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arxiv: 2605.31123 · v1 · pith:GOQV2ZOGnew · submitted 2026-05-29 · ✦ hep-ph · nucl-th

Radiative Corrections to Elastic Lepton-Proton Scattering with Focus on Two-Photon-Exchange Diagrams

Daniel Crowe , Syed Mehedi Hasan , Doreen Wackeroth This is my paper

Pith reviewed 2026-06-28 22:06 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords radiative correctionstwo-photon exchangeelastic lepton-proton scatteringQEDproton form factorsNLO calculationslepton universality
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The pith

Complete next-to-leading-order QED radiative corrections to elastic lepton-proton scattering are calculated with loop-momentum-dependent form factors.

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

The paper calculates all QED radiative corrections at next-to-leading order for elastic electron-proton and muon-proton scattering. It includes the effects of two-photon-exchange diagrams that depend on the proton's internal structure through loop-momentum-dependent form factors. This goes beyond the one-photon-exchange approximation used in earlier analyses. Such corrections matter because precise scattering data are used to extract nucleon structure and test lepton universality, yet discrepancies like the proton radius puzzle persist. A full calculation allows better comparison between theory and experiment.

Core claim

We present a complete calculation of QED radiative corrections to elastic electron-proton and muon-proton scattering at next-to-leading order, taking into account loop-momentum-dependent form factors. In the discussion of their numerical impact on lepton-proton scattering cross sections, we pay special attention to the TPE diagrams and compare them with existing theoretical predictions and lepton-proton scattering data.

What carries the argument

Loop-momentum-dependent form factors incorporated into the two-photon-exchange diagrams at next-to-leading order in QED

Load-bearing premise

The modeling of two-photon-exchange diagrams relies on loop-momentum-dependent form factors whose specific functional form and input values are taken as given.

What would settle it

A precise measurement of the ratio of electron-proton to muon-proton scattering cross sections at kinematics where TPE effects are significant that does not match the calculated corrections would falsify the numerical predictions.

Figures

Figures reproduced from arXiv: 2605.31123 by Daniel Crowe, Doreen Wackeroth, Syed Mehedi Hasan.

Figure 1
Figure 1. Figure 1: FIG. 1: Elastic scattering of a lepton off a nucleon via one-photon exchange (OPE) in the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Feynman diagrams entering into the NLO QED radiative corrections to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Box diagram for lepton proton scattering [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Schematic decomposition of TPE diagrams after partial fraction, where the double [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Our results for [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Comparison of our results (with [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Comparison of our results for [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Comparison of our results for [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The TPE corrections [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: CLAS (left) and OLYMPUS (right) results for [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
read the original abstract

Lepton (electron and muon) scattering experiments are excellent tools to gain insight into the nucleon structure. Elastic electron-proton scattering probes the spatial distribution of charge and magnetization inside the proton, and comparing electron-proton and muon-proton scattering data tests lepton universality. The availability of a plethora of scattering data with increased precision and observed discrepancies such as the proton form factor puzzle and the proton radius puzzle motivated a renewed effort to improve the theoretical framework. Realizing that the one-photon-exchange approximation (OPE), i.e. the Born approximation, is not sufficient, radiative corrections in QED, especially the two-photon-exchange (TPE) diagrams, are under investigation. The TPE diagrams are of special interest among the radiative corrections, since they depend on the proton structure. In this work, we present a complete calculation of QED radiative corrections to elastic electron-proton and muon-proton scattering at next-to-leading order, taking into account loop-momentum-dependent form factors. In the discussion of their numerical impact on lepton-proton scattering cross sections, we pay special attention to the TPE diagrams and compare them with existing theoretical predictions and lepton-proton scattering data.

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

0 major / 2 minor

Summary. The manuscript presents a complete next-to-leading-order QED calculation of radiative corrections to elastic electron-proton and muon-proton scattering. It incorporates loop-momentum-dependent proton form factors into the two-photon-exchange (TPE) diagrams and evaluates the numerical impact of these corrections on cross sections, with comparisons to existing theoretical predictions and experimental data.

Significance. If the derivation holds, the work supplies an explicit NLO framework that improves upon the one-photon-exchange approximation and constant-form-factor treatments of TPE. This is directly relevant to precision extractions of nucleon structure and tests of lepton universality. The explicit dependence on external form-factor inputs is stated, allowing the community to assess sensitivity to proton-structure modeling.

minor comments (2)
  1. [Abstract] Abstract: the kinematic range (e.g., Q² interval or lepton beam energies) over which the numerical impact is evaluated is not stated; adding this would clarify the domain of applicability.
  2. The manuscript would benefit from an explicit statement, perhaps in the introduction or results section, of which specific parametrization (e.g., dipole, Kelly, or other) supplies the loop-momentum-dependent form factors used for the numerical results.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of our work, including the recommendation for minor revision. The report provides no specific major comments to address point by point.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained perturbative calculation

full rationale

The manuscript presents an explicit NLO QED calculation of radiative corrections to elastic lepton-proton scattering, with loop-momentum-dependent form factors supplied as external inputs rather than fitted or defined within the work itself. No load-bearing step reduces by construction to a self-citation, a fitted parameter renamed as a prediction, or an ansatz smuggled via prior author work; the central results are conditional on those inputs and the derivation chain remains independent of the target observables.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The calculation rests on standard QED perturbation theory and external proton form factor parametrizations whose details are not specified here.

axioms (2)
  • standard math Standard perturbative expansion of QED to next-to-leading order is valid for the kinematics considered.
    Invoked by the statement of an NLO calculation.
  • domain assumption Proton structure can be adequately captured by loop-momentum-dependent form factors in the TPE diagrams.
    Central modeling choice stated in the abstract.

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discussion (0)

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Reference graph

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