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arxiv: 1907.08942 · v1 · pith:CRK7ICM3new · submitted 2019-07-21 · ✦ hep-ph · hep-ex

Searching for odderon in exclusive reactions: p p to p p p {bar p}, p p to p p φ φ and p p to p p φ

Antoni Szczurek , Piotr Lebiedowicz This is my paper

Pith reviewed 2026-05-24 18:52 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords odderonexclusive processespomeronLHCWA102phi meson productionC-odd exchange
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0 comments X

The pith

Three exclusive proton-proton reactions are proposed as sources of information on odderon exchange.

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

The paper argues that the processes pp to p p p p-bar, pp to p p phi phi, and pp to p p phi can isolate signals of C = -1 odderon exchange that are hard to separate in elastic scattering data taken at mismatched energies. It sketches the formalism for each reaction, reexamines existing low-energy data from the WA102 experiment, and offers predictions for LHC kinematics where odderon contributions might become visible against Pomeron background. A sympathetic reader would care because confirmation of the odderon would complete the picture of high-energy Regge exchanges and test whether C-odd gluonic degrees of freedom participate in diffractive production.

Core claim

The central claim is that the three listed exclusive reactions can serve as a source of information for odderon exchange because their kinematics and particle content allow the C-odd contribution to be distinguished from the dominant C-even Pomeron exchange; the authors sketch the relevant amplitudes, apply them to WA102 data, and extrapolate to LHC energies.

What carries the argument

Odderon exchange amplitudes in the t-channel of the exclusive reactions, treated alongside Pomeron exchange in a Regge-inspired formalism.

If this is right

  • Low-energy WA102 data can be reinterpreted to place limits on odderon strength in phi production.
  • LHC measurements of these exclusive channels would provide independent evidence for or against the odderon seen in elastic scattering analyses.
  • If observed, the odderon would appear in both four-body and two-body final states with characteristic interference patterns.

Where Pith is reading between the lines

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

  • Similar exclusive channels with other vector mesons could be added to enlarge the data set for odderon searches.
  • The approach could be extended to central exclusive production at lower energies to test energy dependence of the odderon intercept.

Load-bearing premise

Odderon contributions can be cleanly isolated from Pomeron and other exchanges in the kinematics and energies considered.

What would settle it

Measurement at the LHC showing that the cross sections or angular distributions for the three processes remain consistent with pure Pomeron exchange and exhibit no excess attributable to C-odd exchange.

Figures

Figures reproduced from arXiv: 1907.08942 by Antoni Szczurek, Piotr Lebiedowicz.

Figure 1
Figure 1. Figure 1: The “Born level” diagrams for double-pomeron/reggeon central exclusive φφ production and their subsequent decays into K +K −K +K − in proton-proton collisions. In (a) we have the continuum φφ production, in (b) φφ production via an f2 resonance. Other resonances, e.g. of f0- and η-type, can also contribute here. Let us sketch the formalism to descibe the conventional processes. For the f2φφ vertex we take … view at source ↗
Figure 2
Figure 2. Figure 2: The Born level diagrams for diffractive production of a φ-meson pair with one and two odderon exchanges. Our ansatz for the effective propagator of C = −1 odderon follows [9] i∆ (O) µν (s,t) = −igµν ηO M2 0 (sα ′ O) αO(t)−1 , (2.4) αO(t) = αO(0) +α ′ O t , (2.5) where we have M−2 0 = 1 (GeV)−2 for dimensional reasons. Furthermore, we shall assume repre￾sentative values for the odderon parameters ηO = −1, α… view at source ↗
Figure 3
Figure 3. Figure 3: Some diagrams included in the analysis of single φ production. 2.3 pp → pppp¯ Several mechanisms of central pp¯ production were discussed in [7] and the formalism how to calculate relevant diffractive processes (continuum and resonances) was given there. The exchange of C = -1 objects leads to specific asymmetries discussed in [7]. In two dimen￾sions (e.g. η1,η2) we can define the asymmetry: Ae(2) (η,η ′ )… view at source ↗
Figure 4
Figure 4. Figure 4: Invariant mass distributions for the central production of φφ at √ s = 29.1 GeV and |xF,φφ| 6 0.2 together with the WA102 data [11] are shown. The black long-dashed line corresponds to the φ-exchange contribution and the black dashed line corresponds to the f2(2340) contribution. The black dot-dashed line corresponds to the γ-exchange contribution enlarged by a factor 103 . The red dotted line represents t… view at source ↗
Figure 5
Figure 5. Figure 5: The distributions in M4K (the left panels) and in Ydiff (the right panels) for the pp → pp(φφ → K +K −K +K −) reaction calculated for √ s = 13 TeV and |ηK| < 2.5, pt,K > 0.2 GeV. The red and blue solid lines correspond to the complete results with ηO = −1 and ηO = +1, respectively. The results for bPOφ = 1.0 GeV−1 (the top panels) and for bPOφ = 1.5 GeV−1 (the bottom panels) are presented. The absorption e… view at source ↗
Figure 6
Figure 6. Figure 6: The complete results for √ s = 13 TeV and |ηK| < 2.5, pt,K > 0.2 GeV are shown. Here we show results for ηO = −1 and for various values of the odderon intercept αO(0). Here we take aPOφ = 0 and bPOφ = 1 GeV−1 . Odderon could be visible for Mφφ > 6 GeV and/or for Ydi f f > 3. η −2 −1 0 1 2 ) η ( pp A −0.02 −0.01 0 0.01 0.02 pp → pp p , p s = 13 TeV ATLAS kinematics Λoff,E = 1 GeV η 2 2.5 3 3.5 4 4.5 ) η ( p… view at source ↗
Figure 7
Figure 7. Figure 7: Allowed asymmetry for pp¯ production due to odderon-pomeron exchange for ATLAS and LHCb kinematics. [5] E. Martynov and B. Nicolescu, Phys. Lett. B778, 414 (2018). [6] P. Lebiedowicz, O. Nachtmann and A. Szczurek, Phys. Rev. D99, 094034 (2019). [7] P. Lebiedowicz, O. Nachtmann and A. Szczurek, Phys. Rev. D97, 094027 (2018). [8] P. Lebiedowicz, O. Nachtmann and A. Szczurek, a paper in preparation. [9] C. Ew… view at source ↗
read the original abstract

