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REVIEW 4 major objections 6 minor 37 references

Higher order electroweak radiative corrections in lepton-proton scattering using covariant approach

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that quadratic and reducible two-loop electroweak corrections shift the parity-violating asymmetry in elastic lepton-proton scattering by up to several parts per billion, bringing theory into agreement with Qweak and P2…

desk verdict A genuine first calculation of quadratic/reducible two-loop corrections to PV ep/µp scattering, but with unquantified same-order omissions and an overbroad significance claim. read the letter →

arxiv 2507.22097 v1 pith:SZPOW43P submitted 2025-07-29 hep-ph hep-th

Mahumm Ghaffar , Aleksandrs Aleksejevs , Svetlana Barkanova This is my paper · ORCID
classification hep-phhep-th
keywords electroweakradiativecorrectionsparity-violatingasymmetrylepton-protonscatteringNNLOtwo-loopcovariantapproachsoft-photonbremsstrahlungQweakP2experiment
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

This paper computes higher-order electroweak radiative corrections to the parity-violating asymmetry in elastic lepton-proton scattering, going beyond the one-loop level to include quadratic and reducible two-loop contributions (NNLO) in a covariant approach. The authors find these NNLO corrections are sizable at the low-energy kinematics of existing and proposed experiments, shifting the asymmetry by up to several parts per billion. They show that including these terms brings their computed asymmetry into good agreement with the measured Qweak value and the proposed P2 projection. The paper argues that these corrections therefore have to be included in precision searches for physics beyond the Standard Model.

What carries the argument

The central mechanism is the covariant approach of Bardin and Shumeiko, which gives a factorized amplitude-squared built from a contracted leptonic tensor $L_{\mu\nu}$ and hadronic tensor $W_{\mu\nu}$, allowing infrared divergences from vertex corrections to be cancelled analytically by adding soft-photon bremsstrahlung contributions. The NNLO leptonic tensor is constructed from quadratic one-loop graphs and reducible two-loop graphs, with all Passarino-Veltman integrals evaluated numerically using LoopTools; the same tensor machinery also provides one-loop hadronic self-energy corrections attached to the hadronic side.

What would settle it

Complete the electroweak box-diagram contribution using the methods of the cited references and compute the hard-photon bremsstrahlung cross section, then check whether the total NNLO $A_{PV}$ changes by more than the size of the quadratic and two-loop corrections; also verify numerically that the result is unchanged when the soft-photon cutoff $\Delta E = 0.05\sqrt{s}$ is varied.

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Extended reading notes

Core claim

The central claim is that the parity-violating asymmetry $A_{PV}$ in elastic lepton-proton scattering receives significant NNLO electroweak corrections from quadratic one-loop terms and reducible two-loop diagrams, and that these corrections must be included to match the precision of current and future experiments such as Qweak, P2, MOLLER, MUSE, and the EIC. Using a covariant approach that separates the leptonic and hadronic tensors, the authors compute the corrected asymmetry for electron-proton and muon-proton scattering. Their final NNLO results are $-221.19$ ppb at Qweak kinematics compared with the measured $-226.5 \pm 7.3 \pm 5.8$ ppb, and $-65.09$ ppb at P2 kinematics compared with the proposed $-67.34$ ppb.

Load-bearing premise

The calculation assumes the omitted electroweak box diagrams and hard-photon bremsstrahlung do not shift the asymmetry by as much as the computed quadratic and two-loop terms, and that the soft-photon cutoff choice does not bias the infrared-finite result.

Editorial extensions

If this is right

  • The total NNLO corrected asymmetry at Qweak kinematics is roughly $-221.19$ ppb, within about 5 ppb of the measured central value, with the quadratic and reducible two-loop terms together shifting the one-loop result by about 4 ppb at that angle.
  • At P2 kinematics the computed NNLO value of $-65.09$ ppb is close to the proposed target of $-67.34$ ppb, giving a concrete benchmark for the upcoming measurement.
  • The paper provides tables of tree, NLO, and NNLO $A_{PV}$ values for MOLLER, EIC, and MUSE kinematics, usable as signal predictions or background estimates for those programs.
  • Because the NNLO contributions are as large as several ppb while future experiments aim at sub-ppb precision, the paper concludes these corrections must be included in searches for physics beyond the Standard Model.

