Determination of the Odderon amplitude in elastic cross-sections at high energies from scaling and analyticity

B. G. Giraud; C. Royon; J. A. velazquez Corral; R. Peschanski

REVIEW 3 major objections 2 minor 1 cited by

A scaling-plus-analyticity method isolates the Odderon amplitude from LHC and Tevatron elastic data and predicts the pbar-p cross section without free parameters.

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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Scaling plus analyticity applied to TOTEM pp data yields the Odderon amplitude in modulus and phase, with a parameter-free pbar-p prediction matching D0.

T0 review reviewed 2026-07-14 challenge →

load-bearing objection Abstract-only: they extract Odderon modulus and phase from the TOTEM dip residual after a Pomeron scaling fit, then give a parameter-free pbar-p prediction matching D0; the residual-as-Odderon step is load-bearing and uncheckable here. the 3 major comments →

arxiv 2607.11286 v1 pith:DBVNFISP submitted 2026-07-13 hep-ph hep-exnucl-exnucl-th

Determination of the Odderon amplitude in elastic cross-sections at high energies from scaling and analyticity

J. A. velazquez Corral , B. G. Giraud , R. Peschanski , C. Royon This is my paper

classification hep-ph hep-exnucl-exnucl-th PACS 13.85.Dz11.55.Jy12.40.Nn

keywords OdderonPomeronelastic scatteringscaling amplitudeanalyticitydip-bump regionTOTEMD0

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.

The reading

The paper argues that a scaling form already known to describe proton-proton elastic scattering in the dip-bump region at LHC energies also holds for the highest-energy Tevatron proton-antiproton data. Using the standard S-matrix relation that converts energy dependence into the phase of a fixed-signature amplitude, the authors construct the positive-signature (Pomeron) scaling amplitude. A fit of that amplitude to TOTEM proton-proton differential cross sections leaves a residual tension in the dip. That residual is attributed to a negative-signature (Odderon) contribution whose phase is fixed by the same analyticity relation. The resulting Odderon term yields a parameter-free prediction for the proton-antiproton differential cross section that matches D0 measurements, and it allows the Odderon amplitude itself to be extracted in both modulus and phase.

Core claim

A negative-signature (Odderon) amplitude can be isolated in the dip-bump region so that, once its phase is fixed by the energy-to-phase analyticity relation, it produces a parameter-free prediction for the pbar-p differential cross section that agrees with D0, while the same amplitude is extracted in both modulus and phase from the residual tension with TOTEM pp data.

What carries the argument

The energy-to-phase analyticity relation for a fixed-signature amplitude (the Chew relation of S-matrix theory). It converts the measured energy dependence of a scaling amplitude into a unique phase, thereby separating the positive-signature Pomeron from the negative-signature Odderon without additional free parameters.

Load-bearing premise

The leftover mismatch between the pure positive-signature scaling amplitude and the TOTEM dip data is entirely due to a negative-signature Odderon whose phase is fixed by the standard analyticity relation, rather than by other missing even-signature dynamics or experimental systematics.

What would settle it

A new high-precision measurement of the pp or pbar-p differential cross section in the dip-bump region that either restores agreement with a pure positive-signature scaling amplitude or yields a residual whose phase and energy dependence cannot be absorbed by a single Chew-fixed Odderon term.

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

If this is right

The Odderon contribution to elastic scattering is fixed in both modulus and phase once the Pomeron scaling amplitude is known.
The same construction supplies a parameter-free prediction for any future pbar-p differential cross section in the dip-bump region.
Differences between pp and pbar-p elastic cross sections at high energy are quantitatively accounted for by a single analytic Odderon amplitude.
The scaling form verified for both pp and pbar-p can be used as a template for further amplitude analyses at higher LHC energies.

Where Pith is reading between the lines

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

If the extracted Odderon phase is confirmed, it supplies a concrete target for QCD-inspired models of three-gluon exchange in the non-perturbative regime.
The method can be reapplied to forthcoming TOTEM or ATLAS elastic data at 13–14 TeV to test whether the Odderon modulus continues to follow the same scaling.
A similar residual analysis applied outside the dip-bump region would reveal whether the Odderon contribution is localized or persists at larger momentum transfers.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Abstract-only: they extract Odderon modulus and phase from the TOTEM dip residual after a Pomeron scaling fit, then give a parameter-free pbar-p prediction matching D0; the residual-as-Odderon step is load-bearing and uncheckable here.

read the letter

The one thing to know is that this paper claims a concrete Odderon amplitude—modulus and phase—from the residual in the TOTEM pp dip after fitting a positive-signature scaling form, then uses that residual to predict the pbar-p differential cross section at Tevatron energies with no free parameters, in agreement with D0. That is the result they are selling.

