiv 2025
[41]

P. Li, B. Zhou & G.-L. Ma,“Identifyingα-Cluster Configurations in Ne20 via Ultracentral Ne+Ne Collisions”, Phys. Rev. Lett.136, 082302 (2026), arXiv:2504.04688

View on Pith arXiv 2026
[42]

H.-j. Xu, D. Xu, S. Zhao, W. Zhao, H. Song & F. Wang,“Investigation of an octupole breathing mode of Pb208 as a resolution to the elliptical-to-triangular azimuthal anisotropy puzzle in ultracentral relativis- tic heavy ion collisions”, Phys. Rev. C112, L051901 (2025),arXiv:2504.19644

View on Pith Pith review arXiv 2025
[43]

C. Zhang, J. Jia, J. Chen, C. Shen & L. Liu,“Imprints of octupole collectivity in uranium-238 on relativistic heavy-ion flow observables”, Phys. Rev. Res.8, 033018 (2026),arXiv:2504.15245

View on Pith Pith review arXiv 2026
[44]

H. Mehrabpour, Z. Sheibani, L. Yan, C. Zhang & A. Mirjalili,“Nonlinear collective flow reveals the breakdown of quadrupole–hexadecapole scaling in heavy ion collisions”,arXiv:2607.18752

View on Pith Pith review arXiv
[45]

A. Menon Kavumpadikkal Radhakrishnan, S. Prasad, N. Mallick, R. Sahoo & G. G. Barnaföldi, “Constraining α-cluster compactness in 16Oand 20Neat TeV energies using azimuthal anisotropy”, arXiv:2607.26758

View on Pith Pith review arXiv
[46]

G. Giacalone,“Many-body correlations for nuclear physics across scales: from nuclei to quark-gluon plas- mas to hadron distributions”, Eur. Phys. J. A59, 297 (2023),arXiv:2305.19843

View on Pith Pith review arXiv 2023
[47]

T. Duguet, G. Giacalone, S. Jeon & A. Tichai, “Revealing the Harmonic Structure of Nuclear Two- Body Correlations in High-Energy Heavy-Ion Col- lisions”, Phys. Rev. Lett.135, 182301 (2025), arXiv:2504.02481

View on Pith Pith review arXiv 2025
[48]

K. Kumar,“Intrinsic Quadrupole Moments and Shapes of Nuclear Ground States and Excited States”, Phys. Rev. Lett.28, 249 (1972)

View on Pith 1972
[49]

D. Cline,“Nuclear shapes studied by coulomb excita- tion”, Ann. Rev. Nucl. Part. Sci.36, 683 (1986)

View on Pith 1986
[50]

A. Poves, F. Nowacki & Y. Alhassid,“Limits on assigning a shape to a nucleus”, Phys. Rev. C101, 054307 (2020),arXiv:1906.07542

View on Pith Pith review arXiv 2020
[51]

J. Henderson,“Convergence of electric quadrupole rotational invariants from the nuclear shell model”, Phys. Rev. C102, 054306 (2020), arXiv:2005.11210

View on Pith Pith review arXiv 2020
[52]

P. E. Garrett, M. Zielińska & E. Clément,“An experimental view on shape coexistence in nuclei”, Prog. Part. Nucl. Phys.124, 103931 (2022)

View on Pith 2022
[53]

J.-P. Blaizot & G. Giacalone,“Angular struc- ture of many-body correlations in atomic nuclei”, Eur. Phys. J. A61, 220 (2025),arXiv:2504.15421

View on Pith Pith review arXiv 2025
[54]

W. Ke,“From wave-function to fireball geometry: the role of a restored broken symmetry in ultra-relativistic collisions of deformed nuclei”,arXiv:2509.09549

View on Pith Pith review arXiv
[55]

J.-P. Blaizot, G. Giacalone & A. Lovato,“Nuclear collectivity and the harmonic spectrum of two-body correlations”,arXiv:2512.18926

View on Pith arXiv
[56]

S. Bofos, B. Bally, T. Duguet & M. Frosini,“Imaging two-body correlations in atomic nuclei via low- and high-energy processes”, Phys. Lett. B879, 140649 (2026),arXiv:2602.09890

View on Pith Pith review arXiv 2026
[57]

H. Mehrabpour, G. Giacalone & M. W. Luzum,“Tri- axial shapes and the angular structure of nuclear three- body correlations”,arXiv:2604.00619

View on Pith arXiv
[58]

S. Bofos, Y. Li, C. Ding, B. Bally, T. Duguet, M. Frosini & J. Yao,“Quantum effects in the quadrupole rotor picture of ultra-relativistic ion-ion 8 collisions”,arXiv:2605.28813

View on Pith Pith review arXiv
[59]

H.-j. Xu & Q. Wang,“Quantum Symmetry Restora- tion and Emergent Effective Deformation in Relativis- tic Heavy-Ion Collisions”,arXiv:2606.02412

View on Pith Pith review arXiv
[60]

G. Giacalone, G. Nijs & W. van der Schee,“Yoctosec- ond imaging of the ground state of129Xe at the Large Hadron Collider”,arXiv:2606.03993

View on Pith Pith review arXiv
[61]

C. Ding, B. Bally, S. Bofos, T. Duguet, Y. Li & J. Yao, “Ab initio anatomy of quadrupole correlations in16O and 20Ne”,arXiv:2608.22699

View on Pith Pith review arXiv
[62]

D. Teaney & L. Yan,“Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics”, Phys. Rev. C86, 044908 (2012), arXiv:1206.1905

View on Pith Pith review arXiv 2012
[63]

J. Sousa, J. Noronha & M. Luzum,“Initial energy- momentum to final flow: A general framework for heavy-ion collisions”, Phys. Rev. C110, 044909 (2024),arXiv:2405.13600

View on Pith Pith review arXiv 2024
[64]

D. M. Hofman & J. Maldacena,“Conformal collider physics: Energy and charge correlations”, JHEP0805, 012 (2008),arXiv:0803.1467

View on Pith Pith review arXiv 2008
[65]

C. Basham, L. Brown, S. Ellis & S. Love,“Energy Cor- relations in electron-Positron Annihilation in Quan- tum Chromodynamics: Asymptotically Free Perturba- tion Theory”, Phys. Rev. D19, 2018 (1979)

View on Pith 1979
[66]

N. Sveshnikov & F. Tkachov,“Jets and quan- tum field theory”, Phys. Lett. B382, 403 (1996), hep-ph/9512370

View on Pith Pith review arXiv 1996
[67]

G. P. Korchemsky & G. F. Sterman,“Power correc- tions to event shapes and factorization”, Nucl. Phys. B 555, 335 (1999),hep-ph/9902341

View on Pith Pith review arXiv 1999
[68]

