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arxiv: 2606.20327 · v1 · pith:KEGCOJK2new · submitted 2026-06-18 · ✦ hep-ph · hep-ex

Theory Calculations for LDMX and LOHENGRIN beyond Coherent Bethe-Heitler Scattering

Martin Sch\"urmann , Herbert K. Dreiner , Rhorry Gauld This is my paper

Pith reviewed 2026-06-26 16:44 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords dark photonsLDMXLOHENGRINBethe-Heitlerbremsstrahlungincoherent scatteringdiffractive scatteringmissing momentum
0
0 comments X

The pith

Calculations beyond coherent Bethe-Heitler scattering show limited effects on dark photon signals for LDMX and LOHENGRIN, except requiring HCAL extension for LOHENGRIN.

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

This paper computes the differential cross sections for all real emission processes contributing to dark photon production in electron-nucleus scattering, going beyond the usual coherent Bethe-Heitler approximation by including incoherent and diffractive channels from nuclei and nucleons. It incorporates couplings to both electrons and hadrons and accounts for virtual contributions as well. The results indicate that with realistic experimental selections, these additional processes have only a limited effect on the predicted signal and background rates in the MeV to GeV dark photon mass range. However, for the LOHENGRIN experiment, diffractive scattering backgrounds necessitate an extension of its hadronic calorimeter to maintain effective vetoing. A sympathetic reader would care because precise background modeling is essential for the sensitivity of missing-momentum searches for light dark matter.

Core claim

The central claim is that the contributions beyond coherent Bethe-Heitler scattering, including scattering off nuclear constituents and diffractive processes, have only a limited effect on the predicted signal and background in the relevant dark photon mass range when realistic experimental selections are applied. The LOHENGRIN experiment will require an extension of its HCAL to effectively veto background processes from diffractive scattering.

What carries the argument

Differential cross sections for real emission processes up to third order in the electromagnetic fine structure constant and fourth order in the kinetic mixing parameter, including incoherent and diffractive contributions from target nucleus and constituents.

If this is right

  • The LOHENGRIN experiment requires an extension of its HCAL to veto diffractive scattering backgrounds.
  • Contributions beyond coherent Bethe-Heitler have limited effect on signal and background predictions for LDMX and LOHENGRIN under realistic cuts.
  • Virtual dark photon contributions are considered but do not alter the limited impact conclusion.
  • Signal characteristics of the recoiling electron remain largely as in coherent approximation.

Where Pith is reading between the lines

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

  • This implies that coherent-only calculations may suffice for approximate sensitivity estimates in similar experiments.
  • Extensions to other phase space regions or higher energies could reveal larger effects from these processes.
  • Precise inclusion of these terms could improve background rejection strategies in future dark matter searches.

Load-bearing premise

The phase space regions and experimental constraints are assumed sufficient to capture all relevant contributions, and the truncation at third order in the fine-structure constant and fourth in kinetic mixing misses no altering effects.

What would settle it

An experimental observation of diffractive scattering background rates in LOHENGRIN that cannot be vetoed without HCAL extension, or a calculation showing significant changes in signal efficiency from higher-order terms outside the considered orders.

read the original abstract

The Light Dark Matter eXperiment (LDMX), DarkSHINE, and LOHENGRIN are proposed new experiments. They aim to search for missing momentum signals sourced by the direct production of dark photons with masses in the MeV-GeV range in bremsstrahlung processes, in which an electron beam of a few GeV scatters off a fixed target. So far, the signal characteristics, i.e. the behavior of the recoiling electron, have mostly been studied in coherent Bethe-Heitler electron-nucleus scattering with a dark photon that couples only to the Standard Model charged leptons. In this work, we present the calculations of the differential cross sections of all contributing real emission processes up to third order in the electromagnetic fine structure constant and fourth order in the kinetic mixing parameter associated with the dark photon. We consider a dark photon coupling to both the beam electron and the hadronic target and we take into account the scattering off both the target nucleus and its nuclear constituents. Besides real emission processes, we also discuss virtual dark photon contributions and their relevance for the signal prediction. After discussing the different phase space regions and constraints emerging from the experimental setups, we show numerical results of the cross sections and differential distributions, including the signal and dominant background. Within our framework, we find that the LOHENGRIN experiment will require an extension of its HCAL to effectively veto background processes originating from diffractive scattering. Apart from that, the contributions beyond coherent Bethe-Heitler scattering, in the presence of realistic experimental selections, have only a limited effect on the predicted signal and background in the relevant dark photon mass range.

