Energy Correlators: A Journey From Theory to Experiment

Hua Xing Zhu; Ian Moult

Energy Correlators: A Journey From Theory to Experiment

T0 review · 0 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This review argues that correlation functions of the energy flux reaching a detector — energy correlators — are the canonical flat-space observables of quantum field theory, and that recent measurements have made them a working two-way…

desk verdict A landmark review of energy correlators that earns its keep as a map of the field; its headline 'canonical/transform' claims outrun the track-proxy evidence it actually presents. read the letter →

arxiv 2506.09119 v1 pith:ZTGNGD4U submitted 2025-06-10 hep-ph hep-exhep-thnucl-exnucl-th

Ian Moult , Hua Xing Zhu This is my paper · ORCID

classification hep-phhep-exhep-thnucl-exnucl-th

keywords energycorrelatorsflowoperatorslight-rayjetsubstructureQCDcolliderphysicsconformalfieldtheoryaveragenullcondition

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Energy correlators measure how energy flows in correlated directions after a collision: they are correlation functions of energy flow operators $E(\hat n)$, the objects that formal quantum field theory associates with asymptotic flux. This review argues that these observables are the canonical flat-space observables of quantum field theory — the analogue, for colliders, of boundary correlators in anti-de Sitter space and cosmological correlators in de Sitter space — and that they are uniquely positioned to connect formal theory to experiment. The authors' central claim is that recent measurements across electron-positron, electron-proton, proton-proton, and heavy-ion colliders have transformed energy correlators from a theoretical abstraction into a genuine bridge: the same observable family now yields precision extractions of the strong coupling and the top-quark mass, images the transition from quark-gluon physics to confined hadrons, and tests universal properties of quantum field theory such as the average null energy condition. If the claim is right, one observable family simultaneously organizes collider phenomenology and constrains the space of quantum field theories, giving experimentalists and formal theorists a common language.

What carries the argument

The load-bearing object is the energy flow operator $E(\hat n) = \lim_{r\to\infty} \int_0^\infty dt\, r^2 n^i T_{0i}(t, r\hat n)$, the integral of the stress tensor along a null direction — a light-ray operator, known as the average null energy operator, that measures the energy arriving at a detector pointing in direction $\hat n$. Its correlators $\langle E(\hat n_1) E(\hat n_2) \cdots E(\hat n_k)\rangle$ are the observables: in QCD they reduce to weighted cross sections over particle pairs, and via the light-ray OPE they decompose into structure constants times celestial blocks, projecting each measurement onto operators of definite scaling dimension, namely the twist-2 anomalous dimensions. Two further ingredients carry the argument: the mapping between angular scale and time scale in the collinear limit, which lets one plot image the phases of QCD, and the Regge-trajectory structure of light-ray operators, which connects the perturbative QCD picture to the conformal-theory picture.

What would settle it

Take the small-angle limit of the two-point energy correlator measured on tracks in high-energy jets at the LHC, and compare the extracted scaling exponent with the perturbative light-ray OPE prediction after hadronization and detector corrections: a deviation larger than the combined uncertainties would show the observable is not under the claimed perturbative control. A sharper, purely data-side test is the non-perturbative energy sum rule $\int_0^1 dz\, \text{EEC}(z) = 1$ — if track-based data violates it by more than the estimated track-fraction uncertainty, the track realization of the energy operator is not faithful.

Watch

Extended reading notes

Core claim

The paper's central claim is that the correlation functions of energy flow operators, defined as null integrals of the stress tensor at infinity, constitute a canonical class of observables for any quantum field theory, and that this class has now matured into a working experimental program. Concretely: the two-point correlator measured from charged tracks inside jets at the LHC reveals, in a single plot, the power-law scaling of asymptotically free quarks and gluons, the abrupt confinement transition, and the scaling of free hadrons; the three-point correlator has been measured and compared directly with an analytic perturbative calculation; and archival electron-positron data re-analyzed with track-level angular resolution now match next-to-next-to-leading-order predictions. On the formal side, the same operators organize the data of conformal field theories into Regge trajectories, obey a light-ray operator product expansion with computable celestial blocks, and realize the average null energy condition, so collider measurements become measurements of universal QFT structure. The authors' strongest formulation is that detector observables are 'arguably the canonical flat space observables in generic QFTs,' and that the recent wave of measurements 'completely transforms the possibility for interaction between theory and experiment.'

