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arxiv: 2604.11967 · v1 · submitted 2026-04-13 · ✦ hep-ph · hep-th

Recognition: 2 theorem links

· Lean Theorem

Operator structure of power corrections and anomalous scaling in energy correlators

Hao Chen , Yibei Li
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:45 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords energy correlatorspower correctionsanomalous dimensionslight-ray operatorsQCDoperator mixingjet physics
0
0 comments X

The pith

The dijet operator in energy correlators must mix with a triple-jet operator to produce the observed universal anomalous scaling of linear power corrections.

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

This paper uses light-ray operators to trace the origin of universal anomalous scaling in linear power corrections of energy-energy correlators. An explicit one-loop calculation determines the anomalous dimension and shows that the dijet operator alone is insufficient; it must be combined with a specific triple-jet component. This structure explains the scaling behavior from first principles in quantum field theory. A reader would care because it grounds phenomenological power corrections in operator mixing, enabling better theoretical control over non-perturbative effects in collider data.

Core claim

Through an explicit loop calculation, the one-loop anomalous dimension of the relevant operators is derived, revealing that the dijet operator must be combined with a specific triple-jet component to capture the power corrections in the energy-energy correlator.

What carries the argument

Light-ray operators that encode the non-perturbative power corrections and their mixing under renormalization, specifically the combination of dijet and triple-jet operators.

If this is right

  • The universal anomalous scaling is a direct consequence of this operator mixing.
  • This provides a framework to connect operator theory directly to high-precision collider phenomenology.
  • The approach can be extended to other energy correlators and power correction terms.
  • Predictions for the scaling behavior can be tested against experimental measurements at colliders.

Where Pith is reading between the lines

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

  • Similar operator mixing structures may appear in higher-order power corrections or multi-particle correlators.
  • Data from energy correlators could be used to extract the coefficients of these operators more precisely.
  • Extensions to other processes like deep inelastic scattering might reveal analogous anomalous dimensions.

Load-bearing premise

The light-ray operator approach fully captures all non-perturbative power corrections without missing contributions from other operators or higher-order effects.

What would settle it

A higher-loop calculation or precise experimental measurement of the energy correlator that deviates from the predicted anomalous scaling would falsify the claim that this operator combination is sufficient.

Figures

Figures reproduced from arXiv: 2604.11967 by Hao Chen, Yibei Li.

Figure 1
Figure 1. Figure 1: FIG. 1: A schematic illustration of the leading power [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Comparison of the leading power correction to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Energy correlators offer a clean probe of quantum chromodynamics, serving as an ideal laboratory to rigorously investigate non-perturbative power corrections. The recent discovery that linear corrections exhibit a universal anomalous scaling points to a deep, underlying theoretical structure. We uncover the quantum field-theoretic origin of this phenomenon in the energy-energy correlator using light-ray operators. Through an explicit loop calculation, we derive the one-loop anomalous dimension, revealing that the dijet operator must be combined with a specific triple-jet component. This provides a first-principles framework that connects operator theory with high-precision collider phenomenology.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates the operator structure of power corrections in energy-energy correlators using light-ray operators in QCD. Through an explicit one-loop calculation, it derives the anomalous dimension and shows that the dijet operator must mix with a specific triple-jet component to account for the universal anomalous scaling of linear power corrections.

Significance. If the loop calculation and operator basis are complete, the work supplies a first-principles QFT derivation of the recently observed universal scaling, directly linking operator mixing to collider observables. The explicit computation of the one-loop mixing matrix is a clear strength, offering a parameter-free result rather than a fit.

major comments (1)
  1. [one-loop calculation of the anomalous dimension] The one-loop mixing calculation: the central claim that the dijet operator combined with the specified triple-jet component produces the universal anomalous dimension assumes the chosen light-ray operators form a closed basis. The manuscript does not demonstrate that contributions from additional higher-twist or multi-parton operators (such as four-jet configurations or alternative collinear structures) are absent or do not mix at one loop. If such operators contribute to the same power-suppressed terms, the reported anomalous dimension would be incomplete and the connection to universal scaling would not hold.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recognizing the value of the explicit one-loop calculation. We address the major comment below.

read point-by-point responses

  1. Referee: [one-loop calculation of the anomalous dimension] The one-loop mixing calculation: the central claim that the dijet operator combined with the specified triple-jet component produces the universal anomalous dimension assumes the chosen light-ray operators form a closed basis. The manuscript does not demonstrate that contributions from additional higher-twist or multi-parton operators (such as four-jet configurations or alternative collinear structures) are absent or do not mix at one loop. If such operators contribute to the same power-suppressed terms, the reported anomalous dimension would be incomplete and the connection to universal scaling would not hold.

    Authors: We agree that a demonstration of basis closure is necessary to support the central claim. The operator basis in the manuscript is constructed from the twist expansion appropriate to linear power corrections in the energy-energy correlator, restricting to dijet and triple-jet light-ray operators that match the collinear scaling and quantum numbers of the observable. At one-loop order, four-jet and higher configurations are excluded from mixing into the linear term by color factors, momentum conservation, and the fact that they generate only quadratic or higher power corrections in the back-to-back limit. We will add a short subsection that enumerates the possible additional operators and shows explicitly why their one-loop matrix elements do not contribute to the reported anomalous dimension. This clarification will be included in the revised version. revision: partial

Circularity Check

0 steps flagged

No circularity: explicit one-loop derivation from light-ray operators

full rationale

The paper's central claim is an explicit one-loop calculation of the anomalous dimension for the dijet operator mixing with a triple-jet component in the energy-energy correlator. No load-bearing step reduces to a self-definition, a fitted parameter renamed as prediction, or a self-citation chain that is itself unverified. The derivation is presented as first-principles QFT computation; the 'recent discovery' of universal scaling is treated as external motivation rather than an input that forces the result. The operator basis completeness is an assumption open to external falsification, not a circular closure. This is the normal non-circular outcome for a loop-level operator mixing calculation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

No free parameters or new entities are mentioned in the abstract. The work relies on standard assumptions in perturbative QCD and operator product expansions.

axioms (2)
  • domain assumption Energy correlators can be described using light-ray operators in QCD
    The method used to investigate the power corrections.
  • standard math Perturbative loop calculations yield the anomalous dimensions of these operators
    The one-loop calculation is the core of the derivation.

pith-pipeline@v0.9.0 · 5382 in / 1436 out tokens · 115251 ms · 2026-05-10T15:45:39.671559+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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matches
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supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
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unclear
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Forward citations

Cited by 1 Pith paper

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

  1. Hydrodynamics and Energy Correlators

    hep-ph 2026-04 unverdicted novelty 6.0

    Energy-energy correlators in heavy-ion collisions exhibit classical hydrodynamic scaling from collective flow at large angles within the small-angle regime, collective modes at smaller angles, and light-ray OPE at eve...

Reference graph

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