There seem to be recently an evidence for $C =$ -1 exchanges in $p p$ and $p \bar p$ elastic scattering at high energies. The analysis there is difficult as the two processes were not measured at the same (large) energies. Here we discuss three different exclusive processes given in the title as a possible source of information for odderon exchange. A sketch of the formalism is presented for each of the reactions. We consider low energy processes measured in the past by the WA102 collaboration and try to make predictions for the LHC. We discuss possible evidences at the low energies and try to make suggestions for the LHC.

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

2 major / 2 minor

Summary. The manuscript proposes three exclusive proton-proton reactions (pp → p p p p-bar, pp → p p ϕ ϕ, and pp → p p ϕ) as potential sources of information on odderon (C = -1) exchange. It sketches the Regge-theory formalism (amplitudes, propagators, and vertices) for each process, references low-energy WA102 data for qualitative discussion, and offers suggestions for isolating odderon effects at LHC energies.

Significance. If the sketched formalisms can be extended to explicit calculations demonstrating separable odderon contributions, the paper would provide useful guidance for experimental searches at the LHC, complementing the difficult analysis of elastic pp vs p p-bar scattering at mismatched energies.

major comments (2)
  1. [Formalism sketches for the three reactions] The central claim that these processes allow isolation of odderon exchange rests on the sketched formalisms, but no explicit differential cross sections, interference terms between C = -1 and Pomeron amplitudes, or kinematic windows are derived or tabulated for any of the three reactions (see the formalism sketches in the sections following the abstract).
  2. [Low-energy processes and WA102 references] The discussion of WA102 low-energy data references existing measurements but does not compute or show the energy dependence or observables that would establish separability from Pomeron background, leaving the extrapolation to LHC unverified.
minor comments (2)
  1. [Title] The title notation 'p p p {bar p}' is nonstandard; use consistent LaTeX for p p p p-bar throughout.
  2. [Abstract] The abstract states 'there seem to be recently an evidence' without citing the specific elastic-scattering analyses; add references.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below, clarifying the scope of the work while agreeing where additional clarification or discussion can improve the presentation.

read point-by-point responses

  1. Referee: [Formalism sketches for the three reactions] The central claim that these processes allow isolation of odderon exchange rests on the sketched formalisms, but no explicit differential cross sections, interference terms between C = -1 and Pomeron amplitudes, or kinematic windows are derived or tabulated for any of the three reactions (see the formalism sketches in the sections following the abstract).

    Authors: The manuscript is conceived as an exploratory proposal that outlines three exclusive reactions and sketches the Regge-theory amplitudes (including the structure of C = -1 exchanges) to indicate in principle how odderon contributions could be isolated. Explicit numerical evaluation of differential cross sections, full interference terms, or tabulated kinematic windows lies outside the stated scope, which is limited to sketching the formalism and referencing existing low-energy data. We agree that adding a short discussion of possible kinematic regions or qualitative interference patterns derivable from the sketched amplitudes would make the isolation argument more concrete. We will revise the relevant sections to include such guidance without performing new full calculations. revision: partial

  2. Referee: [Low-energy processes and WA102 references] The discussion of WA102 low-energy data references existing measurements but does not compute or show the energy dependence or observables that would establish separability from Pomeron background, leaving the extrapolation to LHC unverified.

    Authors: The WA102 references are used only to provide qualitative context for possible odderon signals observed at lower energies in exclusive channels. No new energy-dependent calculations or separability studies are performed, consistent with the paper's focus on proposing the reactions and sketching the formalism rather than carrying out a global phenomenological analysis. We acknowledge that a quantitative extrapolation to LHC energies would require additional work. In revision we will make the qualitative character of the WA102 discussion explicit and note how the sketched amplitudes could serve as input for future separability studies. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation uses external WA102 data and sketched formalism without reduction to inputs

full rationale

The manuscript sketches amplitudes, Regge propagators and vertex factors for the three listed exclusive channels, references external WA102 low-energy data as input, and extrapolates to LHC kinematics. No equations, fitted parameters or self-citations are exhibited that reduce any claimed prediction or isolation of the C = -1 term to the paper's own inputs by construction. The central claim therefore remains independent of the patterns that would trigger a circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central suggestion rests on the domain assumption that odderon exchange is present and distinguishable in the listed reactions; no free parameters or new invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Odderon exchange contributes measurably to the listed exclusive reactions at LHC energies
    The paper's proposal for using these processes as a source of information presupposes that the odderon signal can be isolated.

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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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Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · 1 internal anchor

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