Load-bearing premise

The practical payoff of the review — precision extractions and clean phase imaging — assumes that what detectors actually measure, namely charged tracks clustered into jets plus controlled corrections for hadronization and detector response, faithfully realizes the theoretical energy flow operator; if track-based normalization or those corrections are not under control in the probed regimes, the advertised precision weakens.

Editorial extensions

If this is right

If this is right, the two-point energy correlator measured on tracks becomes a precision channel for the strong coupling $\alpha_s$ and the top-quark mass, with uncertainties organized by factorization theorems rather than by Monte Carlo modeling.
The collinear-limit scaling of the correlator maps directly onto twist-2 anomalous dimensions, so collider data becomes a direct measurement of QCD operator data — the same data that governs parton evolution.
Multi-point correlators such as the measured three-point non-gaussianity are calculable analytically and measurable directly, opening an experimental window on the perturbative structure of higher-point detector correlators.
Because the energy operator is defined through the stress tensor, the same experimental program can test universal QFT facts — the average null energy condition and the conformal collider bounds — not just QCD.
A single family of observables now spans electron-positron, electron-proton, proton-proton, and heavy-ion collisions, so a theoretical advance in any one system transfers directly to the others.

Reading between the lines

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

The paper notes that the one-point correlator's anisotropy coefficient was computed decades ago and agrees with conformal collider bounds, yet has never been precisely measured; the same track-based technology that resolved the two-point correlator could deliver that measurement from existing electron-positron data.
The review leaves the recombination of rising BFKL Regge trajectories unresolved; a testable implication of its picture is that forward, high-boost energy correlators should show a transition in their scaling exponent as the transient 'opaque' regime gives way to Regge-bounded behavior.
A lattice computation of energy correlators, listed by the review as a future direction, would provide a first-principles check of the perturbative-plus-hadronization split on which the precision claims rest.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This is a review, and it is the best single map of the energy-correlator field I know. If someone asked where to start on light-ray operators, track functions, or the recent ALEPH/CMS/ALICE measurements, I would point them here. The historical narrative is genuinely useful: Sterman's energy flow operator, the Basham et al. EEC, the Hofman-Maldacena revival, and the last few years of analytic NLO/NNLO results are all put in one coherent story. The formal sections on the light-ray OPE, Regge trajectories, and celestial blocks are careful and, as far as I can check, faithful to the literature. The paper earns its keep as a resource.

Where it gets soft is in its agenda-setting claims. The 'canonical flat space observables' line in Section I.C is an assertion, not an argument; there is no criterion offered for canonicity. The 'completely transform the possibility for interaction' line in Section I.F is marketing. Those should be toned down, especially in a review that is supposed to be a neutral guide.

The more substantive issue is the one I want you to look at closely: the flagship experimental results are not measurements of the full energy flow operator. They are charged-hadron proxies from tracking detectors, because calorimeters lack angular resolution. The review cites the track-function factorization literature, but it does not tell the reader how big the corrections are, over what angular range the factorization is expected to hold, or whether the track normalization is universal. The small-angle region that the paper's own figures use to image the confinement transition and extract alpha_s is exactly the regime where theta*Q is a few GeV and hadronization corrections are non-perturbative. This gap is acknowledged only in passing. It does not invalidate the review, but it needs to be stated as an open question, not smoothed over. The stress-test note lands here; I think it is the right concern to raise.

Self-citation is high, but it is earned: these authors built a large part of this line. The external measurements anchor the factual claims. This is a serious piece of work in the review genre, and it deserves a serious referee. My recommendation: accept after minor revision, with two requests—rewrite the two headline phrases as program statements, and add a paragraph that quantifies, even roughly, the track/hadronization systematics in the small-angle regime.

