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Nucleon relativistic weak-neutral axial-vector four-current distributions

T0 review · 2 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The 3D weak-neutral axial charge inside a spin-1/2 hadron is parity-odd and set by the induced pseudotensor form factor, not the axial form factor, so the standard axial radius is not a genuine 3D mean-square radius.

desk verdict A clean calculation with an overstrong headline: the G_T-governed axial density is a theorem within the Breit-frame Wigner prescription, but the paper's own Appendix B shows a different legitimate 3D definition recovers G_A and R_A^2. read the letter →

arxiv 2411.12521 v3 pith:63OCL5GN submitted 2024-11-19 hep-ph nucl-th

Yi Chen This is my paper · ORCID
classification hep-phnucl-th
keywords weak-neutralaxial-vectorformfactorsinducedpseudotensorfactorsecond-classcurrentsBreitframedistributionslight-frontnucleonaxialradiusquantumphase-spaceformalismMeloshrotation
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

The paper studies the full weak-neutral axial-vector four-current distributions inside a general spin-1/2 hadron, now including the second-class current that contributes through the induced pseudotensor form factor $G_T^Z(Q^2)$. Its central claim is that, in the Breit frame, the 3D axial charge distribution $J^0_{5,B}(r)$ is parity-odd and is controlled by $G_T^Z(Q^2)$, not by the axial form factor $G_A^Z(Q^2)$. Because this distribution has zero total charge, the standard 3D mean-square axial radius defined through the slope of $G_A^Z$ is not well-defined. The paper also shows that the second-class current does not contribute to the mean-square axial and spin radii, and it proposes a conjecture that any light-front amplitude can be reproduced from elastic-frame amplitudes in the proper infinite-momentum limit. This matters because the axial radius is a key input for neutrino oscillation experiments and lattice QCD, and the paper says the quantity usually quoted is not a genuine 3D radius.

What carries the argument

The load-bearing object is the Breit-frame axial charge density $J^0_{5,B}(r)$, defined through the quantum phase-space (Wigner) spatial-density formalism as the three-dimensional Fourier transform of the matrix element of $\hat j^0_5$ at $P=0$. Evaluating the full vertex $\Gamma^\mu(P,\Delta)=\gamma^\mu\gamma_5 G_A^Z + \Delta^\mu\gamma_5 G_P^Z/(2M) - \sigma^{\mu\nu}\Delta_\nu\gamma_5 G_T^Z/(2M)$ in that frame gives $J^0_{5,B}(r)$ proportional to the Fourier transform of $(i\Delta\cdot\sigma)G_T^Z(\Delta^2)$, whose parity-odd character makes the total axial charge vanish. The rest of the machinery consists of the G-parity classification that identifies $G_T^Z$ as the second-class current, the covariant Lorentz-transformation and Wigner-rotation formalism connecting Breit, elastic, and light-front frames, and the Melosh rotation that converts canonical spin states into light-front helicity states; the paper also uses the proper infinite-momentum limit of elastic-frame amplitudes to reproduce light-front amplitudes.

What would settle it

Measure $G_T^Z(Q^2)$ directly—for example from the difference between muon-neutrino and electron-neutrino quasi-elastic cross sections or from the full tree-level weak-neutral differential cross section—and compare the parity-odd Breit-frame density $\int d^3\Delta/(2\pi)^3\, e^{-i\Delta\cdot r}\,i\Delta\cdot\sigma\, G_T^Z(\Delta^2)/(2M)$ with the distribution reconstructed from the standard $G_A^Z$-based inverse Abel transform; if the latter matches the observed distribution, the claim that $G_T^Z$ controls the 3D axial charge distribution fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the temporal component of the weak-neutral axial-vector four-current in the Breit frame, $J^0_{5,B}(r)$, is built from the induced pseudotensor form factor $G_T^Z$ rather than the axial form factor $G_A^Z$: $J^0_{5,B}(r) = \int d^3\Delta/(2\pi)^3\, e^{-i\Delta\cdot r}\,(i\Delta\cdot\sigma) G_T^Z(\Delta^2)/(2M)$. The factor $\Delta\cdot\sigma$ makes the distribution parity-odd, so its integral over all space vanishes; consequently the usual mean-square axial radius $\langle r^2_A\rangle = \int d^3r\, r^2 J^0_{5,B}(r)/\int d^3r\, J^0_{5,B}(r)$ is undefined, and the widely quoted $R_A^2 = -6/G_A^Z(0)\, dG_A^Z/dQ^2$ is not the 3D axial charge radius. The spatial components of the current are controlled by $G_A^Z$ and $G_P^Z$ and are identified with the 3D spin distribution. In boosted elastic frames and light-front frames, temporal and longitudinal components mix under boosts but the transverse spin distribution remains free of $G_T^Z$; in every frame the second-class current drops out of the mean-square axial and spin radii. A separate claim is the conjecture that any well-defined light-front amplitude can be obtained from the corresponding elastic-frame amplitude in the proper infinite-momentum limit, which the paper uses to explain distortions in light-front distributions.