Reading between the lines

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

  • If the omitted electroweak box diagrams and hard-photon bremsstrahlung shift $A_{PV}$ by an amount comparable to the computed quadratic and two-loop terms, the quoted agreement with Qweak and P2 could move by a few ppb; completing the box calculation, which the authors identify as their next step, would settle this.
  • The same leptonic-tensor machinery should extend naturally to a polarized proton target and inelastic kinematics, and the authors indicate those directions; the structure-function decomposition is target-agnostic apart from the hadronic form factors.
  • The near-equal percentage corrections for electron and muon scattering in MUSE kinematics suggest lepton-universality tests will be sensitive mainly to the remaining box-diagram terms rather than to the computed NNLO contributions.
  • If future P2 data fall closest to one of the intermediate values in Table III, the soft-photon cutoff choice $\Delta E = 0.05\sqrt{s}$ could be pinned down empirically, effectively turning this cutoff from a residual uncertainty into a fixed parameter of the calculation.
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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

4 major / 6 minor

Summary. The paper calculates parity-violating asymmetries in elastic lepton-proton scattering (ep and mu p) using a covariant leptonic-tensor approach, including tree-level, one-loop (NLO), quadratic, and reducible two-loop (NNLO) electroweak corrections. Numerical results are presented for the kinematics of Qweak, P2, MOLLER, EIC, and MUSE experiments. The authors report that their total NNLO asymmetry agrees with the Qweak measurement and the P2 proposal, and they conclude that the NNLO corrections are significant enough to be included in future BSM searches. The manuscript explicitly states that electroweak box diagrams and hard-photon bremsstrahlung are not included, with box diagrams deferred to a separate paper.

Significance. If the calculation were complete and validated, it would provide a useful extension of one-loop electroweak corrections to parity-violating lepton-proton scattering, with direct relevance to the Qweak, P2, MOLLER, MUSE, and EIC programs. The work uses standard automated tools (FeynArts, FormCalc, FeynCalc, LoopTools), keeps the lepton mass, and does not fit any parameter to the asymmetry data used for comparison; the Qweak and P2 comparisons are after-the-fact consistency checks. The main significance hinges on the size of the new NNLO terms relative to experimental precision, which is exactly where the paper's evidence is incomplete.