Referee Report

0 major / 6 minor

Summary. This is a review article by I. Moult and H. X. Zhu on energy correlators, i.e., correlation functions of energy flow/light-ray operators, and their role both in formal quantum field theory and in collider physics. The paper traces the history from Sterman's energy flux operator and the early PLUTO/OPAL measurements of the energy-energy correlator to the modern operator definition in terms of the stress tensor, and then surveys formal developments: the light-ray OPE, celestial blocks, Regge trajectories, the ANEC, and multi-point correlators in QCD and N=4 super-Yang-Mills. The second half connects these ideas to QCD factorization, power corrections, detector/track functions, and measurements at e+e-, ep, pp, and heavy-ion colliders, with applications ranging from alpha_s extraction and the top quark mass to quarkonium dynamics, BSM searches, and hot/cold nuclear matter. The central thesis is that detector observables are 'arguably the canonical flat space observables in generic QFTs' and that recent high-resolution, track-based measurements provide a genuine bridge between formal theory and experiment.

Significance. If the review's reporting is accurate, it is a valuable interdisciplinary resource: it compiles an unusually wide literature, gives a historically careful account including the resolution of early NLO discrepancies in the EEC, and is candid about several open problems, such as non-perturbative Regge trajectory recombination and detector-resolution limitations. The factual core is anchored by independent experimental measurements and by calculations from multiple groups, so the circularity burden is low; the authors' frequent self-citations are natural in a field they helped create. Because this is a review rather than an original research paper, its central claims are synthetic and programmatic rather than proven here, but the main statements are appropriately hedged with qualifications such as 'arguably' and 'suggests'.

minor comments (6)

[I.A, footnote 1] The footnote reads 'we will interchangeable use'; this should be 'interchangeably', and the list of alternative names for the energy operator could be shortened since the subsequent text introduces the ANEC terminology again.
[I.C and Fig. 6] The claim that detector observables are 'arguably the canonical flat space observables' is central to the paper's narrative, but it remains an analogy rather than an established characterization; I suggest adding one sentence clarifying the sense in which this is canonical and noting that the full space of detector operators is still not classified, a point the paper itself makes in Section II.
[I.E / III.F] The review correctly identifies hadronic calorimeter angular resolution as the reason track-based measurements are used, and it cites the track-function factorization literature; since the bridge argument in Section I.F and the comparisons in Figs. 10-12 rely on charged-track proxies for the energy flow operator, a short summary in Section III.F of the numerical size and scale dependence of track-normalization and hadronization corrections, especially for theta*Q of a few GeV, would help the non-specialist audience assess the robustness of the advertised precision extractions.
[II.B.1] There is a duplicated word in 'The simplest detector correlator is the one-point point function'; it should read 'one-point function'.
[I.F and references] Several citation placeholders appear incomplete in the provided text, for example '(Nambrath, a,b)', 'Hwang', and 'Shen', and the entry '(CMS, 2023, 2025; Chekhovsky et al., 2025)' is awkwardly formatted; the final reference list should be checked for completeness and consistency.
[V.A] For the strong-coupling extractions discussed in Section V.A, a sentence comparing the reported values with the current PDG world average, or pointing to a recent global review, would make the section more useful to readers outside the precision-QCD community.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: this is a review whose factual anchors are external measurements and independent calculations, not a derivation that reduces to its own inputs.

full rationale

I walked the paper's claimed connections between formal QFT, QCD phenomenology, and experiment and found no circular step. The paper is a survey rather than a derivation: its central claims are that energy correlators are a canonical flat-space observable and that recent measurements create a productive theory-experiment bridge. Those claims are anchored by external experimental results (PLUTO, OPAL, CMS Open Data, ALEPH archival data, CMS, ALICE, STAR, H1) and by independent analytic calculations (Basham et al.; Dixon et al.; Henn et al.; Yan and Zhang; Chicherin et al.), not by definitions chosen to reproduce the conclusions. The numerous self-citations are historical attributions or technical references to the authors' own prior calculations; they do not supply the load-bearing evidence for the review's main assertions. The closest thing to a structural assumption is the track-based proxy for the energy flow operator discussed in Section I.E, where the review cites track-function factorization as the basis for computing energy correlators on charged tracks. This is a real assumption about control of hadronization, track normalization, and power corrections in the small-angle regime, and it is a legitimate correctness risk if those corrections are not controlled. But it is not circular: the review does not fit a parameter to a subset of energy-correlator data and then call it a prediction, and no equation in the paper reduces by construction to its own input. The self-citation chain for track functions is external technical support with stated assumptions, not a uniqueness theorem or ansatz smuggled in to forbid alternatives. Accordingly, the appropriate finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The review relies on previously established QFT and QCD formalism and introduces no new fitted parameters, axioms, or entities. The listed assumptions are the load-bearing background needed for the review's practical claims about precision extractions and measurements.

