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REVIEW 4 major objections 5 minor 3 cited by

A boosted-Z jet's EEC peak is a Sudakov effect, not a resonance, and one function predicts it.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · deepseek-v4-flash

2026-08-03 07:11 UTC pith:AK4IAZUL

load-bearing objection The peak in boosted-Z EEC really is the boosted Sudakov back-to-back region, and the Lorentz-invariant shape-function argument is the cleanest part; the headline numerical precision is softer than advertised because the peak sits on a hand-tuned NP envelope. the 4 major comments →

arxiv 2601.20923 v3 pith:AK4IAZUL submitted 2026-01-28 hep-ph hep-ex

High precision heavy-boson-jet substructure with energy correlators

Jack Holguin , Ian Moult , Aditya Pathak , Massimiliano Procura , Siddharth Sule This is my paper
classification hep-ph hep-ex
keywords energy-energy correlatorjet substructureSudakov resummationboosted Z bosonEEC shape functionnon-perturbative power correctionsCollins-Soper kernelmulti-scale jets
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper claims that the sharp peak seen in energy-energy correlators on hadronically decaying boosted Z bosons is not a Breit-Wigner resonance feature of the Z decay, but the boosted Sudakov-resummed back-to-back region of the Z-pole electron-positron EEC. Because the Z is a colour singlet, the peak is controlled by a single Lorentz-invariant EEC shape function determined at the Z pole, so peak position, height, and shape are calculable rather than fitted. The paper derives predictions at N3LL' accuracy for both proton-proton and electron-positron setups, and validates them against event-generator simulations and against boosted experimental Z-pole data. If correct, heavy-boson jet substructure at hadron colliders becomes a clean, lepton-collider-quality probe across a range of effective collision energies.

Core claim

The central claim is that the apparent threshold peak in massive-jet energy correlators originates from Sudakov logarithm resummation in the boson rest frame, not from any resonance-like structure in the decay. The paper shows that by boosting the Z-pole EEC shape function F_EE, the full laboratory-frame spectrum is determined at leading electroweak order through a single formula, up to stated M_Z/p_T and R^2 corrections. The peak position follows from the relation chi_peak^2/4 approximately (M_Z/p_T^Z)^2, and its shape is governed by the same soft function that controls high-precision Z-pole EEC calculations. This is verified by comparing event-generator simulations and by boosting an actua

What carries the argument

The EEC shape function F_EE, a reparametrisation-invariant function of the cross-ratio zbar = q^2 n1.n2 / (2 q.n1 q.n2), together with the exact reparametrisation symmetry E(rho n) = rho^-3 E(n) of the energy-flow operator. This symmetry forces the correlator into a Lorentz-invariant form, so the boosted-frame observable is determined by the same shape function as the Z-pole rest-frame EEC; the Sudakov factorisation of the back-to-back region gives the peak its calculable shape.

Load-bearing premise

The non-perturbative strong-interaction corrections that dominate at the peak survive the boost unchanged and are modelled accurately enough; the paper's treatment of these corrections is the load-bearing step.

What would settle it

A high-statistics measurement of the EEC on Z-tagged jets with transverse momentum around 1 TeV, resolving the peak, would test whether its position and shape match the boosted Z-pole spectrum; deviations beyond the quoted uncertainties at the peak would refute the claimed factorisation.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The peak position scales as chi_peak approximately 2/(beta gamma), i.e. chi_peak^2/4 approximately (M_Z/p_T^Z)^2, so the peak tracks the boost in a simple, testable way.
  • Both proton-proton Z-tagged jets and electron-positron di-Z hadronic decays are predicted from the same Z-pole shape function at N3LL' accuracy with no new non-perturbative inputs.
  • The prediction is validated by event-generator simulations and by boosting existing Z-pole EEC data, meaning hadron-collider measurements can be compared directly to lepton-collider-quality predictions.
  • The approach extends to other colour-singlet decays such as W and Higgs bosons, and lays groundwork for a precise theoretical description of top-quark decay peaks in energy correlators.

