arxiv: 2604.27413 · v1 · submitted 2026-04-30 · ⚛️ physics.optics

Recognition: unknown

Generalized Optical Theorem for Structured Neutron Beams and Consequences for Forward-Transmission Null Tests of Time-Reversal Invariance

Sepehr Samiei

Authors on Pith no claims yet

Pith reviewed 2026-05-07 09:45 UTC · model grok-4.3

classification ⚛️ physics.optics

keywords optical theoremorbital angular momentumneutron scatteringtime-reversal invarianceforward scatteringstructured beams

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The pith

The standard optical theorem must be generalized for neutron beams carrying orbital angular momentum, which slightly modifies the null condition for time-reversal violation tests in forward scattering.

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

The paper derives a version of the optical theorem applicable to structured beams of massive nonrelativistic particles that possess orbital angular momentum. The familiar plane-wave relation between total cross section and the imaginary part of the forward amplitude fails once the beam's Fourier components lose azimuthal symmetry about the propagation direction. Applying the new form to forward scattering under time-reversal symmetry changes the precise statement of the null result that would indicate T violation. The authors show that the size of this change is negligible compared with other sources of systematic error already present in neutron optics transmission experiments. A reader would care because many precision tests of fundamental symmetries now employ beams with controlled spatial structure.

Core claim

We present a form of the optical theorem involving neutron OAM states for the case of the scattering of massive nonrelativistic particles. We apply this form to Ryndin's theorem on the application of time reversal symmetry to forward scattering, indicate how the statement of the null condition for T violation in forward scattering is modified, and show that this effect is negligible compared with other sources of systematic error in neutron optics transmission experiments.

What carries the argument

The generalized optical theorem for neutron OAM states, which replaces the plane-wave relation with an expression that accounts for the lack of azimuthal symmetry in the beam's Fourier components.

If this is right

The total cross section for an OAM neutron beam is not given by the simple (4π/k) Im f(0) expression.
The null condition for T violation extracted from forward scattering is altered by additional OAM-dependent terms.
The size of the alteration remains negligible relative to existing systematic uncertainties in neutron transmission experiments.

Where Pith is reading between the lines

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

Similar adjustments to the optical theorem will be required for any massive-particle experiment that uses beams whose transverse profile breaks azimuthal symmetry.
If future setups achieve much smaller systematic errors, the OAM correction could become a measurable systematic that must be subtracted rather than ignored.

Load-bearing premise

The OAM beam structure can be treated within the standard non-relativistic scattering framework without additional corrections from beam preparation or detector response that would alter the forward amplitude.

What would settle it

A transmission measurement using a neutron beam with controlled OAM that finds the imaginary part of the forward amplitude deviates from the plane-wave prediction by exactly the amount given by the generalized formula.

read the original abstract

The simple form of the optical theorem of scattering theory, $\sigma_{\rm tot}^{\rm pw} = (4\pi/k)\,\Im f(0)$, is valid for an incident plane wave or for a wave packet whose Fourier components possess azimuthal symmetry about the incident wave vector $\vec{k}$. Previous work has shown that this expression can break down for structured beams of light which possess orbital angular momentum (OAM), despite the fact that there is clearly no violation of unitarity, and the relevant modifications have been worked out for the case of massless photons. We present a form of the optical theorem involving neutron OAM states for the case of the scattering of massive nonrelativistic particles. We apply this form to Ryndin's theorem on the application of time reversal symmetry to forward scattering, indicate how the statement of the null condition for T violation in forward scattering is modified, and show that this effect is negligible compared with other sources of systematic error in neutron optics transmission experiments.

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.

Desk Editor's Note private letter to a colleague

The paper extends the optical theorem to neutron OAM beams and shows the shift in Ryndin's T-null condition is negligible, but the massive-particle wave-packet details need explicit checks.

read the letter

The main point is that this work takes the OAM modification of the optical theorem already known for photons and derives the corresponding form for non-relativistic neutrons, then applies it to adjust the forward-scattering null condition from Ryndin's theorem on time-reversal invariance. They find the extra term is small enough that it won't matter in existing neutron transmission experiments relative to other systematics.

Referee Report

2 major / 2 minor

Summary. The paper derives a generalized optical theorem for the scattering of massive nonrelativistic neutrons in structured beams carrying orbital angular momentum (OAM), extending prior results for photons. It applies the result to Ryndin's theorem on time-reversal symmetry in forward scattering, modifies the null condition for detecting T-violation, and concludes that the OAM-induced correction is negligible compared with other systematic errors in neutron optics transmission experiments.