What is actually new is the extraction step itself. They start from a recently derived scaling amplitude for pp, check that the highest-energy Tevatron pbar-p data obey the same scaling, fix the Pomeron piece with the classical Chew energy-to-phase relation from S-matrix analyticity, fit TOTEM, and attribute the leftover tension in the dip to a negative-signature piece. If that residual is genuinely Odderon and the phase relation applies cleanly, you get both a modulus and a phase plus a falsifiable pbar-p curve. That is a useful, focused move in a subfield that has been arguing about TOTEM–D0 comparisons for years. Credit for tying scaling, signature, and the dip-bump region into one parameter-free prediction rather than another multi-parameter model.

The soft spot is exactly that residual attribution, and it is real but not automatically fatal. Without the full text we cannot inspect fit quality, error treatment, or whether other C-even dynamics, experimental systematics, or incompleteness of the scaling form could account for the same residual. Circularity is moderate: under their framing the Odderon is largely what the Pomeron fit leaves behind, then used to predict pbar-p. A referee has to pressure that step. Everything else—analyticity, the scaling check—is standard machinery applied in a clear way on the abstract’s face. The stress-test concern is the same soft spot; nothing stronger is visible from the abstract alone.

This is for people working on high-energy elastic scattering, soft QCD, and the Odderon debate. It is not a field-reorganizing paper, but it is sharp enough and methodologically transparent enough that a serious editor should send it to referees rather than desk-reject. I would not cite from the abstract alone, but I would want the full paper in front of a competent referee.

Referee Report

3 major / 2 minor

Summary. The manuscript argues that scaling amplitudes previously derived for pp elastic scattering in the dip-bump region at LHC energies also describe the highest-energy Tevatron pbar-p differential cross-section. Using the Chew energy-to-phase analyticity relation for a fixed signature, the authors construct the positive-signature (Pomeron) scaling amplitude, fit it to TOTEM pp data, and report residual tension in the experimental dip. Concentrating on the dip/bump region, they attribute that residual to a negative-signature (Odderon) contribution, obtain a parameter-free prediction for the pbar-p differential cross-section that is stated to agree with D0, and extract the Odderon amplitude in both modulus and phase.

Significance. If the residual-to-Odderon attribution is justified and the Chew phase relation is applied without hidden assumptions about the energy dependence of the scaling amplitude, the work would provide a largely parameter-free determination of the Odderon contribution to high-energy elastic scattering, with a concrete, falsifiable pbar-p prediction reported to match D0. The explicit use of S-matrix analyticity and scaling is a methodological strength when those assumptions hold. Only the abstract is available for this review, so fit quality, error treatment, quantitative size of the residual, and the detailed phase extraction cannot be assessed; significance therefore remains conditional on verification of those load-bearing steps in the full text.

major comments (3)

[Abstract] The central claim that residual tension between the Pomeron-only scaling fit and TOTEM pp data in the dip is dominated by a negative-signature Odderon (rather than incomplete C-even dynamics, scaling-form incompleteness, or experimental systematics) is load-bearing for the subsequent parameter-free pbar-p prediction and for the Odderon modulus/phase extraction. The abstract states the attribution but does not quantify the residual, show alternative C-even tests, or demonstrate that systematics are subdominant. Without that demonstration the Odderon identification and the D0 agreement remain conditional.
[Abstract] The prediction for pbar-p is described as parameter-free once the Odderon is fixed from the pp residual. That residual is defined only after a Pomeron scaling-amplitude fit to TOTEM pp data, so the free parameters of that fit enter the residual by construction. The abstract does not state how many free parameters the Pomeron fit carries, whether they are fixed before the dip residual is interpreted, or how fit-parameter uncertainties propagate into the Odderon amplitude and the pbar-p prediction. Clarifying this chain is necessary for the 'parameter-free' claim to be assessable.
[Abstract] Application of the Chew energy-to-phase relation to the scaling amplitude is essential for separating positive- and negative-signature components and for extracting the Odderon phase. The abstract invokes the relation but does not specify the energy dependence assumed for the scaling amplitude, the domain of t over which the phase is taken as fixed by that relation, or any test that the same phase relation is consistent with both the TOTEM and D0 kinematics. A concrete statement of those assumptions is required for the phase extraction to be reproducible.

minor comments (2)

[Abstract] The abstract cites prior work for the scaling amplitudes and for the Chew relation but does not name the quantitative figure of merit (e.g., chi-squared per degree of freedom or residual size in the dip) that defines the reported 'tension' with TOTEM; that metric should be stated when the full text is available.
[Abstract] Notation for 'scaling amplitude' versus the full complex amplitude (modulus and phase) should be made explicit early, so that the step from fitted |A| to phase via analyticity is unambiguous to non-specialists.