I.Moult&H.X.Zhu,“Energy Correlators: A Journey From Theory to Experiment”,arXiv:2506.09119

View on Pith Pith review arXiv
[69]

A. Krasnitz & R. Venugopalan,“Nonperturbative com- putation of gluon minijet production in nuclear colli- sions at very high-energies”, Nucl. Phys. B557, 237 (1999),hep-ph/9809433

View on Pith Pith review arXiv 1999
[70]

J. Barata, M. V. Kuzmin, J. G. Milhano & A. V. Sadofyev,“Giving wake to energy-energy correlators: Hydrodynamic response on the celes- tial sphere”, Phys. Rev. D112, 016005 (2025), arXiv:2412.03616

View on Pith Pith review arXiv 2025
[71]

J. Barata, I. Moult, A. V. Sadofyev & J. M. Silva,“Dissecting Jet Modification in the Quark- Gluon Plasma with Multipoint Energy Correla- tors”, Phys. Rev. Lett.137, 052302 (2026), arXiv:2503.13603

View on Pith Pith review arXiv 2026
[72]

H. Bossi, A. S. Kudinoor, I. Moult, D. Pablos, A. Rai & K. Rajagopal,“Imaging the wakes of jets with energy-energy-energy correlators”, JHEP2412, 073 (2024),arXiv:2407.13818

View on Pith Pith review arXiv 2024
[73]

J. Barata, M. V. Kuzmin, I. Moult, A. V. Sadofyev & J. M. Silva,“Hydrodynamics and Energy Correlators”, arXiv:2604.21971

View on Pith Pith review arXiv
[74]

Z. Yang, Y. He, I. Moult & X.-N. Wang,“Prob- ing the Short-Distance Structure of the Quark-Gluon Plasma with Energy Correlators”, Phys. Rev. Lett. 132, 011901 (2024),arXiv:2310.01500

View on Pith Pith review arXiv 2024
[75]

W. Zhao, V. Koch & F. Yuan,“Particle Correlations in Jets”,arXiv:2507.18790

View on Pith Pith review arXiv
[76]

P. Duan, W. Ke, G.-Y. Qin & L. Wang,“Uncover the correlation between jet energy correlators and multi- plicity fluctuations”,arXiv:2604.01102

View on Pith arXiv
[77]

J. Barata, Y. Peng, A. V. Sadofyev & H. Song,“QCD Matter through the Lens of Energy Correlators, to appear”

View on Pith
[78]

G. Cuomo, E. Firat, F. Nardi & L. Ricci,“Conformal collider physics at large charge”, JHEP2602, 223 (2026),arXiv:2503.21867

View on Pith Pith review arXiv 2026
[79]

D. Chicherin, G. P. Korchemsky, E. Sokatchev & A. Zhiboedov,“Energy correlations in heavy states”, JHEP2311, 134 (2023),arXiv:2306.14330

View on Pith Pith review arXiv 2023
[80]

M. Luzum,“Flow fluctuations and long-range cor- relations: elliptic flow and beyond”, J. Phys. G38, 124026 (2011),arXiv:1107.0592

View on Pith Pith review arXiv 2011
[81]

Y. Feng & F. Wang,“Review of nonflow estima- tion methods and uncertainties in relativistic heavy- ion collisions”, J. Phys. G52, 013001 (2025), arXiv:2407.12731

View on Pith Pith review arXiv 2025
[82]

L. V. Delacrétaz, T. Hartman, S. A. Hartnoll & A. Lewkowycz,“Thermalization, Viscosity and the Averaged Null Energy Condition”, JHEP1810, 028 (2018),arXiv:1805.04194

View on Pith Pith review arXiv 2018
[83]

J. Barata, J. G. Milhano & A. V. Sadofyev,“Picturing QCD jets in anisotropic matter: from jet shapes to energy energy correlators”, Eur. Phys. J. C84, 174 (2024),arXiv:2308.01294

View on Pith Pith review arXiv 2024
[84]

J. Barata, J. G. Milhano, A. V. Sadofyev & J. M. Silva,“Early-Time Dynamics of Heavy-Ion Collisions through Energy Correlators: celestial blocks and the spacetime structure of out-of-equilibrium QCD mat- ter”,arXiv:2512.17009

View on Pith arXiv
[85]

J. Barata, J. Brewer, K. Lee & J. M. Silva,“Heavy Quark Pair Energy Correlators: From Profiling Par- tonic Splittings to Probing Heavy-Flavor Fragmenta- tion”,arXiv:2508.19404

View on Pith Pith review arXiv
[86]

J.-P. Blaizot, W. Broniowski & J.-Y. Ollitrault, “Continuous description of fluctuating eccentricities”, Phys. Lett. B738, 166 (2014),arXiv:1405.3572

View on Pith Pith review arXiv 2014
[87]

S. Floerchinger & U. A. Wiedemann,“Mode-by-mode fluid dynamics for relativistic heavy ion collisions”, Phys. Lett. B728, 407 (2014),arXiv:1307.3453

View on Pith Pith review arXiv 2014
[88]

A. Kurkela, A. Mazeliauskas, J.-F. Paquet, S. Schlicht- ing & D. Teaney,“Effective kinetic description of event-by-event pre-equilibrium dynamics in high- energy heavy-ion collisions”, Phys. Rev. C99, 034910 (2019),arXiv:1805.00961

View on Pith Pith review arXiv 2019
[89]

A. Kirchner, F. Capellino, E. Grossi & S. Floerchinger, “Toward a fluid-dynamic description of an entire heavy- ion collision: From the colliding nuclei to the quark- gluon plasma phase”, Phys.Rev.C112, 024903(2025), arXiv:2410.08169

View on Pith Pith review arXiv 2025
[90]

H. Mehrabpour,“Imprint of α clustering on ab initio correlations in relativistic light ion col- lisions”, Phys. Rev. C113, 034909 (2026), arXiv:2506.12673. 9

View on Pith arXiv 2026
[91]

L. D. McLerran & R. Venugopalan,“Computing quark and gluon distribution functions for very large nuclei”, Phys. Rev. D49, 2233 (1994),hep-ph/9309289

View on Pith Pith review arXiv 1994
[92]

L. D. McLerran & R. Venugopalan,“Gluon distri- bution functions for very large nuclei at small trans- verse momentum”, Phys. Rev. D49, 3352 (1994), hep-ph/9311205

View on Pith Pith review arXiv 1994
[93]

L. D. McLerran & R. Venugopalan,“Green’s functions in the color field of a large nucleus”, Phys. Rev. D50, 2225 (1994),hep-ph/9402335

View on Pith Pith review arXiv 1994
[94]

B. Schenke, C. Shen & P. Tribedy,“Running the gamut of high energy nuclear collisions”, Phys. Rev. C 102, 044905 (2020),arXiv:2005.14682