Load-bearing premise

The central claim rests on accepting the Wigner (quantum phase-space) definition of a spatial distribution—locating the hadron at an average position and momentum—as the physical meaning of where axial charge sits; adopt a different density prescription (Sachs-like or light-front) and the identification of the 3D axial charge distribution with $G_T^Z$ rather than $G_A^Z$ is not necessarily the meaningful statement.

Editorial extensions

If this is right

  • The standard axial radius $R_A^2 = -6/G_A^Z(0)\,dG_A^Z/dQ^2$ is not a genuine 3D mean-square axial charge radius; the true 3D axial charge distribution is governed by $G_T^Z$, so comparisons of this slope with 3D radius measurements are not apples-to-apples.
  • Because $J^0_{5,B}(r)$ is parity-odd, its total charge is zero, so the 3D mean-square axial radius is not well-defined even when $G_T^Z(0)\neq 0$; this is a sharper statement than the earlier $G_T=0$ conclusion that the radius does not exist.
  • The second-class current contributes to the axial charge and longitudinal current distributions but cancels from every mean-square axial and spin radius derived in Breit, elastic, and light-front frames, so the previously reported radius values survive the inclusion of $G_T^Z$.
  • The light-front '+' axial charge distribution coincides with the elastic-frame time distribution at infinite momentum, $J^+_{5,\mathrm{LF}} = J^0_{5,\mathrm{EF}}(\infty) = J^z_{5,\mathrm{EF}}(\infty)$, and the inverse Abel transform of this 2D image does not reproduce the true 3D Breit-frame axial charge distribution.
  • If the proposed conjecture is correct, light-front amplitudes for any well-defined distribution can be derived by a two-step procedure—covariant boost to the elastic frame followed by the proper infinite-momentum limit—making the sources of light-front distortions (boost mixing, Wigner and Melosh rotations) individually identifiable.

Reading between the lines

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

  • If $G_T^Z$ really controls the 3D axial charge distribution, the route to imaging axial charge in the proton runs through direct measurements of the second-class form factor—for example the muon- versus electron-neutrino quasi-elastic cross-section difference or the full tree-level weak-neutral cross section—rather than through the commonly quoted $G_A^Z$ slope; the paper's own numerical assumptio
  • The demonstrated failure of Abel tomography for axial charge suggests that 2D light-front axial densities, however clean their Galilean interpretation, cannot be inverted to any 3D axial density within the Wigner framework; any future attempt to define a 3D axial radius from light-front images would need a different conceptual bridge.
  • A natural test of the framework-dependence is to repeat the calculation with a Sachs-type or light-front definition of spatial density; if a finite 3D axial radius tied to $G_A^Z$ emerges in that prescription, the paper's conclusion is specific to the Wigner definition and not a unique physical statement.
  • The conjecture about reproducing light-front amplitudes from elastic-frame amplitudes, if proven generally, would provide a model-independent derivation of LF distortions for all currents and all spins, connecting the good/bad component lore to explicit boost kinematics.
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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

2 major / 7 minor

Summary. The paper presents a systematic derivation of relativistic weak-neutral axial-vector four-current distributions for a generic spin-1/2 hadron within the quantum phase-space (Wigner) formalism, now including the induced pseudotensor (second-class) form factor G_T^Z. In the Breit frame the time component J0_5B is shown to be parity-odd and to be controlled by G_T^Z rather than by G_A^Z; consequently the standard slope-based quantity R_A^2 = -6/G_A(0) dG_A/dQ^2 is argued not to be a genuine 3D mean-square axial charge radius. The paper also derives elastic-frame and light-front distributions, shows that G_T^Z drops out of the transverse mean-square axial and spin radii, proposes a conjecture that LF amplitudes can be reproduced from EF amplitudes in the infinite-momentum limit, and illustrates the results numerically for the proton using dipole fits and an ad hoc G_T^Z model.