Circularity Check

0 steps flagged

Abstract-only review: no verifiable circular reduction can be exhibited from the available text.

full rationale

Only the abstract is available, so no equations, fit procedures, residual definitions, or self-citation chains can be inspected for a concrete reduction (Eq. X = Eq. Y by construction, or a fitted parameter renamed as a prediction). The abstract describes a standard sequential program: adopt a previously derived scaling form for pp, check it on pbar-p, use the Chew energy-to-phase relation to isolate the positive-signature (Pomeron) amplitude, fit that form to TOTEM pp data, attribute residual dip tension to a negative-signature (Odderon) piece, and thereby obtain a parameter-free pbar-p prediction compared to D0. That narrative is not, by itself, a definitional tautology; whether the residual is free of other C-even dynamics or systematics, and whether the Chew phase is applied without hidden assumptions, are correctness/assumption questions, not circularity that can be quoted from the abstract. Per the hard rules, circularity is claimed only when a specific reduction can be exhibited with a quote; none can. Score 0 with empty steps is the honest outcome for an abstract-only review.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

Central claim rests on a prior scaling amplitude (external to this abstract), the classical S-matrix energy-to-phase relation for definite signature, and a phenomenological fit of the positive-signature piece to TOTEM. The Odderon is not invented here but is identified with the residual after that fit. Free parameters are those of the Pomeron scaling form fitted to pp data; no new particle or force is postulated.

free parameters (1)

Pomeron scaling-amplitude fit parameters (to TOTEM pp)
Abstract states that fitting the positive-signature scaling amplitude to TOTEM differential cross-sections produces tension in the dip; those fit parameters are free numbers fixed by pp data and then held when predicting pbar-p.

axioms (3)

domain assumption S-matrix analyticity implies a definite energy-to-phase relation for a given signature amplitude (Chew).
Invoked explicitly to derive the positive-signature (Pomeron) scaling amplitude phase and to fix the Odderon phase from energy dependence.
domain assumption The previously derived scaling form for elastic amplitudes in the dip-bump region applies to both LHC pp and Tevatron pbar-p.
Abstract checks that Tevatron pbar-p obeys the same scaling; the whole extraction inherits that scaling ansatz from the cited prior work.
ad hoc to paper Residual mismatch of the Pomeron-only fit in the dip is dominated by a negative-signature Odderon contribution rather than other missing dynamics or systematics.
This identification converts fit tension into an Odderon amplitude; it is a modeling choice load-bearing for the central claim.

reviewed 2026-07-14 · how reviews work

0 comments

Cite this review

Pith. "Pith review of Determination of the Odderon amplitude in elastic cross-sections at high energies from scaling and analyticity." pith.science (2026). https://pith.science/paper/DBVNFISP

@misc{pith2026260711286,
  author       = {Pith},
  title        = {Pith review of: Determination of the Odderon amplitude in elastic cross-sections at high energies from scaling and analyticity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DBVNFISP}},
  note         = {Machine review of arXiv:2607.11286}
}

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abstract

Scaling amplitudes describing $pp$ elastic scattering differential cross-sections in the dip-bump region of momentum transfer at the LHC have been recently derived~\cite{scaling}. We check that the same scaling is verified by the $p\bar p$ cross-section at the highest energy of the Tevatron. Applying the general "energy to phase" relation for a given signature, coming from the analiticity properties inherent to the S-Matrix formalism~\cite{chew}, we derive the scaling amplitude with positive signature (i.e. the Pomeron). Fitting the $pp$ differential cross-sections measured by the TOTEM collaboration leads to some tension with data in the experimental dip observed at moderate momentum transfer. Concentrating the study to the dip/bump region, we are able to determine a contribution of a negative signature amplitude (i.e. the Odderon) leading to a parameter free prediction for the $p\bar p$ differential cross-section which is in agreement with the D0 data. The extraction of the Odderon amplitude in both modulus and phase is then performed and discussed.

discussion (0)

Forward citations

Cited by 1 Pith paper

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

Geometric Scaling and the Odderon
hep-ph 2026-07 conditional novelty 5.0

A geometric-scaling model with a crossing-odd amplitude and a maximal-Odderon correction can reproduce low-energy rho data and accommodate the TOTEM 13 TeV rho_pp measurement.

This paper was first reviewed by grok-4.5 on July 14, 2026.

Determination of the Odderon amplitude in elastic cross-sections at high energies from scaling and analyticity

The reading

Core claim §

What carries the argument

Load-bearing premise §

What would settle it §

If this is right

Where Pith is reading between the lines

discussion (0)

Core claim

Load-bearing premise

What would settle it