major comments (4)
  1. [Sec. VI and Conclusions] The central quantitative claim is not yet supported because the calculation omits the gamma-Z box diagrams and hard-photon bremsstrahlung. The text states 'we need to account boxes and hard photon bremsstrahlung cross-section' and defers the gauge-invariant box set to a separate paper, but no numerical estimate of the size of these omitted contributions is given. The gamma-Z box is a one-loop correction to A_PV and is therefore needed already at NLO, not only at NNLO; hard bremsstrahlung is needed to remove the dependence of the soft-photon results on the arbitrary cut Delta-E = 0.05 sqrt(s). Since the computed NNLO shift beyond NLO is only 0.05 ppb at P2 kinematics (Table III), even a small omitted contribution can change the conclusion.
  2. [Sec. III, Eq. (15)-(17); Sec. VI] There is no benchmark of the NLO results against the existing complete one-loop calculations cited in refs. [10]-[15], and the 19 NLO and 21 quadratic structure functions r_i and n_i are not given in the paper or in an ancillary file. The plots in Figs. 5 and 8 show only a subset of these functions. Without a benchmark or explicit expressions, the numerical results cannot be independently checked; this matters because the final ppb-level NNLO statements rely on cancellations among large corrections of about 30%.
  3. [Tables III-IV and Eq. (29)] The quantity called the 'NNLO correction percentage' delta_2_APV is defined relative to the tree-level asymmetry and therefore includes the full NLO correction; it does not measure the size of the new NNLO terms. The incremental NNLO effect is +0.05 ppb at P2 kinematics (one-loop -65.14 ppb, total -65.09 ppb in Table III), far below the projected 0.56 ppb precision, while at Qweak it is -4.08 ppb (one-loop -217.11 ppb, total -221.19 ppb in Table I). The statement that NNLO corrections 'have to be included' is therefore overstated for P2 and should be rephrased in terms of the incremental NNLO shift with an uncertainty estimate.
  4. [Sec. V, Eqs. (26)-(27), Fig. 15] The infrared cancellation at NNLO is asserted analytically, but the only numerical demonstration of cancellation of the photon-mass regulator lambda is shown for the NLO MUSE case in Fig. 15. No numerical scan over lambda or over the soft-photon cutoff Delta-E = 0.05 sqrt(s) is presented for the quadratic and reducible two-loop results. Since Eq. (27) involves both delta_SP and delta_SP^2, a stability test over Delta-E is needed to show that the reported NNLO asymmetries are IR finite and cut independent.
minor comments (6)
  1. [Sec. VII] The quoted Qweak NNLO asymmetry, -221.46 ppb, does not match Table I, which gives -221.19 ppb at theta_lab = 7.9 degrees; please correct and unify the value.
  2. [Sec. I and Sec. VI B] The P2 target asymmetry is given as -39.94 ppb in the introduction and -67.34 ppb in Sec. VI B; clarify which angle and Q^2 each number corresponds to.
  3. [Tables I-XIV] The column label 'Qud-APV' should be spelled out as 'Quadratic-APV' for clarity, and the tables should state explicitly that all entries are in ppb unless otherwise noted.
  4. [Appendix B] The form-factor notation C_i is introduced but the index i is not defined; additionally, 'Sach' should be 'Sachs' in Sec. II.
  5. [Eq. (20)] The relation between h_i and H_i appears to have a dimension problem because of the factor 1/q^2, and the connection to the truncated self-energy is not derived; please clarify this equation.
  6. [Fig. 15] The solid line is claimed to be the IR-finite sum, but no values of the photon-mass parameter lambda are shown; please state the range of lambda over which the cancellation was tested.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NNLO asymmetry calculation is self-contained and uses no fitted inputs or load-bearing self-citations.

full rationale

The paper's central numerical claim is a direct fixed-order calculation of the parity-violating asymmetry A_PV from the Standard Model electroweak Lagrangian, with proton electromagnetic and weak form factors taken from established parametrizations (dipole form factors, Eq. (6), and the standard weak-form-factor relation Eq. (10)). No parameter is fitted to the Qweak, P2, MOLLER, MUSE, or EIC observables that are used for comparison; the experimental values enter only as after-the-fact benchmark points. The NNLO correction percentages quoted in Tables II, IV, VI, VIII, X, XII, and XIV are defined by Eq. (29) relative to the paper's own tree-level result, so they are not circular predictions. The cited prior work by the same authors (refs. [7], [17]-[21]) concerns Moller scattering and is used as methodological background, not as an unverified premise that forces the elastic l-p result. The manuscript explicitly identifies the missing gamma-Z box diagrams and hard-bremsstrahlung contributions (Sec. VI: "we need to account boxes and hard photon bremsstrahlung cross-section"; Sec. III: boxes "will be discussed in a separate paper") and the soft-photon cut is fixed at Delta_E = 0.05 sqrt(s) without a stability study; these are completeness and systematic-uncertainty concerns, not circularity, because the reported numbers do not build those omitted terms in by construction. The derivation chain from Feynman diagrams to leptonic and hadronic tensors to the asymmetry is presented as an independent calculation, with IR cancellation tested at NLO (Fig. 15) and the NNLO IR treatment specified in Eqs. (26)-(27). There is therefore no step in which the output is equivalent to an input by definition or in which a fitted input is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The calculation relies on standard SM inputs and measured form factors; the only hand-set quantities are the dipole scale, the soft-photon cut, and the zero strangeness. The most consequential 'axiom' is the exclusion of box diagrams and hard bremsstrahlung, which the authors disclose but do not quantify.