Significance. The analytic derivations are clean and self-contained: the main relations follow from standard Lorentz covariant matrix elements and the explicit phase-space definition, with no tuned parameter entering the central identification. If the conclusions are read as statements about the Breit-frame Wigner density, the paper provides a useful clarification of the status of R_A^2 and of the role of the second-class current in axial-vector densities. The paper is also transparent about its numerical inputs, and the advertised cancellation of G_T^Z in the mean-square radii is a useful consistency check. The main limitation is that the headline claim is more general than the specific framework in which it is proven.

major comments (2)
  1. [§4.1, Eq. (4.1)-(4.3); Abstract] The headline statement that the 3D axial charge distribution 'is in fact related to G_T^Z rather than G_A^Z' is a theorem about the density defined by Eq. (4.1), not a framework-independent fact. The paper's own Appendix B constructs an alternative 3D density, J0_naive(r), by inverse Abel transformation of the LF density J+_5LF (Eqs. (B.3)-(B.4)), and this density is controlled by G_A^Z with mean-square radius exactly equal to R_A^2 (Eq. (B.6)). The paper rejects J0_naive as not physically meaningful because it differs from the BF density, but this rejection presupposes that Eq. (4.1) is the correct physical definition; no independent physical criterion is supplied. Since the abstract and Section 7 use this result to state that R_A^2 is 'evidently not the 3D mean-square axial radius', the claim as written is too strong. Please qualify the conclusion to the chosen phase-space/Breit-frame prescription and explicitly discuss the prescription dependence, including the LF/Abel alternative.
  2. [§5.2, Eq. (5.7); §6.3, Eq. (6.12)] The advertised cancellation of G_T^Z in the mean-square axial and spin radii is asserted rather than demonstrated. The text states that 'we obtain exactly the same mean-square transverse radii as Ref. [150]' and then concludes that G_T^Z 'does not contribute', but no integral or derivation is shown for the G_T^Z-dependent terms in Eqs. (5.7) and (6.12). Since this cancellation is one of the paper's main results, please provide the relevant steps or an explicit argument showing that the G_T^Z contributions integrate to zero.
minor comments (7)
  1. [§6.1, Eq. (6.6)] In the third line of Eq. (6.6), the amplitude is labeled A⊥_EF but it should be A⊥_LF; this is presumably a typographical error.
  2. [§6.2, Conjecture] The conjecture that any LF amplitude for well-defined LF distributions can be reproduced from EF amplitudes in the proper IMF limit is supported only by three examples and is not proven. Since it is explicitly called a conjecture, it is acceptable as a conjecture, but please ensure it is not used as a premise for later conclusions without making its conjectural status clear.
  3. [Appendix A, Eq. (A.10)] The ansatz G_T^Z = κ_T G_A^Z with κ_T ≈ 0.1 is introduced without an uncertainty, based on a rough mean value from one figure in Ref. [169]. All numerical panels showing J0_5B-dependent quantities (Figs. 2 and 5) are directly proportional to this input; please state explicitly that these panels are illustrative and provide at least a qualitative sensitivity estimate.
  4. [Abstract and §7] The wording 'using weak-neutral axial-vector FFs extracted from experimental data' is correct for G_A^Z and G_P^Z, but G_T^Z is modeled by the ad hoc ansatz (A.10), not extracted. Please rephrase to avoid implying that G_T^Z is experimentally determined.
  5. [§4.2] The quoted numerical values ⟨r_spin^2⟩ ≈ (2.1054 fm)^2 and R_A^2 ≈ (0.6510 fm)^2 are given without uncertainties; if these are central values only, please say so.
  6. [Throughout] There are several typographical issues: 'ansätz' should be 'ansatz', 'four-moment eigenstates' should be 'four-momentum eigenstates', and the phrase 'As the ne plus ultra' in Section 2 is stylistically unusual and should be replaced with a standard expression.
  7. [Appendix B, after Eq. (B.6)] The phrase 'even though we neglect the polarization difference' is unclear; please clarify whether this refers to dropping the longitudinal polarization factor (σ_z)_{s's} from the comparison between J0_naive and J0_5B.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central G_T identification follows by direct substitution into the defining phase-space Fourier transform; all fitted FFs are illustrative inputs, not part of the derivation.