Where Pith is reading between the lines

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

  • If the factorisation holds, the top-quark-mass peak in boosted top jets should be describable by boosting the W rest-frame EEC, making top-mass extraction a parameter-free prediction rather than a Monte-Carlo-calibrated shape.
  • Measuring EECs on boosted Z jets at several transverse momenta should produce curves that, when rescaled by the appropriate boost factor, collapse onto a single universal shape; this is a clean, decisive test of the mechanism.
  • Since backgrounds from mistagged jets follow a power law while the signal peak is Sudakov-shaped, the peak could serve as a background-subtractable calibration handle at hadron colliders, extending the paper's leading-order fake-Z subtraction.
  • The same shape-function boost could be applied to track-based EEC measurements, potentially connecting to higher-statistics future data without full calorimetric coverage.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper studies energy-energy correlators (EECs) on hadronically decaying boosted Z bosons. It argues that the sharp peak at angles ~ M_Z/p_T^jet is not a Breit-Wigner resonance feature but originates from boosting the Sudakov-resummed back-to-back region of the Z-pole e+e- EEC. The central construction uses the reparametrization symmetry of the energy-flow operator to define a Lorentz-invariant EEC shape function F_EE, which is then used to write factorized expressions for the pp Z-jet EEC and the e+e- -> ZZ EEC, Eqs. (3.12)-(3.13). The rest-frame shape function is built from an NLO+N3LL' matched spectrum with a non-perturbative envelope, and alternatively extracted from OPAL data. The predictions are compared with Herwig and Pythia, and the paper also derives an SCET factorization of the back-to-back limit directly in the laboratory frame, verifying consistency with the shape-function approach, and extends the formalism to higher-point correlators.

Significance. If the central claim holds, this is a significant conceptual advance: it identifies the ubiquitous threshold-like peak in heavy-jet EECs with a Sudakov-resummed, frame-boosted e+e- EEC, rather than with a local resonance structure. The paper's strengths are genuine: the symmetry derivation leading to Eqs. (3.6)-(3.13) is clean and internally consistent; the SCET factorization of Sec. 4 independently confirms the consistency of the shape-function picture; and the OPAL-boosted predictions are data-driven and falsifiable. The construction is not circular because F_EE is taken from an external Z-pole input and no parameter of the boosted peak is fitted to the pp/e+e- targets. However, the advertised 'exceptional precision' at the peak is not established: the numerical peak is dominated by the rest-frame back-to-back region, which the authors themselves describe as the most non-perturbative region, and the non-perturbative envelope used there is hand-tuned and carries no propagated uncertainty.

major comments (4)
  1. [§3.1, Eqs. (3.16)-(3.20)] The numerical 'N3LL'+NP' input is not a first-principles N3LL' prediction. Eq. (3.16) matches NLO fixed order to an N3LL' back-to-back result; Eq. (3.17) multiplies by an envelope f_NP whose transition parameters a=0.93, b=0.998 are chosen 'to ensure a smooth, kink-free interpolation', and Ω=0.32 GeV is deliberately set 'slightly larger than the best-fit results... effectively absorbing part of the missing NNLO contributions'. No uncertainty from f_NP or from the Ω shift is propagated into the final bands. Since §3.3 and Fig. 9 show the boosted peak is dominated by the rest-frame back-to-back region, where non-perturbative effects are largest, the abstract's claim that the peak is 'calculable with exceptional precision' is not supported at the peak. Please either propagate a non-perturbative-model uncertainty (e.g., over a, b, Ω, and the functional form of f_NP) or restrict the precision
  2. [§3.2, Figs. 6-8; §3.3] In the pp case, the prediction of Eq. (3.13) is not complete: the normalization N(p_T^Z) is not computed but taken from Herwig's jet p_T spectrum ('the p_T^Z distribution used to compute the blue curve was extracted from simulations using Herwig'), and the fake-Z contribution is modeled by a LO 1/χ power law with a ~4% fraction. The agreement with Herwig therefore tests the boost of the EEC shape function only after generator-dependent inputs are supplied. This should be presented as a hybrid prediction, not as a fully first-principles pp prediction, and the sensitivity to the choice of p_T spectrum and to the fake-Z model should be quantified.
  3. [§3.2, Figs. 5 and 8] The OPAL-based boosted predictions are the strongest independent check in the paper, and the agreement with event generators around the Sudakov peak is encouraging. However, the statement of 'exceptionally close agreement' overstates what is shown. The OPAL data must be interpolated before boosting, the propagated band reflects experimental uncertainties only and not interpolation systematics, and the event generators compared are tuned to Z-pole e+e- data — the same data class used to build the envelope. This comparison supports the qualitative identification of the peak with the boosted Sudakov region, but it does not validate the specific quantitative precision of the non-perturbative envelope. I recommend quantifying the interpolation uncertainty and softening the language accordingly.
  4. [Abstract and §5] The label 'N3LL' accuracy' is used for a prediction whose fixed-order component is NLO, whose non-perturbative component is the f_NP envelope model, and whose Ω parameter partially absorbs missing NNLO pieces. As written, the abstract and conclusions imply a higher accuracy than the calculation delivers. This is a load-bearing wording issue because the paper's headline is 'high precision' and 'exceptional precision'. Please replace the accuracy claims with a precise statement such as 'NLO matched to N3LL' in the back-to-back limit, plus a phenomenological non-perturbative envelope', and adjust the conclusions accordingly.
minor comments (5)
  1. [Eq. (3.26)] The text says 'eqs. (2.14) and (2.14) should be replaced'; the second reference should presumably be Eq. (2.15).
  2. [Eq. (3.18)] The definition of f_NP is hard to parse: the numerator and denominator mix a fixed-order spectrum, a Dokshitzer-model spectrum, and an NLL b2b spectrum. Please clarify the matching structure and the relation between the 'N3LL' b2b' of Eq. (3.16) and the 'NLL b2b' appearing in Eq. (3.18).
  3. [§3.3, Eq. (3.25)] The tail behavior Σ~ z^{-5/2} is stated as 'observed numerically'. If it is not proven analytically, it should be labeled as an empirical observation; if it is a theorem, a derivation or reference should be supplied.
  4. [References] Reference [65] appears as 'to appear [2601.xxxxx]' with a placeholder arXiv number. This should be completed before publication.
  5. [Captions, Figs. 3-5] Several captions describe curves with no visible legend or axis labeling in the text; in particular Fig. 3 is described as 'we plot dΣee/dθ as a function of z', which is confusing since z is used for the e+e- EEC variable and θ for the boosted angle. Please make the variable convention consistent in the captions and text.