free parameters (3)
  • Dipole form factor scale Lambda = sqrt(0.83 m_p)
    Used in the dipole parameterization of the proton and neutron electromagnetic form factors (Appendix B); fitted to elastic scattering data, not to the asymmetry being predicted.
  • Soft photon energy cut delta-E = 0.05 sqrt(s)
    Energy threshold for including soft bremsstrahlung; chosen in Section VI, affects results because hard photon emission is not included.
  • Strange quark axial contribution delta_s = 0
    Set to zero in the axial form factor G_A^Z (Section IV); an external assumption from other measurements, not fitted here.
assumptions (6)
  • domain assumption Standard Model with on-shell renormalization
    Assumed as the theoretical framework for the electroweak corrections (Section III).
  • domain assumption Factorization of the amplitude into leptonic and hadronic tensors (covariant approach)
    Used to compute the squared amplitude via contraction of tensors; valid for the selected graphs but excludes box diagrams (Sections II, III).
  • domain assumption Soft photon approximation in bremsstrahlung
    The emitted photon four-momentum is dropped in the numerator; standard but only valid for photon energies below delta-E (Section V).
  • domain assumption Dipole approximation for proton and neutron form factors
    Adopted in Appendix B; a model that may introduce uncertainty at the small Q^2 of Qweak/P2, though widely used.
  • ad hoc to paper Neglect of box diagrams and hard photon bremsstrahlung
    The paper explicitly states these are deferred; this is a necessary assumption for the presented NNLO numbers to represent the complete NNLO correction, which they do not.
  • domain assumption Unpolarized proton target and no strange quark contribution
    The proton is unpolarized and delta_s is set to zero (Section II); both are stated simplifications.

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Cite this review

Pith. "Pith review of Higher order electroweak radiative corrections in lepton-proton scattering using covariant approach." pith.science (2026). https://pith.science/paper/SZPOW43P

@misc{pith2026250722097,
  author       = {Pith},
  title        = {Pith review of: Higher order electroweak radiative corrections in lepton-proton scattering using covariant approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SZPOW43P}},
  note         = {Machine review of arXiv:2507.22097}
}
read the original abstract

We perform detailed calculations of electroweak radiative corrections to parity violating lepton scattering with a proton target up to quadratic and reducible two-loop level using a covariant approach. Our numerical results are presented at energies relevant for a variety of existing and proposed experimental programs such as Qweak, P2, MOLLER, MUSE, and experiments at the EIC. Analysis shows that such corrections at the Next-to-Next-to-Leading Order (NNLO) are quite significant and have to be included in searches of physics beyond the standard model, matching the increasing precision of the future experimental programs at low-energy scales.

Figures

Figures reproduced from arXiv: 2507.22097 by the authors.

