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REVIEW 1 major objections 1 minor 52 references

Odderon exchange in high-energy $K^0_S$ regeneration at the LHC

T0 review · 1 major / 1 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read The paper argues that a high-energy K0L-to-K0S regeneration experiment at the LHC can serve as a practical, independent probe of Odderon exchange, provided neutron-induced backgrounds are suppressed by one to two orders of magnitude.

desk verdict Feasibility study for LHC neutral-kaon regeneration: solid kinematics and background work, but the headline Odderon signal is a favorable-case benchmark, not a robust prediction. read the letter →

arxiv 2608.01768 v1 pith:PYEBON4F submitted 2026-08-03 hep-ph

P. Filip , M. Taševský , V. A. Khoze , R. Pasechnik , M. G. Ryskin , B. G. Zakharov This is my paper · ORCID
classification hep-ph
keywords Odderonneutral-kaonregenerationK0L-K0Smixingcrossing-oddexchangeReggetheoryLHCforwardphysicsneutron-inducedbackgroundcoherent
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

Odderon exchange is a firm prediction of QCD, but it is hard to isolate because the dominant high-energy scattering amplitude is even under charge conjugation. This paper argues that neutral-kaon regeneration—the in-matter conversion of K0L into K0S—offers an independent handle, because the regeneration amplitude is directly sensitive to the difference between kaon and antikaon scattering, i.e. to crossing-odd exchanges. It quantifies two LHC-compatible modes: coherent forward regeneration of 1–2 TeV kaons, where a benchmark 20-degree Odderon phase shifts the K0→π0π0 decay-vertex distribution by 20–40%, and non-forward regeneration at 0.2–0.8 TeV, where the Odderon could dominate a window 0.4<|t|<1 GeV^2 with a per-nucleon cross section of 0.05–0.1 microbarn. The catch is that primary K0S survival, an electromagnetic photon-exchange background, and neutron-induced neutral-only strangeness production must each be controlled; the paper gives the quantitative conditions under which the measurement would be feasible.

What carries the argument

The load-bearing object is the K0L→K0S regeneration amplitude, proportional to the difference of the forward K0 and anti-K0 scattering amplitudes in matter. Because the Odderon is a crossing-odd (C=-1) exchange, it enters this difference directly, changing both the magnitude and the phase of the regenerated amplitude. The phase shift, benchmarked at 20 degrees, interferes with the direct CP-violating K0L→ππ decay and distorts the K0→ππ decay-vertex distribution behind the regenerator; in the non-forward mode the paper computes the full amplitude as the sum of a three-gluon Odderon term, a Pomeron–Odderon cut and an omega-Reggeon term, and compares the resulting differential cross section wit

What would settle it

Measure the exclusive neutral-only reactions n + A -> Sigma0/Lambda0 + K0 and n + A -> K0 + anti-K0 on carbon and lead at neutron energies near 1.5 TeV. If the fiducial cross sections come out several times larger than the roughly 1.5 microbarn per nucleon quoted here, the 20-to-200-fold suppression needed for signal-to-background of order one is not achievable and the non-forward proposal fails. Alternatively, measure the coherent 2 TeV K0L-to-K0S regeneration phase behind a copper regenerator with a source-to-regenerator distance above 1 km; if the phase shift comes out well below 5 degrees,

Watch

Extended reading notes

Core claim

The paper's central claim is that neutral-kaon regeneration at the LHC can be developed into a practical independent Odderon measurement, and that the obstacles are quantitative rather than fatal. In the coherent forward mode at kaon energies around 2 TeV, a benchmark crossing-odd phase shift of 20 degrees would distort the K0→π0π0 decay-vertex intensity behind realistic copper, carbon or lead regenerators by 20–40% over distances of 20–150 m; with O(10^3) reconstructed decays the effect is at about the 3 sigma level, so O(10^4) decays are required. That mode, however, cannot run at the existing 140 m absorber position because 27% of 2 TeV primary K0S survive to the regenerator; a 620–650 m

Load-bearing premise

The benchmark three-gluon Odderon amplitude, with an effective gluon mass near 0.17 GeV and a 20-degree phase shift, must be a fair stand-in for the true crossing-odd amplitude at LHC energies; if the actual Odderon coupling is much smaller, has a different t-dependence, or the phase is much less than 20 degrees, the predicted signal shrinks and the measurement may be impossible.