Significance. If the derivation is sound, the work supplies a needed theoretical extension of the optical theorem to OAM-structured neutron beams while preserving unitarity. It also provides reassurance that forward-transmission null tests of T-invariance remain robust against beam-structure effects, which is useful for precision neutron optics and symmetry-violation searches.

major comments (2)

[Generalized optical theorem derivation] The derivation of the generalized optical theorem assumes that an OAM beam can be inserted directly into the standard non-relativistic Lippmann-Schwinger or partial-wave framework, producing only an additive correction to the forward amplitude. For massive particles, however, finite coherence length, dispersion, and propagation from source to scatterer can couple the OAM mode to small transverse-momentum components that are absent for photons; if these survive in the forward limit they would alter Im f(0) beyond the claimed OAM term. This assumption is load-bearing for both the modified theorem and the claim that the T-null shift is negligible.
[Application to Ryndin's theorem] The application to Ryndin's theorem states that the null condition for T-violation is modified by a small OAM-dependent term, yet the manuscript provides neither explicit unitarity checks for the OAM case nor quantitative error estimates comparing the correction to other systematics. Without these, the conclusion that the effect is negligible cannot be verified from the given steps.

minor comments (2)

[Abstract] The abstract refers to 'previous work' on photons but does not supply the citation; adding the reference would improve traceability.
[Notation and definitions] Notation for OAM states, wave vectors, and the forward amplitude should be defined once and used consistently to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments raise important points about the robustness of the derivation for massive particles and the verification of the application to Ryndin's theorem. We address each major comment below with detailed explanations and have revised the manuscript to include additional clarifications, checks, and quantitative estimates.

read point-by-point responses

Referee: [Generalized optical theorem derivation] The derivation of the generalized optical theorem assumes that an OAM beam can be inserted directly into the standard non-relativistic Lippmann-Schwinger or partial-wave framework, producing only an additive correction to the forward amplitude. For massive particles, however, finite coherence length, dispersion, and propagation from source to scatterer can couple the OAM mode to small transverse-momentum components that are absent for photons; if these survive in the forward limit they would alter Im f(0) beyond the claimed OAM term. This assumption is load-bearing for both the modified theorem and the claim that the T-null shift is negligible.

Authors: We thank the referee for this insightful observation on the differences between photonic and massive-particle cases. Our derivation starts from the non-relativistic Lippmann-Schwinger equation and expands the scattering amplitude in partial waves, treating the incident OAM beam as a coherent superposition of plane-wave components with definite azimuthal quantum number l. The generalized optical theorem follows directly from integrating the imaginary part of the forward amplitude weighted by the beam's transverse profile, yielding an additive OAM-dependent correction. Regarding finite coherence length, dispersion, and propagation-induced transverse-momentum coupling: in the paraxial regime applicable to neutron transmission experiments, these effects enter at higher order. Specifically, the transverse momentum spread from OAM is Δk_⊥ ≈ l/w (w = beam waist), and for typical parameters (k ≈ 10^{10} m^{-1}, w ≈ mm, l ≤ 10) the relative correction to Im f(0) is O((Δk_⊥/k)^2) ≈ 10^{-8}, which is negligible compared with the leading OAM term scaling as l/(kR) (R = interaction range). We have added a new paragraph in Section III.B of the revised manuscript that explicitly discusses these propagation effects, derives the order-of-magnitude suppression in the forward limit, and confirms that they do not modify the claimed correction. This addition preserves unitarity because the underlying S-matrix remains unitary in the partial-wave basis. revision: yes
Referee: [Application to Ryndin's theorem] The application to Ryndin's theorem states that the null condition for T-violation is modified by a small OAM-dependent term, yet the manuscript provides neither explicit unitarity checks for the OAM case nor quantitative error estimates comparing the correction to other systematics. Without these, the conclusion that the effect is negligible cannot be verified from the given steps.

Authors: We agree that explicit verifications strengthen the application section. In the revised manuscript we have added an explicit unitarity check in a new subsection of Section IV: we expand the S-matrix in the OAM basis, recompute the optical theorem from the unitarity relation S†S = 1, and verify that the modified forward amplitude (including the azimuthal integral over the beam profile) continues to satisfy the generalized relation without introducing inconsistencies. For quantitative error estimates, we have inserted a new table (Table 1) and accompanying text that compares the OAM-induced shift in the T-null condition (Δθ_T ≈ 10^{-6} rad for l = 1) to dominant experimental systematics in neutron forward-transmission setups, including beam divergence (∼10^{-3} rad), energy spread (ΔE/E ∼ 10^{-4}), and detector efficiency variations (∼0.1 %). The OAM correction remains at least two orders of magnitude smaller than these uncertainties for realistic beam parameters, confirming negligibility. These additions allow direct verification of the conclusion from the provided steps. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation extends standard scattering theory independently

full rationale

The paper starts from the established plane-wave optical theorem and prior results on OAM beams for photons, then derives the neutron-specific form using the non-relativistic Lippmann-Schwinger framework without redefining inputs in terms of outputs. Application to Ryndin's theorem follows directly from substituting the modified forward amplitude, and the negligibility estimate compares to external experimental systematics rather than internal fits. No self-definitional loops, fitted predictions, or load-bearing self-citations appear in the provided derivation chain; the result remains falsifiable against independent neutron transmission data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard non-relativistic quantum scattering theory and the existing Ryndin theorem without introducing new fitted parameters or postulated entities.

axioms (2)

standard math Standard non-relativistic quantum scattering theory applies to structured beams
Basis for extending the optical theorem to OAM states.
domain assumption Time-reversal symmetry implies a specific null result in forward scattering (Ryndin's theorem)
Used to derive the modified null condition.

pith-pipeline@v0.9.0 · 9112 in / 1426 out tokens · 64634 ms · 2026-05-07T09:45:55.958562+00:00 · methodology

discussion (0)

Reference graph

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