assumptions (3)

domain assumption The energy flow operator E(n) defined by the stress tensor at asymptotic infinity is a well-defined, infrared and collinear safe observable in QCD.
Used throughout Sections I and III; makes energy correlators calculable in perturbation theory.
domain assumption Factorization theorems (SCET, Collins-Soper-Sterman) separate hard, collinear, soft, and non-perturbative contributions in hadron collisions.
Assumed in Sections I.E and IV.C when translating perturbative calculations into LHC and nuclear environments.
domain assumption Track-based measurements can be treated as high-resolution proxies for the energy flow operator with calculable detector and hadronization corrections.
Assumed in Sections I.E, IV.C, and V; needed to connect theory to experimental energy correlators.

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Cite this review

Pith. "Pith review of Energy Correlators: A Journey From Theory to Experiment." pith.science (2026). https://pith.science/paper/ZTGNGD4U

@misc{pith2026250609119,
  author       = {Pith},
  title        = {Pith review of: Energy Correlators: A Journey From Theory to Experiment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZTGNGD4U}},
  note         = {Machine review of arXiv:2506.09119}
}

read the original abstract

Collider experiments offer a unique opportunity to explore the Standard Model (SM), and to search for new physics, new interactions, and new principles of nature. The theoretical abstraction of a collider, namely the study of correlations in asymptotic fluxes, provides one of the most basic examples of an observable in quantum field theory (QFT) and quantum gravity. Energy flux is described in QFT by energy flow operators, a particular example of light-ray operators. In addition to their central role in the theoretical description of collider physics, energy flow operators play an important role in diverse areas of formal QFT and gravity, providing a connection between real world collider phenomenology, and the deep underlying principles of QFT. Recently it has become possible to measure correlation functions of energy flow operators in a wide variety of collider experiments, providing an exciting new connection between collider physics and formal theory. In this review, we provide a survey of recent progress in our understanding of energy operators and their correlators, highlighting their importance in both formal theory and collider phenomenology, and in particular, their great potential for bridging these areas to provide new ways to understand the real world. We intend this article as a resource for both formal theorists interested in understanding how light-ray operators are being applied in particle and nuclear physics, as well as for experimentalists interested in the theoretical motivation for these observables. Most importantly, we aim to stimulate further interaction between the formal, phenomenological and experimental communities through the common lens of energy correlators.

Figures

Figures reproduced from arXiv: 2506.09119 by the authors.

**Figure 2.** FIG. 2: The evolution of the study of energy flux in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3: Three interesting observables in QFT: ampli [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (91 more)

**Figure 5.** Figure 5: FIG. 5: Multi-point energy correlators, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6: Analogous to boundary local correlators for AdS space (Λ [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: FIG. 7: The Riemann surface for the leading Regge tra [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: FIG. 8: Jet substructure as a new search channel at the [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9: A comparison of standard jet substructure [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

**Figure 10.** Figure 10: FIG. 10: The first study of the two-point energy correla [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

**Figure 11.** Figure 11: FIG. 11: A measurement of the non-gaussianity of the [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

**Figure 12.** Figure 12: FIG. 12: Measurements of the energy correlators with extremely high angular resolution providing a clear view of the [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

**Figure 13.** Figure 13: FIG. 13: An illustration of an energy operator in a Pen [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]

**Figure 14.** Figure 14: FIG. 14: A schematic Regge trajectory in a weakly [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]

**Figure 15.** Figure 15: FIG. 15: An illustration of the Chew-Frautschi plots in [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]

**Figure 16.** Figure 16: FIG. 16: Computations of the leading Regge trajecto [PITH_FULL_IMAGE:figures/full_fig_p021_16.png]

**Figure 17.** Figure 17: FIG. 17: The LO, NLO and NNLO contributions to the [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]

**Figure 18.** Figure 18: FIG. 18: Upper Panel: Discrepancies between numerical [PITH_FULL_IMAGE:figures/full_fig_p026_18.png]

**Figure 19.** Figure 19: FIG. 19: A plot of the three-point correlator as a function [PITH_FULL_IMAGE:figures/full_fig_p027_19.png]