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 paper calculates differential cross sections for real emission processes in dark photon production via electron bremsstrahlung off nuclei up to O(α³, ε⁴), including coherent/incoherent and leptonic/hadronic channels with a dark photon coupling to both electrons and hadrons. It also discusses virtual contributions and, after applying experimental phase-space constraints for LDMX, DarkSHINE and LOHENGRIN, concludes that beyond-coherent-Bethe-Heitler effects have only limited impact on signal and background in the relevant mass range, except that LOHENGRIN requires an HCAL extension to veto diffractive-scattering backgrounds.

Significance. If the order truncation and phase-space coverage are complete, the work supplies a more systematic perturbative input for background modeling in missing-momentum dark-photon searches, directly informing the design of the LOHENGRIN veto system and the robustness of sensitivity projections for all three experiments. The explicit treatment of nuclear constituents and higher-order real emissions is a concrete advance over the coherent Bethe-Heitler approximation used in prior studies.

major comments (1)
  1. [virtual contributions and numerical results sections] The central claim that beyond-coherent-Bethe-Heitler contributions have only limited effect (except for the LOHENGRIN HCAL recommendation) rests on the completeness of the retained O(α³, ε⁴) real-emission and virtual terms. The discussion of virtual contributions does not quantify their size relative to the kept orders inside the exact LOHENGRIN phase space after experimental selections; if O(ε⁶) interference or O(α⁴) processes become non-negligible in the diffractive or high-missing-momentum tails, both the limited-effect statement and the veto recommendation could shift.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and for recognizing the systematic treatment of higher-order contributions as an advance over prior coherent Bethe-Heitler approximations. We address the single major comment below. We agree that explicit quantification of virtual terms inside the precise post-selection LOHENGRIN phase space was not provided and will strengthen that discussion in revision.

read point-by-point responses

  1. Referee: [virtual contributions and numerical results sections] The central claim that beyond-coherent-Bethe-Heitler contributions have only limited effect (except for the LOHENGRIN HCAL recommendation) rests on the completeness of the retained O(α³, ε⁴) real-emission and virtual terms. The discussion of virtual contributions does not quantify their size relative to the kept orders inside the exact LOHENGRIN phase space after experimental selections; if O(ε⁶) interference or O(α⁴) processes become non-negligible in the diffractive or high-missing-momentum tails, both the limited-effect statement and the veto recommendation could shift.

    Authors: We acknowledge that while the manuscript discusses virtual dark-photon contributions and their relevance (Section on virtual contributions), it does not supply explicit numerical ratios of O(ε⁶) or O(α⁴) terms relative to the retained O(α³, ε⁴) real-emission channels after the full LOHENGRIN experimental selections. Power counting indicates that O(ε⁶) interference is suppressed by an extra ε² (with ε ≲ 10^{-2}–10^{-3} in the probed range) and O(α⁴) by an additional factor of α ≈ 1/137, rendering both negligible even in the diffractive or high-missing-momentum tails relative to the leading terms. Nevertheless, we agree that a dedicated estimate inside the exact phase space would strengthen the central claim. In the revised manuscript we will add a short paragraph (or appendix) providing order-of-magnitude estimates for these higher-order pieces under the LOHENGRIN cuts, confirming that they remain below the percent level and do not alter the limited-impact conclusion or the HCAL-extension recommendation. No new calculations are required; the estimates follow directly from the existing coupling and phase-space analysis already presented. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit perturbative cross-section calculations independent of fitted inputs or self-citation chains

full rationale

The paper computes differential cross sections for real emission and virtual processes up to O(α³ ε⁴) from first-principles QED matrix elements, incorporating coherent/incoherent scattering off nuclei and constituents, then applies experimental phase-space cuts to obtain numerical signal/background distributions. No step reduces a prediction to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness claim, or renames an empirical pattern; the limited-effect conclusion follows directly from the truncated perturbative results under the stated selections. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Abstract-only review limits visibility into specific parameters or assumptions; the work rests on standard perturbative QED and the dark-photon model without new fitted quantities or entities introduced in the provided text.

axioms (2)
  • standard math Perturbative expansion of QED processes up to third order in the fine-structure constant
    Invoked to compute real emission cross sections
  • domain assumption Kinetic mixing between the dark photon and the ordinary photon
    Standard modeling assumption for dark-photon phenomenology
invented entities (1)
  • Dark photon no independent evidence
    purpose: Mediator particle carrying missing momentum in electron scattering
    Postulated within the dark-photon model; no new independent evidence supplied

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Reference graph

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