Editorial extensions

If this is right

  • In the coherent mode, a conservative 20-degree Odderon phase produces a 20–40% distortion of the K0→π0π0 vertex distribution behind Cu, C or Pb regenerators at 2 TeV; 10^3 decays would show only about a 3 sigma effect, so 10^4 decays are needed for a definitive observation.
  • At the present 140 m source-to-regenerator distance, primary K0S from the interaction point contaminate a 2 TeV beam at the 27% level, ruling out coherent regeneration; moving to a 620–650 m forward cavern reduces that contamination to a few times 10^-3.
  • In the non-forward mode at 0.2–0.8 TeV, the Odderon-dominated window 0.4<|t|<1 GeV^2 has a per-nucleon cross section of 0.05–0.1 microbarn, 3–10 times the omega-Reggeon background at 200 GeV and much larger at 800 GeV; the signal drops sharply if the effective gluon mass is 0.7 GeV.
  • The dominant background is neutron-induced neutral-only strangeness production, roughly 1.5 microbarn per nucleon; reducing it by one to two orders of magnitude with active regenerators, forward-neutron and forward-photon tagging, and double-regenerator subtraction is the precondition for signal-to-background of order one or better.
  • The competing C=-1 photon-exchange amplitude is comparable to the Pomeron–Odderon signal in the coherent mode and must be constrained with targets of different Z/A before that mode can be interpreted as a clean Odderon measurement.

Reading between the lines

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

  • The paper does not explore this, but the predicted drop of the neutral-only strangeness yield with neutron energy means a scan in kaon momentum across 0.2–0.8 TeV could separate the energy-flat Odderon signal from the steeper omega-Reggeon background, rather than relying on a single |t| window.
  • Because the coherent mode's photon-exchange background is as large as the Odderon signal, a hydrogen-versus-lead comparison would not only subtract that C=-1 amplitude but could turn the measurement into a probe of the kaon electromagnetic form factor at forward kinematics.
  • The double-regenerator subtraction principle could be tested at existing fixed-target energies first: the relevant exclusive neutron-nucleus cross sections are measurable, and their A-dependence would determine whether the factor-of-ten amplitude-to-background ratio needed for the subtraction actually holds.
  • If the Odderon-dominated window is confirmed, neutral-kaon regeneration becomes a third class of Odderon observable beyond elastic proton scattering and rho measurements, providing a cross-check on the sign and size of the crossing-odd coupling that current fits leave uncertain.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The paper revisits the possibility of observing the Odderon via K0_L -> K0_S regeneration using high-energy neutral kaons from 13.6 TeV pp collisions at the LHC. It contains two complementary studies: (i) coherent forward regeneration at TeV energies, where the Odderon-induced regeneration phase is claimed to produce a 20–40% distortion of the K0 -> pi0 pi0 decay-vertex distribution for |Delta phi_o| = 20 degrees, but where primary-K0_S survival and a competing photon-exchange C = -1 amplitude limit the interpretation; and (ii) non-forward regeneration at 0.2–0.8 TeV, where the paper identifies an Odderon-dominated window 0.4 < |t| < 1 GeV^2 with per-nucleon signal 0.05–0.1 microbarn for an effective gluon mass m_g = 0.17 GeV, and quantifies neutron-induced and triple-Regge backgrounds. The paper concludes that the TAN baseline at L_IP = 140 m is excluded for the coherent mode, that an FPF-like distance would be needed, and that the non-forward mode requires one to two orders of magnitude background suppression, proposing an active double-regenerator subtraction strategy. Throughout, the authors are explicit that they establish feasibility conditions rather than a definitive Odderon measurement.

Significance. If the benchmark assumptions hold, the paper provides a valuable, detailed feasibility study of an independent Odderon observable, with new quantitative elements: realistic regenerator geometries with attenuation, a bin-wise primary-K0_S contamination figure of merit, an estimate of the competing electromagnetic C = -1 amplitude, and a first Monte Carlo characterization of dangerous neutron-induced neutral-only backgrounds. The paper is transparent about its model dependence and carefully distinguishes reproduced curves from new predictions. Its main value is in identifying the experimental and theoretical ingredients—background suppression, target choice, phase-benchmark sensitivity—that a future proposal would need. The quantitative non-forward signal, however, rests on a single regulator choice, and the paper itself shows that an equally motivated choice eliminates the claimed window; this weakens the robustness of the central feasibility conclusion.