**Figure 20.** Figure 20: FIG. 20: Multi-point correlators in the collinear limit [PITH_FULL_IMAGE:figures/full_fig_p028_20.png]

**Figure 21.** Figure 21: FIG. 21: A plot of the four-point energy correlator in [PITH_FULL_IMAGE:figures/full_fig_p029_21.png]

**Figure 23.** Figure 23: FIG. 23: Correlation functions of local operators can [PITH_FULL_IMAGE:figures/full_fig_p031_23.png]

**Figure 24.** Figure 24: FIG. 24: The light-ray OPE allows multi-point detec [PITH_FULL_IMAGE:figures/full_fig_p031_24.png]

**Figure 25.** Figure 25: FIG. 25: The action of Lorentz symmetry on the celestial [PITH_FULL_IMAGE:figures/full_fig_p032_25.png]

**Figure 26.** Figure 26: FIG. 26: Multi-point correlators of detector operators [PITH_FULL_IMAGE:figures/full_fig_p034_26.png]

**Figure 28.** Figure 28: FIG. 28: The even and odd-spin data for the three-point [PITH_FULL_IMAGE:figures/full_fig_p035_28.png]

**Figure 29.** Figure 29: FIG. 29: In a gauge theory, the leading contribution to [PITH_FULL_IMAGE:figures/full_fig_p036_29.png]

**Figure 30.** Figure 30: FIG. 30: The two-point correlator of light-ray operators [PITH_FULL_IMAGE:figures/full_fig_p037_30.png]

**Figure 31.** Figure 31: FIG. 31: The two loop perturbative corrections to the [PITH_FULL_IMAGE:figures/full_fig_p038_31.png]

**Figure 32.** Figure 32: FIG. 32: Using an effective field theory description of [PITH_FULL_IMAGE:figures/full_fig_p038_32.png]

**Figure 33.** Figure 33: FIG. 33: Correlation functions of detector operators pro [PITH_FULL_IMAGE:figures/full_fig_p039_33.png]

**Figure 34.** Figure 34: FIG. 34: Upper Panel: The full angle two-point correla [PITH_FULL_IMAGE:figures/full_fig_p040_34.png]

**Figure 35.** Figure 35: FIG. 35: The rich structure of QCD, as exemplified by the two-point energy correlator. Starting from the UV, probed [PITH_FULL_IMAGE:figures/full_fig_p041_35.png]

**Figure 36.** Figure 36: FIG. 36: The factorization of the energy correlator in the [PITH_FULL_IMAGE:figures/full_fig_p044_36.png]

**Figure 37.** Figure 37: FIG. 37: Measurements of the scaling exponent of the [PITH_FULL_IMAGE:figures/full_fig_p045_37.png]

**Figure 38.** Figure 38: FIG. 38: A calculation of the EEC in the back-to-back [PITH_FULL_IMAGE:figures/full_fig_p046_38.png]

**Figure 39.** Figure 39: FIG. 39: Top Panel: Cusped Wilson lines appearing [PITH_FULL_IMAGE:figures/full_fig_p047_39.png]

**Figure 40.** Figure 40: FIG. 40: The back-to-back limit of the energy correlator [PITH_FULL_IMAGE:figures/full_fig_p048_40.png]

**Figure 41.** Figure 41: FIG. 41: The co-planar limit of the three-point correlator [PITH_FULL_IMAGE:figures/full_fig_p049_41.png]

**Figure 43.** Figure 43: FIG. 43: The two-point correlator in the bulk of distribu [PITH_FULL_IMAGE:figures/full_fig_p050_43.png]

**Figure 45.** Figure 45: FIG. 45: A comparison of the scale evolution of the non [PITH_FULL_IMAGE:figures/full_fig_p051_45.png]

**Figure 46.** Figure 46: FIG. 46: Illustration of the non-perturbative corrections [PITH_FULL_IMAGE:figures/full_fig_p052_46.png]

**Figure 47.** Figure 47: FIG. 47: Comparision of the TMD-based model for the [PITH_FULL_IMAGE:figures/full_fig_p053_47.png]

**Figure 49.** Figure 49: FIG. 49: The gluon track function, as extracted from [PITH_FULL_IMAGE:figures/full_fig_p054_49.png]