View on Pith Pith review arXiv 2020
[95]

H. Mäntysaari & P. Singh,“Energy dependence of the deformed nuclear structure at small-x”, Eur. Phys. J. C85, 1449 (2025),arXiv:2411.14934

View on Pith Pith review arXiv 2025
[96]

H. Mäntysaari, B. Schenke, C. Shen & W. Zhao, “Collision-Energy Dependence in Heavy-Ion Collisions from Nonlinear QCD Evolution”, Phys. Rev. Lett. 135, 022302 (2025),arXiv:2502.05138

View on Pith Pith review arXiv 2025
[97]

A. Krasnitz & R. Venugopalan,“The Initial energy density of gluons produced in very high-energy nu- clear collisions”, Phys. Rev. Lett.84, 4309 (2000), hep-ph/9909203

View on Pith Pith review arXiv 2000
[98]

T. Lappi,“Energy density of the glasma”, Phys. Lett. B643, 11 (2006),hep-ph/0606207

View on Pith Pith review arXiv 2006
[99]

J. L. Albacete, P. Guerrero-Rodríguez & C. Marquet, “Initial correlations of the Glasma energy-momentum tensor”, JHEP1901, 073 (2019), arXiv:1808.00795

View on Pith Pith review arXiv 2019
[100]

F. Zhou, G. Giacalone & J.-Y. Ollitrault,“Size of the quark-gluon plasma in ultracentral collisions: Impact of initial density fluctuations on the average trans- verse momentum”, Phys. Rev. C113, 044910 (2026), arXiv:2511.04605

View on Pith Pith review arXiv 2026
[101]

A. Budhraja & B. Singh,“Exploitingν-dependence of projected energy correlators in HICs”, Phys. Lett. B 872, 140079 (2026),arXiv:2503.20019

View on Pith arXiv 2026
[102]

P. Bozek,“Transverse-momentum–flow correlations in relativistic heavy-ion collisions”, Phys. Rev. C93, 044908 (2016),arXiv:1601.04513

View on Pith Pith review arXiv 2016
[103]

G. Giacalone,“Observing the deformation of nuclei with relativistic nuclear collisions”, Phys. Rev. Lett. 124, 202301 (2020),arXiv:1910.04673

View on Pith Pith review arXiv 2020
[104]

B. Schenke, C. Shen & D. Teaney,“Transverse mo- mentum fluctuations and their correlation with elliptic flow in nuclear collision”, Phys. Rev. C102, 034905 (2020),arXiv:2004.00690

View on Pith Pith review arXiv 2020
[105]

G. Giacalone, F. G. Gardim, J. Noronha-Hostler & J.-Y. Ollitrault,“Correlation between mean trans- verse momentum and anisotropic flow in heavy- ion collisions”, Phys. Rev. C103, 024909 (2021), arXiv:2004.01765

View on Pith Pith review arXiv 2021
[106]

G. Giacalone,“Constraining the quadrupole de- formation of atomic nuclei with relativistic nu- clear collisions”, Phys. Rev. C102, 024901 (2020), arXiv:2004.14463

View on Pith Pith review arXiv 2020
[107]

J. Jia, S. Huang & C. Zhang,“Probing nuclear quadrupole deformation from correlation of ellip- tic flow and transverse momentum in heavy ion collisions”, Phys. Rev. C105, 014906 (2022), arXiv:2105.05713

View on Pith Pith review arXiv 2022
[108]

B. Bally, M. Bender, G. Giacalone & V. Somà, “Evidence of the triaxial structure of 129Xe at the Large Hadron Collider”, Phys. Rev. Lett.128, 082301 (2022),arXiv:2108.09578

View on Pith Pith review arXiv 2022
[109]

S. Zhao, H.-j. Xu, Y. Zhou, Y.-X. Liu & H. Song,“Exploring the Nuclear Shape Phase Tran- sition in Ultra-Relativistic 129Xe+129Xe Collisions at the LHC”, Phys. Rev. Lett.133, 192301 (2024), arXiv:2403.07441

View on Pith Pith review arXiv 2024
[110]

K. Hagino & M. Kitazawa,“Probing surface vi- brations of spherical nuclei in relativistic heavy- ion collisions”, Phys. Rev. C112, L041901 (2025), arXiv:2508.05125

View on Pith Pith review arXiv 2025
[111]

H. Chen, I. Moult, J. Thaler & H. X. Zhu, “Non-Gaussianities in Collider Energy Flux”, arXiv:2205.02857

View on Pith Pith review arXiv
[112]

P. Carzon, M. Martinez, M. D. Sievert, D. E. Wertepny & J. Noronha-Hostler,“Monte Carlo event generator for initial conditions of conserved charges in nuclear geometry”, Phys. Rev. C105, 034908 (2022), arXiv:1911.12454

View on Pith Pith review arXiv 2022
[113]

J. Sousa, M. D. Sievert, J. Noronha-Hostler, P. Car- zon & M. Luzum,“Initial-state charge density predicts final-state net charge flow in heavy-ion collisions”, Phys. Lett. B880, 140806 (2026), arXiv:2505.16038. 10 SUPPLEMENTAL MATERIAL

View on Pith Pith review arXiv 2026
[114]

Energy-flow harmonics away from midrapidity In this appendix we generalize Eq.(7) to arbitrary pseu- dorapidities and to finite pseudorapidity windows. The powers of coshη depend on the measure and on whether the observable is weighted by energy or by transverse en- ergy. We therefore keep these choices explicit through- out. Unless stated otherwise,η den...

View on Pith
[115]

In particular, the solid angle integration measure is dΩ =|sinθdθ|dϕ= dηdϕ cosh2η.(25) The energy-flow operator event-wise expectation value can be written asEev(η,ϕ )≡ dE dΩ ⏐⏐ ev. On the other hand, we define the transverse-energy density per unit pseudorapidity and azimuth as Fev(η,ϕ)≡ dET dηdϕ ⏐⏐⏐⏐ ev , E T =Esinθ= E coshη .(26) Using Eq. (25) and dE/...

View on Pith
[116]

Response functional and long-wavelength expansion In this Appendix we give a more explicit formulation of the response mapH introduced in the main text, and we clarify the two approximations on which the main analysis rests: an expansion in the amplitude of the event-by-event fluctuations around a smooth background, and, within the linear term of that exp...

View on Pith
[117]

Rotational covariance of the response kernels Here we derive the constraint that rotational symmetry places on the kernels mapping initial perturbations to the asymptotic energy-flow harmonics, and in particular the angular form quoted in Eq. (17). The only inputs are an azimuthally symmetric mean initial configuration and the rotational covariance of the...