full rationale

The central claim that the Breit-frame 3D axial charge distribution J^0_{5,B}(r) is governed by the induced pseudotensor form factor G_T^Z rather than G_A^Z is obtained by direct, parameter-free substitution: Eq. (4.1) defines J^0_{5,B} as the Fourier transform of the time component of the axial-vector current in the Breit frame, and Eq. (4.2) gives the Lorentz-covariant decomposition of that time component as proportional to i Delta·sigma G_T^Z(Delta^2) plus no G_A^Z term. Inserting (4.2) into (4.1) yields (4.3) with no fitted parameter and no appeal to a prior result for the G_T identification. The vanishing of the total axial charge in Eq. (4.4) and the cancellation of G_T in the mean-square transverse axial/spin radii in Eqs. (5.7) and (6.12) are algebraic consequences of the Fourier representation and current-component structure, so they are not predictions forced by a fit. The numerical figures use external FFs from Appendix A (MiniBooNE dipole fit, PPD/chiPT G_P^Z, and the Day-McFarland-inspired ansatz G_T^Z = kappa_T G_A^Z), and the paper explicitly labels these as illustrations rather than as inputs to the analytic derivation. Self-citations to Refs. [148-150] supply the quantum phase-space framework and prior axial-radius analysis, but the load-bearing algebra is reproduced in this paper's own equations, so the citations are supporting context rather than a circular chain. Appendix B actually strengthens the non-circularity: it explicitly derives the alternative Abel-inverted density J^0_{5,naive}(r) that would reproduce R_A^2, showing that the distinction between the two prescriptions is a definition-dependent interpretational issue, not a hidden reuse of the conclusion. The proposed conjecture about LF amplitudes being reproducible from EF amplitudes in the IMF limit is explicitly presented as a conjecture based on worked examples, not as a result derived from itself. Thus no step reduces by construction to its own input; the framework dependence of the '3D axial radius' terminology is a physical-interpretation concern, not circular reasoning.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's central analytic results rest on the standard three-form-factor decomposition of the axial current and on the quantum phase-space interpretation of densities. The numerical illustrations additionally rely on dipole fits to neutrino data and on an ad hoc scaling for G_T. No new entities are introduced; the LF-EF conjecture is a methodological conjecture rather than a new object.

free parameters (4)
  • M_A^Z (axial dipole mass for G_A^Z) = 1.0500 ± 0.0107 GeV
    Fitted in this work via Eq. (A.1) dipole ansatz to MiniBooNE neutral-current elastic data (Refs. [15,18,184]); used for all proton illustrations.
  • G_A^Z(0) = 0.65520 ± 0.00465
    Fixed from world average G_A^W(0)=1.2754±0.0013 and lattice strange axial charge Δs=-0.0350±0.0092 (Appendix A); used to normalize distributions.
  • κ_T (G_T^Z/G_A^Z scaling) = ≈0.1
    Rough mean of G_T^W(0)/G_A^W(0) from Ref. [169], used to construct the G_T^Z ansatz (A.10); no uncertainty propagated.
  • M_A^W, G_s^A(0), M_s^A, G_s^P(0), M_s^P = from literature (Refs. [95,46])
    Inputs from prior fits used to reconstruct G_Z^A, G_Z^P via Eq. (A.2); not fitted in this paper.
assumptions (5)
  • standard math Matrix element of the weak-neutral axial-vector current is parametrized by exactly three form factors G_A^Z, G_P^Z, G_T^Z (Eq. (2.2))
    Follows from Lorentz covariance, parity, hermiticity; standard in the literature (Refs. [61,93]).
  • domain assumption The quantum phase-space formalism (Eqs. (3.1)-(3.2)) defines the physical spatial distributions; the Breit frame (P=0) is the average rest frame
    The paper adopts the Wigner-distribution interpretation, citing Refs. [143,144,148,149]; the central claim about 'the 3D axial charge distribution' is meaningful only within this framework.
  • domain assumption G-parity classification: G_T^Z is a second-class current and vanishes if G-parity is exact; it is nonzero in general
    Used to justify including G_T; standard Weak interaction textbook result (Weinberg [158]).
  • ad hoc to paper G_T^Z(Q^2) = κ_T G_A^Z(Q^2) with κ_T≈0.1 (Eq. (A.10))
    Adopted for numerical illustration only, following the assumption in Ref. [169]; the paper states the real G_T is likely different.
  • ad hoc to paper The conjecture that any LF amplitude for well-defined LF distributions can be reproduced from EF amplitudes in the proper IMF limit
    Proposed in Sec. 6.2 based on examples; not proven, used to explain distortions.