Figure 1
Figure 1. FIG. 1. Tree-level Feynman diagrams for lepton-proton ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Tree-level electroweak leptonic diagram in case [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. One-loop level electroweak leptonic tensor diagram [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (21 more)
Figure 7
Figure 7. Figure 7: FIG. 7. Quadratic level electroweak graphs obtained by [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Examples of self-energy and vertex correction dia [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Quadratic level leptonic tensor structure functions [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Example of contributions coming in reducible two-loop level electroweak leptonic tensor. [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Splitting of the reducible two-loop level diagram into a single loop one at each end of the leptonic and hadronic sides. [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Tree-level electroweak hadronic diagrams with off [PITH_FULL_IMAGE:figures/full_fig_p007_11.png]
Figure 14
Figure 14. Figure 14: FIG. 14. One-loop level electroweak bremsstrahlung process [PITH_FULL_IMAGE:figures/full_fig_p008_14.png]
Figure 13
Figure 13. Figure 13: FIG. 13. NLO level electroweak hadronic tensor structure [PITH_FULL_IMAGE:figures/full_fig_p008_13.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Test for IR-divergence cancellation using MUSE [PITH_FULL_IMAGE:figures/full_fig_p009_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Treatment of IR divergence at reducible two-loop level by including [PITH_FULL_IMAGE:figures/full_fig_p010_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Treatment of IR divergence due to the product of vertex and self-energy graphs at quadratic level by including [PITH_FULL_IMAGE:figures/full_fig_p010_17.png]
Figure 18
Figure 18. Figure 18: FIG. 18. SPB treatment for IR divergence in quadratic NNLO photon vertex-squared contribution. This includes the sum of [PITH_FULL_IMAGE:figures/full_fig_p011_18.png]
Figure 20
Figure 20. Figure 20: FIG. 20. P2 kinematics: Tree level (dotted line), NLO level [PITH_FULL_IMAGE:figures/full_fig_p011_20.png]
Figure 21
Figure 21. Figure 21: FIG. 21. MOLLER kinematics: Tree level (dotted line), NLO [PITH_FULL_IMAGE:figures/full_fig_p012_21.png]
Figure 22
Figure 22. Figure 22: FIG. 22. EIC kinematics: Tree level (dotted line), NLO level [PITH_FULL_IMAGE:figures/full_fig_p012_22.png]
Figure 23
Figure 23. Figure 23: FIG. 23. MUSE ( [PITH_FULL_IMAGE:figures/full_fig_p012_23.png]
Figure 26
Figure 26. Figure 26: FIG. 26 [PITH_FULL_IMAGE:figures/full_fig_p013_26.png]
Figure 27
Figure 27. Figure 27: FIG. 27. P2 kinematics: Tree+NLO [PITH_FULL_IMAGE:figures/full_fig_p014_27.png]
Figure 29
Figure 29. Figure 29: FIG. 29. EIC kinematics at [PITH_FULL_IMAGE:figures/full_fig_p015_29.png]
Figure 30
Figure 30. Figure 30: FIG. 30. MUSE kinematics for [PITH_FULL_IMAGE:figures/full_fig_p016_30.png]
Figure 31
Figure 31. Figure 31: FIG. 31. MUSE kinematics for [PITH_FULL_IMAGE:figures/full_fig_p016_31.png]

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Works this paper leans on

37 extracted references · 32 canonical work pages

  1. [10]

    Accardi et al., Electron-ion collider: The next qcd frontier - understanding the glue that binds us all, Eur

    A. Accardi et al., Electron-ion collider: The next qcd frontier - understanding the glue that binds us all, Eur. Phys. J. A 52, 268 (2016)

    work page 2016

  2. [15]

    W. J. Marciano and A. Sirlin, Some general properties of the o(α) corrections to parity violation in atoms, Phys. Rev. D 29, 75 (1984)

    work page 1984

  3. [1]

    (17) where n1−21 are the quadratic leptonic structure func- tions and are calculated using the FormCalc and Loop- Tools packages

    Quadratic NNLO level electroweak leptonic tensor The electroweak quadratic leptonic tensor ( LQD µν ) ob- tained in this way has the following form: LQD µν = n1gµν + n2k2µk1ν + n3k1µk2ν + n4ϵs1,µ,ν,k1 + n5ϵs1,µ,ν,k2 +n6ϵµ,ν,k1,k2 +n7k2µs1ν+n8k2νs1µ+n9k2µk2ν+ n10ϵs1,µ,k1,k2 k2,ν + n11ϵs1,ν,k1,k2 k2µ + n12k1νk1µ+ n13ϵµ,ν,k2,k1 + n14s1νk1µ + n15s1µk1ν + n16ϵ...

    work page

  4. [2]

    ¯u(k2)(˙ιeγβ) × ml + /k1 − /kγ (k1 − kγ)2 − m2 l (˙ιeγα)u(k1) # ϵ∗ α(kγ), (MZ in,SP B)β =

    Reducible two-loop level electroweak leptonic tensor Another way of obtaining the electroweak radiative corrections which are of the order of α4 is by multiply- ing the tree-level diagram with the reducible two-loop graphs. Such graphs include a double self-energy and a vertex correction attached with a self-energy diagrams, as shown in Fig.[9]. The lepto...

    work page arXiv

  5. [3]

    T. D. Lee and C. N. Yang, Question of parity conserva- tion in weak interactions, Phys. Rev. 104, 254 (1956)

    work page 1956

  6. [4]

    C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson, Experimental test of parity conservation in beta decay, Phys. Rev. 105, 1413 (1957)

    work page 1957

  7. [5]