**Figure 51.** Figure 51: FIG. 51: A calculation of the EEC on tracks in [PITH_FULL_IMAGE:figures/full_fig_p055_51.png]

**Figure 53.** Figure 53: FIG. 53: Predictions for inclusive small- [PITH_FULL_IMAGE:figures/full_fig_p056_53.png]

**Figure 54.** Figure 54: FIG. 54: The light-ray OPE in QCD enabled the re [PITH_FULL_IMAGE:figures/full_fig_p057_54.png]

**Figure 55.** Figure 55: FIG. 55: A comparison of the different collider geome [PITH_FULL_IMAGE:figures/full_fig_p057_55.png]

**Figure 56.** Figure 56: FIG. 56: Hadron-hadron colliders enable collisions of multiple hadronic species. Energy correlator observables have [PITH_FULL_IMAGE:figures/full_fig_p058_56.png]

**Figure 57.** Figure 57: FIG. 57: Top Panel: Measurements of the energy corre [PITH_FULL_IMAGE:figures/full_fig_p059_57.png]

**Figure 58.** Figure 58: FIG. 58: The highest energy measurements of the energy [PITH_FULL_IMAGE:figures/full_fig_p060_58.png]

**Figure 61.** Figure 61: FIG. 61: An illustration of the distinct kinematic re [PITH_FULL_IMAGE:figures/full_fig_p061_61.png]

**Figure 63.** Figure 63: FIG. 63: The transverse energy-energy correlator [PITH_FULL_IMAGE:figures/full_fig_p063_63.png]

**Figure 64.** Figure 64: FIG. 64: Calculations of the TEEC at the LHC. In the [PITH_FULL_IMAGE:figures/full_fig_p063_64.png]

**Figure 65.** Figure 65: FIG. 65: In hadronic events at the LHC, energy correla [PITH_FULL_IMAGE:figures/full_fig_p065_65.png]

**Figure 66.** Figure 66: FIG. 66: The measurement of the two-point energy corre [PITH_FULL_IMAGE:figures/full_fig_p066_66.png]

**Figure 67.** Figure 67: FIG. 67: Measurements of the two-point energy corre [PITH_FULL_IMAGE:figures/full_fig_p066_67.png]

**Figure 68.** Figure 68: FIG. 68: CMS measurements of the ratio of the three-point to two-point projected energy correlators inside high [PITH_FULL_IMAGE:figures/full_fig_p067_68.png]

**Figure 69.** Figure 69: FIG. 69: Measurements of the ratio of the three-point to [PITH_FULL_IMAGE:figures/full_fig_p067_69.png]

**Figure 70.** Figure 70: FIG. 70: A simulation of the shape dependent four-point [PITH_FULL_IMAGE:figures/full_fig_p068_70.png]

**Figure 71.** Figure 71: FIG. 71: Measurements of the [PITH_FULL_IMAGE:figures/full_fig_p068_71.png]

**Figure 74.** Figure 74: FIG. 74: Top Panel: The expected phase diagram of [PITH_FULL_IMAGE:figures/full_fig_p070_74.png]

**Figure 75.** Figure 75: FIG. 75: Collisions of heavy nuclei provide the opportunity to study rich initial state dynamics, in the form of [PITH_FULL_IMAGE:figures/full_fig_p071_75.png]

**Figure 76.** Figure 76: FIG. 76: The presence of a droplet of QGP imprints itself [PITH_FULL_IMAGE:figures/full_fig_p072_76.png]

**Figure 78.** Figure 78: FIG. 78: Measurement of the two-point energy correlator [PITH_FULL_IMAGE:figures/full_fig_p073_78.png]

**Figure 79.** Figure 79: FIG. 79: A measurement of the two-point energy cor [PITH_FULL_IMAGE:figures/full_fig_p074_79.png]

**Figure 80.** Figure 80: FIG. 80: Data from ALICE for the two-point energy cor [PITH_FULL_IMAGE:figures/full_fig_p074_80.png]

**Figure 81.** Figure 81: FIG. 81: The asymmetry of the TEEC as a probe gluon [PITH_FULL_IMAGE:figures/full_fig_p075_81.png]

**Figure 83.** Figure 83: FIG. 83: Calculations of the three-point to two-point [PITH_FULL_IMAGE:figures/full_fig_p076_83.png]