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Cite this review

Pith. "Pith review of Nucleon relativistic weak-neutral axial-vector four-current distributions." pith.science (2026). https://pith.science/paper/63OCL5GN

@misc{pith2026241112521,
  author       = {Pith},
  title        = {Pith review of: Nucleon relativistic weak-neutral axial-vector four-current distributions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/63OCL5GN}},
  note         = {Machine review of arXiv:2411.12521}
}
abstract

Relativistic full weak-neutral axial-vector four-current distributions inside a general spin-$\frac{1}{2}$ hadron are systematically studied for the first time, where the second-class current contribution associated with the induced pseudotensor form factor (FF) is included. We clearly demonstrate that the 3D axial charge distribution, being parity-odd in the Breit frame, is in fact related to the induced pseudotensor FF $G_T^Z(Q^2)$ rather than the axial FF $G_A^Z(Q^2)$. We study the frame-dependence of full axial-vector four-current distributions for a moving hadron, and compare them with their light-front counterparts. We revisit the role played by the Melosh rotation, and understand more easily and intuitively the origins of distortions appearing in light-front distributions (relative to the Breit frame ones) using the conjecture that we propose in this work. In particular, we show that the second-class current contribution, although explicitly included, does not contribute in fact to the mean-square axial and spin radii. We finally illustrate our results in the case of a proton using the weak-neutral axial-vector FFs extracted from experimental data.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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Reference graph

Works this paper leans on

201 extracted references · 15 canonical work pages · cited by 2 Pith papers

  1. [150]

    Y. Chen, Y. Li, C. Lorcé and Q. Wang,Nucleon axial radius, Phys. Rev. D110 (2024) L091503 [2405.12943]

    arXiv 2024

  2. [1]

    Gao and M

    H. Gao and M. Vanderhaeghen,The proton charge radius, Rev. Mod. Phys.94 (2022) 015002 [2105.00571]

    arXiv 2022

  3. [2]

    Li et al.,Measured proton electromagnetic structure deviates from theoretical predictions, Nature 611 (2022) 265 [2210.11461]

    R. Li et al.,Measured proton electromagnetic structure deviates from theoretical predictions, Nature 611 (2022) 265 [2210.11461]

    arXiv 2022

  4. [3]

    Singh,The Effect of final state interactions and deuteron binding in neutrino νd → µ−pp, Nucl

    S.K. Singh,The Effect of final state interactions and deuteron binding in neutrino νd → µ−pp, Nucl. Phys. B 36 (1972) 419

    1972

  5. [4]

    Mann et al.,Study of the reactionν + n → µ− + p, Phys

    W.A. Mann et al.,Study of the reactionν + n → µ− + p, Phys. Rev. Lett.31 (1973) 844

    1973

  6. [5]

    Barish et al.,Study of neutrino interactions in hydrogen and deuterium: Description of the experiment and study of the reactionν + d → µ− + p + ps, Phys