View on Pith
[118]

Thickness weighting and nuclear multipole Here we reduce the covariance of the deposited energy density to the nuclear multipole correlator of the main text. We consider a central collision of two statistically independent identical nuclei, with thickness functions tX ev(x) = ¯t(r) +δtX ev(x), X= +,−,(72) where r =|x|, the common mean profile is azimuthal...

View on Pith

Forward citations

Cited by 2 Pith papers

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

Elliptic and triangular flow responses in O+O and Ne+Ne collisions from hydrodynamics and kinetic theory
nucl-th 2026-11 conditional novelty 6.0 of 10

Ne+Ne-to-O+O elliptic flow ratios agree between hydrodynamics and kinetic theory at the Bayesian-compatible viscosity, while triangular-flow ratios differ and, in peripheral collisions, kinetic theory matches the meas...
Linking chiral nuclear forces to light-ion collisions: a global sensitivity analysis
nucl-th 2026-11 conditional novelty 5.0 of 10

Quadrupole flow correlations in 16O and 20Ne respond additively to all 16 NNLO chiral-EFT constants, with 20Ne dominated by the 3P2 spin-orbit contact and 16O by 3S1 contacts, in directions orthogonal to the energy an...

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

J. Jia et al.,“Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart”, Nucl. Sci. Tech.35, 220 (2024), arXiv:2209.11042

View on Pith Pith review arXiv 2024

[2] [2]

PHOBOS Collaboration, S. Manly et al.,“System size, energy and pseudorapidity dependence of directed and elliptic flow at RHIC”, Nucl. Phys. A774, 523 (2006),nucl-ex/0510031

View on Pith Pith review arXiv 2006

[3] [3]

PHOBOS Collaboration, B. Alver et al.,“System size, energy, pseudorapidity, and centrality dependence of elliptic flow”, Phys. Rev. Lett.98, 242302 (2007), nucl-ex/0610037

View on Pith Pith review arXiv 2007

[4] [4]

M. Miller & R. Snellings,“Eccentricity fluctuations and its possible effect on elliptic flow measurements”, nucl-ex/0312008

View on Pith Pith review arXiv

[5] [5]

R. S. Bhalerao & J.-Y. Ollitrault,“Eccentricity fluc- tuations and elliptic flow at RHIC”, Phys. Lett. B 641, 260 (2006),nucl-th/0607009

View on Pith Pith review arXiv 2006

[6] [6]

PHOBOS Collaboration, B. Alver et al.,“Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions”, Phys. Rev. C77, 014906 (2008),arXiv:0711.3724

View on Pith Pith review arXiv 2008

[7] [7]

B. Alver & G. Roland,“Collision geometry fluctu- ations and triangular flow in heavy-ion collisions”, Phys. Rev. C81, 054905 (2010),arXiv:1003.0194, [Erratum: Phys.Rev.C 82, 039903 (2010)]

View on Pith Pith review arXiv 2010

[8] [8]

motivates retaining this lowest mode, such that sub- stituting h(1) n (r,φ )≃g n0rneinφ, wheregn0 is a response coefficient, into Eq. (15) gives (forn≥2) ⟨ f2 n ⟩ ev≃|g n0|2⟨ |ϵn,n|2⟩ ev,(18) up to higher-radial modes and nonlinear corrections. Some remarks are in order. At linear order, Eq.(18) has the same structure as the mode-by-mode construction of F...

View on Pith

[9] [9]

D. Teaney & L. Yan,“Triangularity and Dipole Asym- metry in Heavy Ion Collisions”, Phys. Rev. C83, 064904 (2011),arXiv:1010.1876

View on Pith Pith review arXiv 2011

[10] [10]

U. Heinz & R. Snellings,“Collective flow and viscosity in relativistic heavy-ion collisions”, Ann. Rev. Nucl. Part. Sci.63, 123 (2013), arXiv:1301.2826

View on Pith Pith review arXiv 2013

[11] [11]

J.-Y. Ollitrault,“Measures of azimuthal anisotropy in high-energy collisions”, Eur. Phys. J. A59, 236 (2023),arXiv:2308.11674

View on Pith Pith review arXiv 2023

[12] [12]

STAR Collaboration, L. Adamczyk et al.,“Az- imuthal anisotropy in U+U and Au+Au collisions at RHIC”, Phys. Rev. Lett.115, 222301 (2015), arXiv:1505.07812

View on Pith Pith review arXiv 2015

[13] [13]

STAR Collaboration, M. I. Abdulhamid et al.,“Imag- ing shapes of atomic nuclei in high-energy nuclear col- lisions”, Nature635, 67 (2024),arXiv:2401.06625

View on Pith Pith review arXiv 2024

[14] [14]

STAR Collaboration,“Imaging nuclear shape through anisotropic and radial flow in high-energy heavy-ion collisions”, Rept. Prog. Phys.88, 108601 (2025), arXiv:2506.17785

View on Pith arXiv 2025

[15] [15]

ALICE Collaboration, S. Acharya et al.,“Anisotropic flow in Xe-Xe collisions at √sNN =5.44 TeV”, Phys. Lett. B784, 82 (2018),arXiv:1805.01832

View on Pith Pith review arXiv 2018

[16] [16]

CMS Collaboration, A. M. Sirunyan et al.,“Charged- particle angular correlations in XeXe collisions at√sNN =5.44 TeV”, Phys. Rev. C100, 044902 (2019), arXiv:1901.07997

View on Pith Pith review arXiv 2019

[17] [17]

ATLAS Collaboration, G. Aad et al.,“Measurement of the azimuthal anisotropy of charged-particle pro- duction inXe +Xe collisions at√sNN = 5.44TeV with the ATLAS detector”, Phys. Rev. C101, 024906 (2020),arXiv:1911.04812

View on Pith Pith review arXiv 2020

[18] [18]

ATLAS Collaboration, G. Aad et al.,“Correlations between flow and transverse momentum in Xe+Xe and Pb+Pb collisions at the LHC with the ATLAS detector: A probe of the heavy-ion initial state and nu- clear deformation”, Phys. Rev. C107, 054910 (2023), arXiv:2205.00039

View on Pith Pith review arXiv 2023

[19] [19]

ALICE Collaboration,“Exploring nuclear struc- ture with multiparticle azimuthal correlations at the LHC”, Phys. Lett. B869, 139855 (2025), arXiv:2409.04343

View on Pith arXiv 2025

[20] [20]

CMS Collaboration, A. Hayrapetyan et al.,“Char- acterizing the initial state and dynamical evolu- tion in XeXe and PbPb collisions using multiparti- cle cumulants”, Phys. Lett. B876, 140359 (2026), arXiv:2510.26766

View on Pith Pith review arXiv 2026

[21] [21]