    First Determination of the Weak Charge of the Proton

    D. Androic et al. (Qweak), First Determination of the Weak Charge of the Proton, Phys. Rev. Lett.111, 141803 (2013), arXiv:1307.5275 [nucl-ex]

    work page Pith review arXiv 2013

  8. [6]

    The Q_weak Experimental Apparatus

    T. Allison et al. (Qweak), The Q weak experimental apparatus, Nucl. Instrum. Meth. A 781, 105 (2015), arXiv:1409.7100 [physics.ins-det]

    work page Pith review arXiv 2015

Show all 37 references
  1. [7]

    Androi´ c, D

    D. Androi´ c, D. Armstrong, A. Asaturyan, T. Averett, J. Balewski, K. Bartlett, J. Beaufait, R. Beminiwattha, J. Benesch, F. Benmokhtar, J. Birchall, R. Carlini, J. Cornejo, S. Dusa, M. Dalton, C. Davis, W. Deconinck, J. Diefenbach, J. Dowd, and S. Zhamkochyan, Precision measu...

    2019

  2. [8]

    Becker et al., The p2 experiment - a future high- precision measurement of the weak mixing angle at low momentum transfer, Eur

    D. Becker et al., The p2 experiment - a future high- precision measurement of the weak mixing angle at low momentum transfer, Eur. Phys. J. A 54, 208 (2018)

    2018

  3. [9]

    Aleksejevs, S

    A. Aleksejevs, S. Barkanova, A. Ilyichev, and V. Zykunov, Electroweak radiative corrections for polarized Moller scattering at future 11 GeV JLab exper- iment, Phys. Rev. D 82, 093013 (2010), arXiv:1008.3355 [hep-ph]. 19

    2010 arXiv

  4. [11]

    Gilman et al

    R. Gilman et al. (MUSE), Technical Design Report for the Paul Scherrer Institute Experiment R-12-01.1: Studying the Proton ”Radius” Puzzle with µp Elastic Scattering, (2017), arXiv:1709.09753 [physics.ins-det]

    2017 arXiv

  5. [12]

    Musolf and T

    M. Musolf and T. Donnelly, The interpretation of parity-violating electron-scattering experiments, Nuclear Physics A 546, 509 (1992)

    1992

  6. [13]

    Musolf and B

    M. Musolf and B. R. Holstein, Electroweak corrections to parity-violating neutral current scattering, Physics Let- ters B 242, 461 (1990)

    1990

  7. [14]

    M. J. Musolf and B. R. Holstein, Observability of the anapole moment and neutrino charge radius, Phys. Rev. D 43, 2956 (1991)

    1991

  8. [16]

    A. V. Afanasev and N. P. Merenkov, Large logarithms in the beam normal spin asymmetry of elastic electron- proton scattering, Phys. Rev. D 70, 073002 (2004)

    2004

  9. [17]

    Akushevich, A

    I. Akushevich, A. Ilyichev, and N. M. Shumeiko, Qed ra- diative effects in the processes of exclusive photon elec- troproduction from polarized protons with the next-to- leading accuracy, Phys. Rev. D 90, 033001 (2014)

    2014

  10. [18]

    Czarnecki and W

    A. Czarnecki and W. J. Marciano, Electroweak radiative corrections to polarized mo/ller scattering asymmetries, Phys. Rev. D 53, 1066 (1996)

    1996

  11. [19]

    Aleksejevs, S

    A. Aleksejevs, S. Barkanova, A. Ilyichev, Y. Kolomensky, and V. Zykunov, One-loop electroweak corrections for polarized Moller scattering at different renormalization schemes and conditions, Phys. Part. Nucl.44, 161 (2013), arXiv:1010.4185 [hep-ph]

    2013 arXiv

  12. [20]

    A. G. Aleksejevs, S. G. Barkanova, and V. A. Zykunov, Precise calculations of observables of polarized Moller scattering: From JLAB to ILC energies, Phys. Atom. Nucl. 75, 209 (2012)

    2012

  13. [21]