    S.J. Barish et al.,Study of neutrino interactions in hydrogen and deuterium: Description of the experiment and study of the reactionν + d → µ− + p + ps, Phys. Rev. D16 (1977) 3103

    1977

  7. [6]

    Baker, A.M

    N.J. Baker, A.M. Cnops, P.L. Connolly, S.A. Kahn, H.G. Kirk, M.J. Murtagh et al., Quasielastic neutrino scattering: a measurement of the weak nucleon axial vector Form-Factor, Phys. Rev. D23 (1981) 2499

    1981

  8. [7]

    Miller et al.,Study of the reactionνµ + d → µ− + p + ps, Phys

    K.L. Miller et al.,Study of the reactionνµ + d → µ− + p + ps, Phys. Rev. D26 (1982) 537

    1982

Show all 201 references
  1. [8]

    Kitagaki et al.,High-energy quasielastic νµ + n → µ− + p scattering in deuterium, Phys

    T. Kitagaki et al.,High-energy quasielastic νµ + n → µ− + p scattering in deuterium, Phys. Rev. D 28 (1983) 436

    1983

  2. [9]

    Horstkotte, A

    J. Horstkotte, A. Entenberg, R.S. Galik, A.K. Mann, H.H. Williams, W. Kozanecki et al., Measurement of Neutrino - Proton and Anti-neutrinos - Proton Elastic Scattering, Phys. Rev. D 25 (1982) 2743. – 28 –

    1982

  3. [10]

    Ahrens et al.,Measurement of neutrino-proton and antineutrino-proton elastic scattering, Phys

    L.A. Ahrens et al.,Measurement of neutrino-proton and antineutrino-proton elastic scattering, Phys. Rev. D35 (1987) 785

    1987

  4. [11]

    Allasia et al.,Investigation of exclusive channels inν/ ¯ν-deuteron charged current interactions, Nucl

    D. Allasia et al.,Investigation of exclusive channels inν/ ¯ν-deuteron charged current interactions, Nucl. Phys. B 343 (1990) 285

    1990

  5. [12]

    Kitagaki et al.,Study of νd → µ−pps and νd → µ−∆++(1232)ns using the BNL 7-foot deuterium filled bubble chamber, Phys

    T. Kitagaki et al.,Study of νd → µ−pps and νd → µ−∆++(1232)ns using the BNL 7-foot deuterium filled bubble chamber, Phys. Rev. D42 (1990) 1331

    1990

  6. [13]

    K2K collaboration, Measurement of the quasi-elastic axial vector mass in neutrino-oxygen interactions, Phys. Rev. D74 (2006) 052002 [hep-ex/0603034]

    2006 arXiv

  7. [14]

    MiniBooNE collaboration, First Measurement of the Muon Neutrino Charged Current Quasielastic Double Differential Cross Section, Phys. Rev. D81 (2010) 092005 [1002.2680]

    2010 arXiv

  8. [15]

    MiniBooNE collaboration, Measurement of the Neutrino Neutral-Current Elastic Differential Cross Section on Mineral Oil atEν ∼ 1 GeV, Phys. Rev. D82 (2010) 092005 [1007.4730]

    2010 arXiv

  9. [16]

    CLAS collaboration, Measurement of the generalized form factors near threshold via γ∗p → nπ+ at high Q2, Phys. Rev. C 85 (2012) 035208 [1201.0903]

    2012 arXiv

  10. [17]

    MINERνA collaboration, Measurement of muon antineutrino quasielastic scattering on a hydrocarbon target atEν ∼3.5 GeV, Phys. Rev. Lett.111 (2013) 022501 [1305.2234]

    2013 arXiv

  11. [18]

    MiniBooNE collaboration, Measurement of the Antineutrino Neutral-Current Elastic Differential Cross Section, Phys. Rev. D91 (2015) 012004 [1309.7257]

    2015 arXiv

  12. [19]

    Meyer, M

    A.S. Meyer, M. Betancourt, R. Gran and R.J. Hill,Deuterium target data for precision neutrino-nucleus cross sections, Phys. Rev. D93 (2016) 113015 [1603.03048]

    2016 arXiv

  13. [20]

    MINER vAcollaboration, Measurement of the axial vector form factor from antineutrino–proton scattering, Nature 614 (2023) 48