**Figure 84.** Figure 84: FIG. 84: Theoretical uncertainty estimates for the cal [PITH_FULL_IMAGE:figures/full_fig_p077_84.png]

**Figure 85.** Figure 85: FIG. 85: The energy correlator on a jet from a decaying [PITH_FULL_IMAGE:figures/full_fig_p078_85.png]

**Figure 86.** Figure 86: FIG. 86: A plot of the three-point energy correlator on [PITH_FULL_IMAGE:figures/full_fig_p078_86.png]

**Figure 87.** Figure 87: FIG. 87: Upper Panel: An illustration of the quarkonium [PITH_FULL_IMAGE:figures/full_fig_p079_87.png]

**Figure 88.** Figure 88: FIG. 88: In the left (right) plot, nomalous longitudinal [PITH_FULL_IMAGE:figures/full_fig_p080_88.png]

**Figure 89.** Figure 89: FIG. 89: A LO illustration for the measurement of NEC [PITH_FULL_IMAGE:figures/full_fig_p081_89.png]

**Figure 90.** Figure 90: FIG. 90: Scaling evolution as imprinted in the angular [PITH_FULL_IMAGE:figures/full_fig_p081_90.png]

**Figure 91.** Figure 91: FIG. 91: A comparison of the perturbative logarithmic [PITH_FULL_IMAGE:figures/full_fig_p082_91.png]

**Figure 93.** Figure 93: FIG. 93: The SSA of track-based NEC as a function of [PITH_FULL_IMAGE:figures/full_fig_p082_93.png]

**Figure 95.** Figure 95: FIG. 95: Energy correlators from the back-to-back limit [PITH_FULL_IMAGE:figures/full_fig_p083_95.png]

**Figure 96.** Figure 96: FIG. 96: An extraction of the Collins-Soper kernel from [PITH_FULL_IMAGE:figures/full_fig_p083_96.png]

**Figure 97.** Figure 97: FIG. 97: Detailed studies of the angular dependence of [PITH_FULL_IMAGE:figures/full_fig_p084_97.png]

**Figure 98.** Figure 98: FIG. 98: Interference pattern in azimuthal angle of [PITH_FULL_IMAGE:figures/full_fig_p085_98.png]

**Figure 99.** Figure 99: FIG. 99: Top Panel: The detector configuration that [PITH_FULL_IMAGE:figures/full_fig_p085_99.png]

**Figure 101.** Figure 101: FIG. 101: The ratio of the two-point energy correlator [PITH_FULL_IMAGE:figures/full_fig_p087_101.png]

**Figure 104.** Figure 104: FIG. 104: Projected N-point energy correlators com [PITH_FULL_IMAGE:figures/full_fig_p088_104.png]

**Figure 105.** Figure 105: FIG. 105: A comparison of the ratio of two-point corre [PITH_FULL_IMAGE:figures/full_fig_p089_105.png]

**Figure 106.** Figure 106: FIG. 106: Energy correlators in [PITH_FULL_IMAGE:figures/full_fig_p090_106.png]

**Figure 107.** Figure 107: FIG. 107: A schematic of the operator product expan [PITH_FULL_IMAGE:figures/full_fig_p090_107.png]

**Figure 109.** Figure 109: FIG. 109: The modification of energy correlators in nu [PITH_FULL_IMAGE:figures/full_fig_p091_109.png]

**Figure 108.** Figure 108: FIG. 108: A comparison of the unbiased CMS data for [PITH_FULL_IMAGE:figures/full_fig_p091_108.png]

**Figure 110.** Figure 110: FIG. 110: The total cross section for [PITH_FULL_IMAGE:figures/full_fig_p092_110.png]

**Figure 112.** Figure 112: FIG. 112: The gauge theory bootstrap combines IR and [PITH_FULL_IMAGE:figures/full_fig_p093_112.png]

**Figure 113.** Figure 113: FIG. 113: An illustration of bounds on [PITH_FULL_IMAGE:figures/full_fig_p094_113.png]

**Figure 114.** Figure 114: FIG. 114: A summary of different approaches to flat [PITH_FULL_IMAGE:figures/full_fig_p096_114.png]

**Figure 115.** Figure 115: FIG. 115: An illustration of a realization of an energy [PITH_FULL_IMAGE:figures/full_fig_p097_115.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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