    Aleksejevs, S

    A. Aleksejevs, S. Barkanova, Y. Kolomensky, E. Kuraev, and V. Zykunov, Quadratic electroweak corrections for polarized møller scattering, Phys. Rev. D 85, 013007 (2012)

    2012

  14. [22]

    Aleksejevs, S

    A. Aleksejevs, S. Barkanova, Y. Bystritskiy, A. Ilyichev, E. Kuraev, and V. Zykunov, Parity violating moller scat- tering asymmetry up to the two-loop level, (2012)

    2012

  15. [23]

    Aleksejevs, S

    A. Aleksejevs, S. Barkanova, and V. Zykunov, Two-loop effects in low-energy electroweak measurements, Nuclear and Particle Physics Proceedings 273-275, 2259 (2016), 37th International Conference on High Energy Physics (ICHEP)

    2016

  16. [24]

    Bardin and N

    D. Bardin and N. Shumeiko, On an exact calculation of the lowest-order electromagnetic correction to the point particle elastic scattering, Nuclear Physics B 127, 242 (1977)

    1977

  17. [25]

    Afanasev, I

    A. Afanasev, I. Akushevich, V. Burkert, and K. Joo, Qed radiative corrections in processes of exclusive pion elec- troproduction, Phys. Rev. D 66, 074004 (2002)

    2002

  18. [26]

    Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput

    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140, 418 (2001), arXiv:hep-ph/0012260

    2001 arXiv

  19. [27]

    Hahn and M

    T. Hahn and M. P´ erez-Victoria, Automated one-loop cal- culations in four and d dimensions, Computer Physics Communications 118, 153 (1999)

    1999

  20. [28]

    Shtabovenko, R

    V. Shtabovenko, R. Mertig, and F. Orellana, FeynCalc 9.3: New features and improvements, Comput. Phys. Commun. 256, 107478 (2020), arXiv:2001.04407 [hep- ph]

    2020 arXiv

  21. [29]

    Gorchtein, Beam normal spin asymmetry in the quasireal compton scattering approximation, Phys

    M. Gorchtein, Beam normal spin asymmetry in the quasireal compton scattering approximation, Phys. Rev. C 73, 055201 (2006)

    2006

  22. [30]

    P. G. Blunden, W. Melnitchouk, and J. A. Tjon, Two- photon exchange and elastic electron-proton scattering, Phys. Rev. Lett. 91, 142304 (2003)

    2003

  23. [31]

    R. E. Cutkosky, Singularities and discontinuities of Feyn- man amplitudes, J. Math. Phys. 1, 429 (1960)

    1960

  24. [32]

    A. V. Afanasev and C. E. Carlson, Two-photon-exchange correction to parity-violating elastic electron-proton scat- tering, Phys. Rev. Lett. 94, 212301 (2005), arXiv:hep- ph/0502128

    2005

  25. [33]

    W. F. L. Hollik, Radiative Corrections in the Standard Model and their Role for Precision Tests of the Elec- troweak Theory, Fortsch. Phys. 38, 165 (1990)

    1990

  26. [34]

    Denner, Techniques for calculation of electroweak ra- diative corrections at the one loop level and results for W physics at LEP-200, Fortsch

    A. Denner, Techniques for calculation of electroweak ra- diative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41, 307 (1993), arXiv:0709.1075 [hep-ph]

    1993 arXiv

  27. [35]

    ’t Hooft and M

    G. ’t Hooft and M. Veltman, Scalar one-loop integrals, Nuclear Physics B 153, 365 (1979)

    1979

  28. [36]

    Benesch et al

    J. Benesch et al. (MOLLER), The MOLLER Exper- iment: An Ultra-Precise Measurement of the Weak Mixing Angle Using M \oller Scattering, (2014), arXiv:1411.4088 [nucl-ex]

    2014 arXiv

  29. [37]

    Gilman et al., Studying the proton ”radius” puzzle with µp elastic scattering, (2013)

    R. Gilman et al., Studying the proton ”radius” puzzle with µp elastic scattering, (2013)

    2013

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Reviewed August 6, 2026 · model on record in the stance chip above.