major comments (1)
  1. [Section 8, Eq. (29)] Equation (29) quotes B/S ~ 20 r_n with r_n the neutron-to-K0_L flux ratio. The numerical value 20 depends on the per-nucleon background sigma_bg ~ 1.5 microbarn and on the signal 0.05–0.1 microbarn. For m_g = 0.7 GeV the signal drops by more than two orders of magnitude, so B/S becomes ~ 2000–20000 r_n, making the required suppression far more severe than the stated 'one to two orders of magnitude'. The summary and abstract should carry this caveat: the quoted suppression requirement applies only to the m_g = 0.17 GeV benchmark. Without this qualification, a reader could overestimate the robustness of the non-forward feasibility statement.
minor comments (1)
  1. [Section 8] The figure of merit in Eq. (8) is said not to be used numerically. It would be either used in the sensitivity estimate or moved to an appendix to avoid raising expectations.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the coherent-phase and non-forward-signal estimates are explicitly benchmark model inputs, not fitted predictions, and the paper disclaims independent Odderon determination.

full rationale

The paper is a conditional feasibility study, and its derivation chain does not equate any prediction to its inputs by construction. The closest candidate is the coherent-mode benchmark: Eq. (6) is fitted to the old intensities of Ref. [10], returning a 45-degree Odderon phase, and then |Delta_phi_o| = 20 degrees is adopted for the projections. But the paper explicitly states that this fit 'validates the normalisation and phase conventions of Eq. (6); it must not be interpreted as an independent determination of the Odderon phase', and it labels 20 degrees 'a conservative benchmark'. The 20-40% distortion shown in Fig. 2 is therefore the consequence of a stated model assumption, not a claim that the data require the Odderon. Similarly, the non-forward window 0.4 < |t| < 1 GeV^2 is obtained from the three-gluon amplitude Eq. (10) with m_g = 0.17 GeV; the paper itself reports that with m_g = 0.7 GeV the signal drops by more than two orders of magnitude and moves to |t| > 1 GeV^2 (Section 8), presenting the two masses as 'a deliberately broad range' of regulator uncertainty rather than as a uniquely determined value. The self-citations to Refs. [10,13] provide the phenomenological amplitude model with disclosed assumptions; they are not invoked as an external uniqueness theorem, nor is the target result assumed in order to derive itself. The Summary further limits the claim: 'a definitive proposal would require a detector-level simulation and a quantitative fit connecting the benchmark Odderon phase shift to modern constraints on the crossing-odd amplitude.' Thus the central quantitative results are transparently benchmark-dependent, but no step reduces an output to an input by construction or renames a fit as a prediction. Score 2 reflects minor reliance on self-cited model input that is not load-bearing circularity.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central numbers depend on a small set of assumed QCD inputs: the existence and perturbative form of the Odderon, the frozen coupling and infrared condition, the effective gluon mass, the quasi-eikonal parameter, and the omega-Reggeon parametrization. The paper also relies on generator-level simulations (PYTHIA/UrQMD) for backgrounds and on a simplified attenuation model. No new entities are invented. The honesty lies in labeling most of these as benchmarks, but they are still free assumptions.

free parameters (6)
  • Effective gluon mass m_g = 0.17 GeV and 0.7 GeV (two benchmarks)
    Regulates the three-gluon Odderon amplitude, Eq. (10); signal size and t-shape change by over two orders of magnitude between the two values (Sections 4, 8).
  • Frozen alpha_s (alpha_fr_s) = ~1.04
    Adjusted to satisfy the DKT infrared condition Eq. (11); enters the running-coupling integral in T_Odd.
  • Quasi-eikonal parameter C = 1 and 1.8
    Phenomenological enhancement for the Pomeron-Odderon cut, Eq. (12), following Ref [13].
  • Odderon phase benchmark Delta phi_o = 20 deg at ~1-2 TeV (45 deg in reproduction of Ref [10])
    Assumed C-odd phase distortion for coherent mode, taken from older same-group estimates; controls the projected 20-40% decay-vertex distortion (Sections 3, 8).
  • Harari omega-Reggeon parameters = g0=-19, g1=17, a=2.79 GeV^-2, b=8.78 GeV^-4, B=82 GeV^-2, alpha(0)=0.43, alpha'=0.88 GeV^-2
    From Ref [25] fit to data; contribute the competing omega-Reggeon amplitude in non-forward mode, Eqs. (13)-(14).
  • Hadron form-factor parametrization = Gaussian vs pole with radii R_N, R_K from Ref [10]
    Model uncertainty in T_Odd and T_R; explicit values not given in the text, and the spread is used as an uncertainty band.
assumptions (7)
  • domain assumption Existence of a C-odd Regge singularity (Odderon) with intercept alpha_Odd(0) ~ 1 formed by three reggeized gluons in QCD with N_c=3.
    Section 1, introduction; the entire search target is assumed to exist and couple to kaons with the perturbative three-gluon coupling.
  • domain assumption The three-gluon Odderon amplitude is given by Eq. (10) with running alpha_s and effective gluon mass m_g.
    Section 4; inherited from Refs [10,13], not independently derived or tested here.
  • domain assumption Frozen alpha_s adjusted to the DKT infrared condition Eq. (11) yields the correct infrared behavior.
    Section 4; determines the normalization of the Odderon amplitude.
  • standard math Kaon regeneration evolves as a two-state quantum system with optical potential Eq. (4) and a common attenuation factor Eq. (5).
    Section 2.1; standard formalism, though with simplified common attenuation for K0_L and K0_S.
  • domain assumption The omega-Reggeon contribution is described by the Harari model Eqs. (13)-(14) with parameters from Ref [25].
    Section 4; used for the competing C-odd background.
  • domain assumption PYTHIA 8.3 and UrQMD provide reliable order-of-magnitude rates for exclusive neutral-only strangeness production (25)-(26).
    Section 7.1; authors call these diagnostics and state a final estimate requires detector-level simulation.
  • domain assumption Primary K0_S flux at the regenerator follows Eq. (17) with equal K0_S and K0_L production at the interaction point.
    Section 6; contamination estimates rely on this survival formula and epsilon_S^0 ~ 1.