Circularity Check

0 steps flagged

No significant circularity: the boosted-Z EEC is a Lorentz boost of an externally constrained Z-pole shape function; pp-level MC-input caveats are disclosed and do not affect the core derivation.

full rationale

The central derivation is self-contained rather than circular. The EEC shape function F_EE is defined from the Z-pole e+e- spectrum via Eq. (3.9), and the boosted predictions in Eqs. (3.12) and (3.13) are obtained by evaluating that same Lorentz-invariant shape function at the reparametrization-invariant cross ratio zbar = q^2 n1.n2 / (2 q.n1 q.n2). No parameter of the boosted peak is fitted to the pp or e+e- ZZ comparison targets; the OPAL-based boosted predictions are a direct data-to-data boost. The rest-frame input is anchored in independent external results: analytic NLO [41], N3LL' resummation [47,48], OPAL data [32], and the Dokshitzer dispersive model [46]; lattice-QCD Collins-Soper citations [26-30] are also independent. The paper's own caveats are accuracy limitations, not circularity: the NP envelope parameters a=0.93, b=0.998 are chosen for a smooth interpolation, Omega=0.32 GeV is deliberately shifted to absorb missing NNLO, and Sec. 3.3 states NP effects are largest at the peak. These weaken the 'exceptional precision' claim but do not make the derivation circular. The pp comparison does take N(p_T) from Herwig and the fake-Z fraction from the same MC, so that specific Herwig agreement is partly by construction, but the paper explicitly discloses this and the e+e- and OPAL-based checks remain independent. No circular step is found.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The paper introduces no new particles, forces, or physical entities. Its theoretical input is: (1) standard light-ray symmetry, (2) standard QCD factorization results taken from the literature, (3) the non-perturbative envelope model with hand-chosen parameters, and (4) the Herwig-supplied p_T spectrum and fake-Z fraction for the pp validation. The free parameters are concentrated in the NP envelope, the rest-frame power-correction parameter, and the pp modeling inputs — none of them are fitted to the boosted peak that the paper predicts, which is why the circularity burden is low.