STAR Collaboration, M. Abdallah et al.,“Search for the chiral magnetic effect with isobar collisions at√sNN=200 GeV by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider”, Phys. Rev. C 105, 014901 (2022),arXiv:2109.00131

View on Pith arXiv 2022

[22] [22]

ATLAS Collaboration, G. Aad et al.,“Measurement of the azimuthal anisotropy of charged particles in√sNN = 5.36TeV O16+O16 and Ne20+Ne20 colli- sions with the ATLAS detector”, Phys. Rev. C113, 045205 (2026),arXiv:2509.05171

View on Pith Pith review arXiv 2026

[23] [23]

ALICE Collaboration, I. J. Abualrob et al.,“Ev- idence of Nuclear Geometry-Driven Anisotropic Flow in O+O and Ne+Ne Collisions at √sNN = 5.36TeV”, Phys. Rev. Lett.137, 082301 (2026), arXiv:2509.06428

View on Pith Pith review arXiv 2026

[24] [24]

CMS Collaboration, A. Hayrapetyan et al.,“Obser- vation of Long-Range Collective Flow in O+O and Ne+Ne Collisions and Implications for Nuclear Struc- ture Studies”, Phys. Rev. Lett.137, 082302 (2026), arXiv:2510.02580

View on Pith Pith review arXiv 2026

[25] [25]

ATLAS Collaboration, G. Aad et al.,“Measurements of charged-particle pseudorapidity and transverse mo- mentum distributions in O+O and Ne+Ne collisions at √sNN = 5 .36TeV with the ATLAS detector”, arXiv:2606.20257

View on Pith Pith review arXiv

[26] [26]

LHCb Collaboration, R. Aaij et al.,“Unveiling the shape of the20Ne nucleus by measuring the flow coef- ficients with cumulants in PbNe and PbAr collisions at√sNN = 70.9GeV”,arXiv:2509.12399

View on Pith arXiv

[27] [27]

J. Jia,“Shape of atomic nuclei in heavy ion collisions”, Phys. Rev. C105, 014905 (2022), arXiv:2106.08768

View on Pith Pith review arXiv 2022

[28] [28]

J. Jia,“Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions”, Phys. Rev. C 105, 044905 (2022),arXiv:2109.00604. 7

View on Pith Pith review arXiv 2022

[29] [29]

G. Giacalone, J. Noronha-Hostler, M. Luzum & J.-Y. Ollitrault,“Hydrodynamic predictions for 5.44 TeV Xe+Xe collisions”, Phys. Rev. C97, 034904 (2018), arXiv:1711.08499

View on Pith Pith review arXiv 2018

[30] [30]

C. Zhang & J. Jia,“Evidence of Quadrupole and Octupole Deformations in Zr96+Zr96 and Ru96+Ru96 Collisions at Ultrarelativistic Ener- gies”, Phys. Rev. Lett.128, 022301 (2022), arXiv:2109.01631

View on Pith Pith review arXiv 2022

[31] [31]

G. Nijs & W. van der Schee,“Inferring nuclear struc- ture from heavy isobar collisions using Trajectum”, SciPost Phys.15, 041 (2023),arXiv:2112.13771

View on Pith Pith review arXiv 2023

[32] [32]

S. Zhao, H.-j. Xu, Y.-X. Liu & H. Song,“Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs”, Phys. Lett. B839, 137838 (2023),arXiv:2204.02387

View on Pith Pith review arXiv 2023

[33] [33]

W. Ryssens, G. Giacalone, B. Schenke & C. Shen,“Evidence of Hexadecapole Deforma- tion in Uranium-238 at the Relativistic Heavy Ion Collider”, Phys. Rev. Lett.130, 212302 (2023), arXiv:2302.13617

View on Pith Pith review arXiv 2023

[34] [34]

Y. Wang, S. Zhao, B. Cao, H.-j. Xu & H. Song,“Ex- ploring the compactness ofα clusters in O16 nuclei with relativistic O16+O16 collisions”, Phys. Rev. C 109, L051904 (2024),arXiv:2401.15723

View on Pith Pith review arXiv 2024

[35] [35]

X.-L. Zhao, Z.-W. Lin, Y. Zhou, C. Zhang & G.-L. Ma,“Nuclear cluster structure effect in 16O+16O collisions at the top RHIC energy”, Phys. Lett. B874, 140254 (2026),arXiv:2404.09780

View on Pith arXiv 2026

[36] [36]

G. Giacalone et al.,“Exploiting Ne20 Isotopes for Precision Characterizations of Collectivity in Small Systems”, Phys. Rev. Lett.135, 012302 (2025), arXiv:2402.05995

View on Pith Pith review arXiv 2025

[37] [37]

G. Giacalone et al.,“Anisotropic Flow in Fixed- Target Pb208+Ne20 Collisions as a Probe of Quark- Gluon Plasma”, Phys. Rev. Lett.134, 082301 (2025), arXiv:2405.20210

View on Pith Pith review arXiv 2025

[38] [38]

N.M.Fortier, S.Jeon&C.Gale,“Heavy-ion collisions as probes of nuclear structure”, Phys. Rev. C111, L011901 (2025),arXiv:2405.17526

View on Pith Pith review arXiv 2025

[39] [39]

H. Mäntysaari, B. Schenke, C. Shen & W. Zhao, “Probing nuclear structure of heavy ions at en- ergies available at the CERN Large Hadron Collider”, Phys. Rev. C110, 054913 (2024), arXiv:2409.19064

View on Pith Pith review arXiv 2024

[40] [40]

L.-M. Liu, H.-C. Wang, S.-J. Li, C. Zhang, J. Xu, Z.-Z. Ren, J. Jia & X.-G. Huang,“Directly probing existence of α-cluster structure in Ne20 by relativistic heavy- ion collisions”, Phys. Rev. C111, L021901 (2025), arXiv:2502.08057

View on Pith Pith review arXiv 2025

[41] [41]

P. Li, B. Zhou & G.-L. Ma,“Identifyingα-Cluster Configurations in Ne20 via Ultracentral Ne+Ne Collisions”, Phys. Rev. Lett.136, 082302 (2026), arXiv:2504.04688

View on Pith arXiv 2026

[42] [42]

H.-j. Xu, D. Xu, S. Zhao, W. Zhao, H. Song & F. Wang,“Investigation of an octupole breathing mode of Pb208 as a resolution to the elliptical-to-triangular azimuthal anisotropy puzzle in ultracentral relativis- tic heavy ion collisions”, Phys. Rev. C112, L051901 (2025),arXiv:2504.19644

View on Pith Pith review arXiv 2025

[43] [43]

C. Zhang, J. Jia, J. Chen, C. Shen & L. Liu,“Imprints of octupole collectivity in uranium-238 on relativistic heavy-ion flow observables”, Phys. Rev. Res.8, 033018 (2026),arXiv:2504.15245