    2023

  14. [21]

    Pate, D.W

    S.F. Pate, D.W. McKee and V. Papavassiliou,Strange Quark Contribution to the Vector and Axial Form Factors of the Nucleon: Combined Analysis of G0, HAPPEx, and Brookhaven E734 Data, Phys. Rev. C 78 (2008) 015207 [0805.2889]

    2008 arXiv

  15. [22]

    S.F. Pate, V. Papavassiliou, J.P. Schaub, D.P. Trujillo, M.V. Ivanov, M.B. Barbaro et al., Global fit of electron and neutrino elastic scattering data to determine the strange quark contribution to the vector and axial form factors of the nucleon, Phys. Rev. D109 (2024) 093001...

    2024 arXiv

  16. [23]

    OPERA collaboration, Final results on neutrino oscillation parameters from the OPERA experiment in the CNGS beam, Phys. Rev. D100 (2019) 051301 [1904.05686]

    2019 arXiv

  17. [24]

    16 (2020) 558 [1901.09445]

    Double Chooz collaboration, Double Chooz θ13 measurement via total neutron capture detection, Nature Phys. 16 (2020) 558 [1901.09445]

    2020 arXiv

  18. [25]

    T2K, Super-Kamiokande collaboration, First Joint Oscillation Analysis of Super-Kamiokande Atmospheric and T2K Accelerator Neutrino Data, Phys. Rev. Lett.134 (2025) 011801 [2405.12488]

    2025

  19. [26]

    DUNE collaboration, DUNE Phase II: scientific opportunities, detector concepts, technological solutions, JINST 19 (2024) P12005 [2408.12725]

    2024

  20. [27]

    KamLAND collaboration, First measurement of the strange axial coupling constant using neutral-current quasielastic interactions of atmospheric neutrinos at KamLAND, Phys. Rev. D 107 (2023) 072006 [2211.13911]. – 29 –

    2023 arXiv

  21. [28]

    Daya Baycollaboration, Search for a Sub-eV Sterile Neutrino using Daya Bay’s Full Dataset, Phys. Rev. Lett.133 (2024) 051801 [2404.01687]

    2024

  22. [29]

    IceCube collaboration, Measurement of atmospheric neutrino oscillation parameters using convolutional neural networks with 9.3 years of data in IceCube DeepCore, 2405.02163

    arXiv

  23. [30]

    JUNO collaboration, Potential to identify neutrino mass ordering with reactor antineutrinos at JUNO*, Chin. Phys. C 49 (2025) 033104 [2405.18008]

    2025

  24. [31]

    NOvA collaboration, Dual-Baseline Search for Active-to-Sterile Neutrino Oscillations in NOvA, Phys. Rev. Lett.134 (2025) 081804 [2409.04553]

    2025 arXiv

  25. [32]

    Bhattacharya, V

    T. Bhattacharya, V. Cirigliano, S. Cohen, R. Gupta, H.-W. Lin and B. Yoon,Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD, Phys. Rev. D94 (2016) 054508 [1606.07049]

    2016 arXiv

  26. [33]

    Liang, Y.-B

    J. Liang, Y.-B. Yang, K.-F. Liu, A. Alexandru, T. Draper and R.S. Sufian,Lattice Calculation of Nucleon Isovector Axial Charge with Improved Currents, Phys. Rev. D96 (2017) 034519 [1612.04388]

    2017 arXiv

  27. [34]

    Green, N

    J. Green, N. Hasan, S. Meinel, M. Engelhardt, S. Krieg, J. Laeuchli et al.,Up, down, and strange nucleon axial form factors from lattice QCD, Phys. Rev. D95 (2017) 114502 [1703.06703]

    2017 arXiv

  28. [35]

    Gupta, Y.-C

    R. Gupta, Y.-C. Jang, H.-W. Lin, B. Yoon and T. Bhattacharya,Axial Vector Form Factors of the Nucleon from Lattice QCD, Phys. Rev. D96 (2017) 114503 [1705.06834]

    2017 arXiv

  29. [36]

    D.-L. Yao, L. Alvarez-Ruso and M.J. Vicente-Vacas,Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory, Phys. Rev. D96 (2017) 116022 [1708.08776]