free parameters (5)
  • Omega (non-perturbative power-correction parameter) = 0.32 +/- 0.05 GeV
    Universal NP parameter in the rest-frame EEC fixed-order region; set 'slightly larger than the best-fit results reported in the literature... effectively absorbing part of the missing NNLO contributions' (Sec 3.1). Enters the shape function and therefore the boosted peak.
  • f_NP interpolation parameters a, b = a = 0.93, b = 0.998
    Chosen 'to ensure a smooth, kink-free interpolation while preserving the sum rule' (Eqs. 3.18-3.20). They set the boundary between the fixed-order region and the Dokshitzer-model NP region, modulating the peak.
  • alpha_s(M_Z) = 0.118
    Standard external input used in the rest-frame spectrum; not fitted here, but controls the Sudakov normalization and hence the boosted peak height.
  • Z-jet p_T spectrum N(p_T) = Taken from Herwig 7.3 simulation
    The normalization for the pp prediction over the p_T bin is taken from Herwig, making the pp-vs-Herwig comparison partially self-referential (Sec 3.2, Figs. 6-8).
  • Fake-Z jet fraction = ~4-5% of selected jets
    Fraction of selected jets modeled as quark/gluon jets with a 1/chi EEC; estimated from the same event-generator samples used for the comparison (Sec 3.2, Fig. 7).
axioms (6)
  • standard math Reparametrization invariance of the energy-flow operator: E(rho n) = rho^{-3} E(n), forcing the EEC correlator into the form of Eq. (3.8) with a single cross-ratio z_bar.
    Light-ray operator formalism; the celestial dimension of E is fixed by the energy-momentum tensor being renormalization-group invariant. Cited to [37-39]. This is the load-bearing symmetry of the boost construction.
  • domain assumption The Z-pole e+e- EEC determines F_EE, which is q^2-independent near the on-shell limit (narrow-width approximation, Eq. 3.11).
    Uses the narrow-width limit to project q^2 -> M_Z^2, dropping the M_Z^2/q^2 dependence of F_EE. Standard for Z physics; valid since Gamma_Z/M_Z ~ 2.7%.
  • domain assumption Factorization of pp -> Z+X and e+e- -> ZZ into a production tensor x Breit-Wigner x H_EEC at leading power in M_Z/p_T and R (Eqs. 2.3, 2.14-2.15, 2.20-2.21).
    Standard hadronic/leptonic tensor factorization; neglects gamma/W interference and out-of-jet contamination at M_Z/p_T and R^2 suppression. Stated in Sec 2.1-2.2.
  • domain assumption Back-to-back EEC factorization of Moult-Zhu [49] and the N3LL' / N4LL calculations of [47,48,24].
    External results used as input for the rest-frame spectrum; not re-derived here. The paper's own numerical construction is a subtractive match (Eqs. 3.15-3.16).
  • ad hoc to paper Non-perturbative physics in the back-to-back limit is described by the Dokshitzer dispersive/gluer model and a multiplicative envelope f_NP(z) that factors from the perturbative spectrum.
    This factorization of NP effects is a modeling choice specific to this paper (Eqs. 3.17-3.18) with hand-chosen parameters; the paper states NP effects are largest at the peak (Sec 3.3).
  • domain assumption Complete Z-tagging efficiency, R large compared to the decay-product separation but small enough for R^2 power corrections, and p_T,i/p_T^Z ~= E_i/Q in the small-angle limit.
    Stated in Sec 2.1 and used to equate the pp observable with the boosted e+e- one; breaks down for R > 0.4 or p_T < 600 GeV (Sec 3.3), where the peak 'becomes misaligned'.

pith-pipeline@v1.3.0-alltime-deepseek · 6 in / 22062 out tokens · 241967 ms · 2026-08-03T07:11:25.699157+00:00 · methodology

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read the original abstract

Energy-correlator-based jet substructure has gained significant attention in recent years. One of the notable applications has been the study of multi-scale jets, where distinct physical scales manifest as features localised in different angular regions of the correlator. In this article, we present the first high-precision study of energy correlators on the simplest multi-scale jets: heavy boson jets. In such systems, the boson mass $M$ introduces an additional scale, generating a sharp peak at angles $\sim M/p_T^{\rm jet}$. We show that this feature can be computed directly by boosting the EEC spectrum measured in $e^+e^- \rightarrow {\rm hadrons}$ at the $Z$ pole. We identify that the peak arises from boosting the well-studied Sudakov factorisation governing the back-to-back limit of the two-point correlator. As a result, the feature is controlled by Sudakov resummation, not a Breit-Wigner-like structure in the $Z$ decay, and is therefore calculable with exceptional precision. We provide predictions at N$^3$LL$'$ accuracy for both $pp$ $Z$-tagged jets and $e^+e^-$ di-$Z$ production, and compare them to Herwig and Pythia simulations, finding close agreement. We also demonstrate that the boosted-$Z$ spectrum can be constructed directly by boosting OPAL measurements at the $Z$ pole. In this light, energy-correlator jet substructure on the hadronic decays of heavy bosons at the LHC provide access to clean, lepton-collider-like measurements across a wide range of effective centre-of-mass energies set by the boson jet transverse momentum.

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Reference graph

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