View on Pith Pith review arXiv 2026

[44] [44]

H. Mehrabpour, Z. Sheibani, L. Yan, C. Zhang & A. Mirjalili,“Nonlinear collective flow reveals the breakdown of quadrupole–hexadecapole scaling in heavy ion collisions”,arXiv:2607.18752

View on Pith Pith review arXiv

[45] [45]

A. Menon Kavumpadikkal Radhakrishnan, S. Prasad, N. Mallick, R. Sahoo & G. G. Barnaföldi, “Constraining α-cluster compactness in 16Oand 20Neat TeV energies using azimuthal anisotropy”, arXiv:2607.26758

View on Pith Pith review arXiv

[46] [46]

G. Giacalone,“Many-body correlations for nuclear physics across scales: from nuclei to quark-gluon plas- mas to hadron distributions”, Eur. Phys. J. A59, 297 (2023),arXiv:2305.19843

View on Pith Pith review arXiv 2023

[47] [47]

T. Duguet, G. Giacalone, S. Jeon & A. Tichai, “Revealing the Harmonic Structure of Nuclear Two- Body Correlations in High-Energy Heavy-Ion Col- lisions”, Phys. Rev. Lett.135, 182301 (2025), arXiv:2504.02481

View on Pith Pith review arXiv 2025

[48] [48]

K. Kumar,“Intrinsic Quadrupole Moments and Shapes of Nuclear Ground States and Excited States”, Phys. Rev. Lett.28, 249 (1972)

View on Pith 1972

[49] [49]

D. Cline,“Nuclear shapes studied by coulomb excita- tion”, Ann. Rev. Nucl. Part. Sci.36, 683 (1986)

View on Pith 1986

[50] [50]

A. Poves, F. Nowacki & Y. Alhassid,“Limits on assigning a shape to a nucleus”, Phys. Rev. C101, 054307 (2020),arXiv:1906.07542

View on Pith Pith review arXiv 2020

[51] [51]

J. Henderson,“Convergence of electric quadrupole rotational invariants from the nuclear shell model”, Phys. Rev. C102, 054306 (2020), arXiv:2005.11210

View on Pith Pith review arXiv 2020

[52] [52]

P. E. Garrett, M. Zielińska & E. Clément,“An experimental view on shape coexistence in nuclei”, Prog. Part. Nucl. Phys.124, 103931 (2022)

View on Pith 2022

[53] [53]

J.-P. Blaizot & G. Giacalone,“Angular struc- ture of many-body correlations in atomic nuclei”, Eur. Phys. J. A61, 220 (2025),arXiv:2504.15421

View on Pith Pith review arXiv 2025

[54] [54]

W. Ke,“From wave-function to fireball geometry: the role of a restored broken symmetry in ultra-relativistic collisions of deformed nuclei”,arXiv:2509.09549

View on Pith Pith review arXiv

[55] [55]

J.-P. Blaizot, G. Giacalone & A. Lovato,“Nuclear collectivity and the harmonic spectrum of two-body correlations”,arXiv:2512.18926

View on Pith arXiv

[56] [56]

S. Bofos, B. Bally, T. Duguet & M. Frosini,“Imaging two-body correlations in atomic nuclei via low- and high-energy processes”, Phys. Lett. B879, 140649 (2026),arXiv:2602.09890

View on Pith Pith review arXiv 2026

[57] [57]

H. Mehrabpour, G. Giacalone & M. W. Luzum,“Tri- axial shapes and the angular structure of nuclear three- body correlations”,arXiv:2604.00619

View on Pith arXiv

[58] [58]

S. Bofos, Y. Li, C. Ding, B. Bally, T. Duguet, M. Frosini & J. Yao,“Quantum effects in the quadrupole rotor picture of ultra-relativistic ion-ion 8 collisions”,arXiv:2605.28813

View on Pith Pith review arXiv

[59] [59]

H.-j. Xu & Q. Wang,“Quantum Symmetry Restora- tion and Emergent Effective Deformation in Relativis- tic Heavy-Ion Collisions”,arXiv:2606.02412

View on Pith Pith review arXiv

[60] [60]

G. Giacalone, G. Nijs & W. van der Schee,“Yoctosec- ond imaging of the ground state of129Xe at the Large Hadron Collider”,arXiv:2606.03993

View on Pith Pith review arXiv

[61] [61]

C. Ding, B. Bally, S. Bofos, T. Duguet, Y. Li & J. Yao, “Ab initio anatomy of quadrupole correlations in16O and 20Ne”,arXiv:2608.22699

View on Pith Pith review arXiv

[62] [62]

D. Teaney & L. Yan,“Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics”, Phys. Rev. C86, 044908 (2012), arXiv:1206.1905

View on Pith Pith review arXiv 2012

[63] [63]

J. Sousa, J. Noronha & M. Luzum,“Initial energy- momentum to final flow: A general framework for heavy-ion collisions”, Phys. Rev. C110, 044909 (2024),arXiv:2405.13600

View on Pith Pith review arXiv 2024

[64] [64]

D. M. Hofman & J. Maldacena,“Conformal collider physics: Energy and charge correlations”, JHEP0805, 012 (2008),arXiv:0803.1467

View on Pith Pith review arXiv 2008

[65] [65]

C. Basham, L. Brown, S. Ellis & S. Love,“Energy Cor- relations in electron-Positron Annihilation in Quan- tum Chromodynamics: Asymptotically Free Perturba- tion Theory”, Phys. Rev. D19, 2018 (1979)

View on Pith 1979

[66] [66]

N. Sveshnikov & F. Tkachov,“Jets and quan- tum field theory”, Phys. Lett. B382, 403 (1996), hep-ph/9512370

View on Pith Pith review arXiv 1996

[67] [67]

G. P. Korchemsky & G. F. Sterman,“Power correc- tions to event shapes and factorization”, Nucl. Phys. B 555, 335 (1999),hep-ph/9902341

View on Pith Pith review arXiv 1999

[68] [68]

I.Moult&H.X.Zhu,“Energy Correlators: A Journey From Theory to Experiment”,arXiv:2506.09119

View on Pith Pith review arXiv

[69] [69]

A. Krasnitz & R. Venugopalan,“Nonperturbative com- putation of gluon minijet production in nuclear colli- sions at very high-energies”, Nucl. Phys. B557, 237 (1999),hep-ph/9809433

View on Pith Pith review arXiv 1999

[70] [70]

J. Barata, M. V. Kuzmin, J. G. Milhano & A. V. Sadofyev,“Giving wake to energy-energy correlators: Hydrodynamic response on the celes- tial sphere”, Phys. Rev. D112, 016005 (2025), arXiv:2412.03616