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Cite this review

Pith. "Pith review of Odderon exchange in high-energy $K^0_S$ regeneration at the LHC." pith.science (2026). https://pith.science/paper/PYEBON4F

@misc{pith2026260801768,
  author       = {Pith},
  title        = {Pith review of: Odderon exchange in high-energy $K^0_S$ regeneration at the LHC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PYEBON4F}},
  note         = {Machine review of arXiv:2608.01768}
}
abstract

We revisit the possibility of detecting the Odderon exchange through high-energy neutral-kaon regeneration, focusing on the in-matter $K^0_L\to K^0_S$ conversion of $(\sim\!0.2-2)$~TeV $K^0_L$ mesons originating from $pp$ collisions at $\sqrt{s}=13.6$~TeV, and on the practical constraints of realizing such a measurement in the very-forward region of an LHC interaction point. The analysis has two complementary parts. First, we reproduce the original coherent-forward-regeneration estimates for a liquid-hydrogen regenerator and extend them to realistic C, Cu and Pb regenerators of an LHC-compatible geometry, including neutral-kaon attenuation. We show that an Odderon-induced regeneration phase produces a measurable distortion of the $K^0\to\pi^0\pi^0$ decay-vertex distribution at TeV kaon energies, but that the survival of primary $K^0_S$ mesons from the interaction point imposes severe baseline requirements, while a competing electromagnetic $C=-1$ (photon-exchange) amplitude limits the interpretation of the coherent mode as a clean Odderon measurement. Second, we examine non-forward (diffractive) regeneration at lower kaon energies of $0.2-0.8$~TeV, where the primary-$K^0_S$ contamination is naturally suppressed, and estimate the competing Odderon, Pomeron--Odderon-cut, $\omega$-Reggeon and photon-exchange contributions to the regeneration amplitude. We identify neutron-induced neutral-only strangeness production and inelastic Regge backgrounds as the dominant limitations, quantify the background suppression required for an observable Odderon signal, and formulate the ingredients of an active double-regenerator subtraction strategy.

Figures

Figures reproduced from arXiv: 2608.01768 by the authors.

Figure 1
Figure 1. The ratio of the ππ decay intensity behind the regenerator to that without a regenerator, I±(τ ), for an LH2 regenerator of several lengths. The ratio is shown for 2 TeV kaons as a function of the kaon proper time τ in units of the K0 S mean lifetime τS, without the K0 absorption in the LH2 regenerator (our curves are to be compared with [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. The ratio of the ππ decay intensity with a regenerator to that without a regenerator, I±(∆X), calculated for 500 GeV and 2 TeV kaons as a function of the distance of the ππ decay vertex from the regenerator, for Cu, Pb and C regenerators, with the effect of K0 absorption included. The ratios without (with) the Odderon exchange are shown by the full (dashed) curves. the authors of Ref. [10] obtained from their own mo… view at source ↗
Figure 3
Figure 3. Predictions for the non-forward K0 S regeneration cross section on protons for three values of the K0 L momentum and two values of the effective gluon mass, using Gaussian form factors. The red curve shows the cross section due to the ω-Reggeon contribution alone; the black and green curves show the predictions for the full amplitude (TOdd + TP ⊗Odd + TR) for C = 1 and C = 1.8, respectively. here, together with the … view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: PYTHIA 8.3 particle-level information from [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Momentum dependence of the coherent regeneration amplitude [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: UrQMD estimate of the yields of the (semi)exclusive neutral-only re [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Predictions of the cross section (as a function of [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: Odderon amplitudes for the non-forward regeneration of [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]

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