View on Pith Pith review arXiv 2025

[71] [71]

J. Barata, I. Moult, A. V. Sadofyev & J. M. Silva,“Dissecting Jet Modification in the Quark- Gluon Plasma with Multipoint Energy Correla- tors”, Phys. Rev. Lett.137, 052302 (2026), arXiv:2503.13603

View on Pith Pith review arXiv 2026

[72] [72]

H. Bossi, A. S. Kudinoor, I. Moult, D. Pablos, A. Rai & K. Rajagopal,“Imaging the wakes of jets with energy-energy-energy correlators”, JHEP2412, 073 (2024),arXiv:2407.13818

View on Pith Pith review arXiv 2024

[73] [73]

J. Barata, M. V. Kuzmin, I. Moult, A. V. Sadofyev & J. M. Silva,“Hydrodynamics and Energy Correlators”, arXiv:2604.21971

View on Pith Pith review arXiv

[74] [74]

Z. Yang, Y. He, I. Moult & X.-N. Wang,“Prob- ing the Short-Distance Structure of the Quark-Gluon Plasma with Energy Correlators”, Phys. Rev. Lett. 132, 011901 (2024),arXiv:2310.01500

View on Pith Pith review arXiv 2024

[75] [75]

W. Zhao, V. Koch & F. Yuan,“Particle Correlations in Jets”,arXiv:2507.18790

View on Pith Pith review arXiv

[76] [76]

P. Duan, W. Ke, G.-Y. Qin & L. Wang,“Uncover the correlation between jet energy correlators and multi- plicity fluctuations”,arXiv:2604.01102

View on Pith arXiv

[77] [77]

J. Barata, Y. Peng, A. V. Sadofyev & H. Song,“QCD Matter through the Lens of Energy Correlators, to appear”

View on Pith

[78] [78]

G. Cuomo, E. Firat, F. Nardi & L. Ricci,“Conformal collider physics at large charge”, JHEP2602, 223 (2026),arXiv:2503.21867

View on Pith Pith review arXiv 2026

[79] [79]

D. Chicherin, G. P. Korchemsky, E. Sokatchev & A. Zhiboedov,“Energy correlations in heavy states”, JHEP2311, 134 (2023),arXiv:2306.14330

View on Pith Pith review arXiv 2023

[80] [80]

M. Luzum,“Flow fluctuations and long-range cor- relations: elliptic flow and beyond”, J. Phys. G38, 124026 (2011),arXiv:1107.0592

View on Pith Pith review arXiv 2011

[81] [81]

Y. Feng & F. Wang,“Review of nonflow estima- tion methods and uncertainties in relativistic heavy- ion collisions”, J. Phys. G52, 013001 (2025), arXiv:2407.12731

View on Pith Pith review arXiv 2025

[82] [82]

L. V. Delacrétaz, T. Hartman, S. A. Hartnoll & A. Lewkowycz,“Thermalization, Viscosity and the Averaged Null Energy Condition”, JHEP1810, 028 (2018),arXiv:1805.04194

View on Pith Pith review arXiv 2018

[83] [83]

J. Barata, J. G. Milhano & A. V. Sadofyev,“Picturing QCD jets in anisotropic matter: from jet shapes to energy energy correlators”, Eur. Phys. J. C84, 174 (2024),arXiv:2308.01294

View on Pith Pith review arXiv 2024

[84] [84]

J. Barata, J. G. Milhano, A. V. Sadofyev & J. M. Silva,“Early-Time Dynamics of Heavy-Ion Collisions through Energy Correlators: celestial blocks and the spacetime structure of out-of-equilibrium QCD mat- ter”,arXiv:2512.17009

View on Pith arXiv

[85] [85]

J. Barata, J. Brewer, K. Lee & J. M. Silva,“Heavy Quark Pair Energy Correlators: From Profiling Par- tonic Splittings to Probing Heavy-Flavor Fragmenta- tion”,arXiv:2508.19404

View on Pith Pith review arXiv

[86] [86]

J.-P. Blaizot, W. Broniowski & J.-Y. Ollitrault, “Continuous description of fluctuating eccentricities”, Phys. Lett. B738, 166 (2014),arXiv:1405.3572

View on Pith Pith review arXiv 2014

[87] [87]

S. Floerchinger & U. A. Wiedemann,“Mode-by-mode fluid dynamics for relativistic heavy ion collisions”, Phys. Lett. B728, 407 (2014),arXiv:1307.3453

View on Pith Pith review arXiv 2014

[88] [88]

A. Kurkela, A. Mazeliauskas, J.-F. Paquet, S. Schlicht- ing & D. Teaney,“Effective kinetic description of event-by-event pre-equilibrium dynamics in high- energy heavy-ion collisions”, Phys. Rev. C99, 034910 (2019),arXiv:1805.00961

View on Pith Pith review arXiv 2019

[89] [89]

A. Kirchner, F. Capellino, E. Grossi & S. Floerchinger, “Toward a fluid-dynamic description of an entire heavy- ion collision: From the colliding nuclei to the quark- gluon plasma phase”, Phys.Rev.C112, 024903(2025), arXiv:2410.08169

View on Pith Pith review arXiv 2025

[90] [90]

H. Mehrabpour,“Imprint of α clustering on ab initio correlations in relativistic light ion col- lisions”, Phys. Rev. C113, 034909 (2026), arXiv:2506.12673. 9

View on Pith arXiv 2026

[91] [91]

L. D. McLerran & R. Venugopalan,“Computing quark and gluon distribution functions for very large nuclei”, Phys. Rev. D49, 2233 (1994),hep-ph/9309289

View on Pith Pith review arXiv 1994

[92] [92]

L. D. McLerran & R. Venugopalan,“Gluon distri- bution functions for very large nuclei at small trans- verse momentum”, Phys. Rev. D49, 3352 (1994), hep-ph/9311205

View on Pith Pith review arXiv 1994

[93] [93]

L. D. McLerran & R. Venugopalan,“Green’s functions in the color field of a large nucleus”, Phys. Rev. D50, 2225 (1994),hep-ph/9402335

View on Pith Pith review arXiv 1994

[94] [94]

B. Schenke, C. Shen & P. Tribedy,“Running the gamut of high energy nuclear collisions”, Phys. Rev. C 102, 044905 (2020),arXiv:2005.14682

View on Pith Pith review arXiv 2020

[95] [95]

H. Mäntysaari & P. Singh,“Energy dependence of the deformed nuclear structure at small-x”, Eur. Phys. J. C85, 1449 (2025),arXiv:2411.14934

View on Pith Pith review arXiv 2025

[96] [96]

H. Mäntysaari, B. Schenke, C. Shen & W. Zhao, “Collision-Energy Dependence in Heavy-Ion Collisions from Nonlinear QCD Evolution”, Phys. Rev. Lett. 135, 022302 (2025),arXiv:2502.05138

View on Pith Pith review arXiv 2025

[97] [97]

A. Krasnitz & R. Venugopalan,“The Initial energy density of gluons produced in very high-energy nu- clear collisions”, Phys. Rev. Lett.84, 4309 (2000), hep-ph/9909203

View on Pith Pith review arXiv 2000

[98] [98]

T. Lappi,“Energy density of the glasma”, Phys. Lett. B643, 11 (2006),hep-ph/0606207

View on Pith Pith review arXiv 2006

[99] [99]

J. L. Albacete, P. Guerrero-Rodríguez & C. Marquet, “Initial correlations of the Glasma energy-momentum tensor”, JHEP1901, 073 (2019), arXiv:1808.00795

View on Pith Pith review arXiv 2019

[100] [100]

F. Zhou, G. Giacalone & J.-Y. Ollitrault,“Size of the quark-gluon plasma in ultracentral collisions: Impact of initial density fluctuations on the average trans- verse momentum”, Phys. Rev. C113, 044910 (2026), arXiv:2511.04605

View on Pith Pith review arXiv 2026

[101] [101]

A. Budhraja & B. Singh,“Exploitingν-dependence of projected energy correlators in HICs”, Phys. Lett. B 872, 140079 (2026),arXiv:2503.20019

View on Pith arXiv 2026

[102] [102]

P. Bozek,“Transverse-momentum–flow correlations in relativistic heavy-ion collisions”, Phys. Rev. C93, 044908 (2016),arXiv:1601.04513

View on Pith Pith review arXiv 2016

[103] [103]

G. Giacalone,“Observing the deformation of nuclei with relativistic nuclear collisions”, Phys. Rev. Lett. 124, 202301 (2020),arXiv:1910.04673

View on Pith Pith review arXiv 2020

[104] [104]

B. Schenke, C. Shen & D. Teaney,“Transverse mo- mentum fluctuations and their correlation with elliptic flow in nuclear collision”, Phys. Rev. C102, 034905 (2020),arXiv:2004.00690

View on Pith Pith review arXiv 2020

[105] [105]

G. Giacalone, F. G. Gardim, J. Noronha-Hostler & J.-Y. Ollitrault,“Correlation between mean trans- verse momentum and anisotropic flow in heavy- ion collisions”, Phys. Rev. C103, 024909 (2021), arXiv:2004.01765

View on Pith Pith review arXiv 2021

[106] [106]

G. Giacalone,“Constraining the quadrupole de- formation of atomic nuclei with relativistic nu- clear collisions”, Phys. Rev. C102, 024901 (2020), arXiv:2004.14463

View on Pith Pith review arXiv 2020

[107] [107]

J. Jia, S. Huang & C. Zhang,“Probing nuclear quadrupole deformation from correlation of ellip- tic flow and transverse momentum in heavy ion collisions”, Phys. Rev. C105, 014906 (2022), arXiv:2105.05713

View on Pith Pith review arXiv 2022

[108] [108]

B. Bally, M. Bender, G. Giacalone & V. Somà, “Evidence of the triaxial structure of 129Xe at the Large Hadron Collider”, Phys. Rev. Lett.128, 082301 (2022),arXiv:2108.09578

View on Pith Pith review arXiv 2022

[109] [109]

S. Zhao, H.-j. Xu, Y. Zhou, Y.-X. Liu & H. Song,“Exploring the Nuclear Shape Phase Tran- sition in Ultra-Relativistic 129Xe+129Xe Collisions at the LHC”, Phys. Rev. Lett.133, 192301 (2024), arXiv:2403.07441

View on Pith Pith review arXiv 2024

[110] [110]

K. Hagino & M. Kitazawa,“Probing surface vi- brations of spherical nuclei in relativistic heavy- ion collisions”, Phys. Rev. C112, L041901 (2025), arXiv:2508.05125

View on Pith Pith review arXiv 2025

[111] [111]

H. Chen, I. Moult, J. Thaler & H. X. Zhu, “Non-Gaussianities in Collider Energy Flux”, arXiv:2205.02857

View on Pith Pith review arXiv

[112] [112]

P. Carzon, M. Martinez, M. D. Sievert, D. E. Wertepny & J. Noronha-Hostler,“Monte Carlo event generator for initial conditions of conserved charges in nuclear geometry”, Phys. Rev. C105, 034908 (2022), arXiv:1911.12454

View on Pith Pith review arXiv 2022

[113] [113]

J. Sousa, M. D. Sievert, J. Noronha-Hostler, P. Car- zon & M. Luzum,“Initial-state charge density predicts final-state net charge flow in heavy-ion collisions”, Phys. Lett. B880, 140806 (2026), arXiv:2505.16038. 10 SUPPLEMENTAL MATERIAL

View on Pith Pith review arXiv 2026

[114] [114]

Energy-flow harmonics away from midrapidity In this appendix we generalize Eq.(7) to arbitrary pseu- dorapidities and to finite pseudorapidity windows. The powers of coshη depend on the measure and on whether the observable is weighted by energy or by transverse en- ergy. We therefore keep these choices explicit through- out. Unless stated otherwise,η den...

View on Pith

[115] [115]

In particular, the solid angle integration measure is dΩ =|sinθdθ|dϕ= dηdϕ cosh2η.(25) The energy-flow operator event-wise expectation value can be written asEev(η,ϕ )≡ dE dΩ ⏐⏐ ev. On the other hand, we define the transverse-energy density per unit pseudorapidity and azimuth as Fev(η,ϕ)≡ dET dηdϕ ⏐⏐⏐⏐ ev , E T =Esinθ= E coshη .(26) Using Eq. (25) and dE/...

View on Pith

[116] [116]

Response functional and long-wavelength expansion In this Appendix we give a more explicit formulation of the response mapH introduced in the main text, and we clarify the two approximations on which the main analysis rests: an expansion in the amplitude of the event-by-event fluctuations around a smooth background, and, within the linear term of that exp...

View on Pith

[117] [117]

Rotational covariance of the response kernels Here we derive the constraint that rotational symmetry places on the kernels mapping initial perturbations to the asymptotic energy-flow harmonics, and in particular the angular form quoted in Eq. (17). The only inputs are an azimuthally symmetric mean initial configuration and the rotational covariance of the...

View on Pith

[118] [118]

Thickness weighting and nuclear multipole Here we reduce the covariance of the deposited energy density to the nuclear multipole correlator of the main text. We consider a central collision of two statistically independent identical nuclei, with thickness functions tX ev(x) = ¯t(r) +δtX ev(x), X= +,−,(72) where r =|x|, the common mean profile is azimuthal...

View on Pith