    2017 arXiv

  30. [37]

    Hasan, J

    N. Hasan, J. Green, S. Meinel, M. Engelhardt, S. Krieg, J. Negele et al.,Computing the nucleon charge and axial radii directly atQ2 = 0 in lattice QCD, Phys. Rev. D97 (2018) 034504 [1711.11385]

    2018 arXiv

  31. [38]

    PACScollaboration, Nucleon form factors on a large volume lattice near the physical point in 2+1 flavor QCD, Phys. Rev. D98 (2018) 074510 [1807.03974]

    2018 arXiv

  32. [39]

    Shintani, K.-I

    E. Shintani, K.-I. Ishikawa, Y. Kuramashi, S. Sasaki and T. Yamazaki,Nucleon form factors and root-mean-square radii on a (10.8 fm)4 lattice at the physical point, Phys. Rev. D 99 (2019) 014510 [1811.07292]

    2019 arXiv

  33. [40]

    Hasan, J

    N. Hasan, J. Green, S. Meinel, M. Engelhardt, S. Krieg, J. Negele et al.,Nucleon axial, scalar, and tensor charges using lattice QCD at the physical pion mass, Phys. Rev. D99 (2019) 114505 [1903.06487]

    2019 arXiv

  34. [41]

    Y.-C. Jang, R. Gupta, B. Yoon and T. Bhattacharya,Axial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation, Phys. Rev. Lett.124 (2020) 072002 [1905.06470]

    2020 arXiv

  35. [42]

    RQCD collaboration, Nucleon axial structure from lattice QCD, JHEP 05 (2020) 126 [1911.13150]

    2020 arXiv

  36. [43]

    Lin,Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD, Phys

    H.-W. Lin,Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD, Phys. Rev. Lett.127 (2021) 182001 [2008.12474]

    2021 arXiv

  37. [44]

    Alexandrou et al.,Nucleon axial and pseudoscalar form factors from lattice QCD at the physical point, Phys

    C. Alexandrou et al.,Nucleon axial and pseudoscalar form factors from lattice QCD at the physical point, Phys. Rev. D103 (2021) 034509 [2011.13342]. – 30 –

    2021

  38. [45]

    Nucleon Matrix Elements (NME) collaboration, Precision nucleon charges and form factors using (2+1)-flavor lattice QCD, Phys. Rev. D105 (2022) 054505 [2103.05599]

    2022 arXiv

  39. [46]

    Alexandrou, S

    C. Alexandrou, S. Bacchio, M. Constantinou, K. Hadjiyiannakou, K. Jansen and G. Koutsou,Quark flavor decomposition of the nucleon axial form factors, Phys. Rev. D 104 (2021) 074503 [2106.13468]

    2021 arXiv

  40. [47]

    PACScollaboration, Calculation of the derivative of nucleon form factors inNf = 2 + 1 lattice QCD atMπ = 138 MeV on a (5.5 fm)3 volume, Phys. Rev. D104 (2021) 074514 [2107.07085]

    2021 arXiv

  41. [48]

    Meyer et al.,Nucleon Axial Form Factor from Domain Wall on HISQ, PoS LA TTICE2021(2022) 081 [2111.06333]

    A.S. Meyer et al.,Nucleon Axial Form Factor from Domain Wall on HISQ, PoS LA TTICE2021(2022) 081 [2111.06333]

    2022 arXiv

  42. [49]

    Schulz, D

    T. Schulz, D. Djukanovic, G. von Hippel, J. Koponen, H.B. Meyer, K. Ottnad et al., Isovector Axial Vector Form Factors of the Nucleon from Lattice QCD withNf = 2 + 1 O(a)-improved Wilson Fermions, PoS LA TTICE2021(2022) 577 [2112.00127]

    2022 arXiv

  43. [50]

    Alexandrou, S

    C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen et al.,Nucleon form factors fromNf=2+1+1 twisted mass QCD at the physical point, PoS LA TTICE2021(2022) 250 [2112.06750]

    2022 arXiv

  44. [51]

    Lin,Nucleon helicity generalized parton distribution at physical pion mass from lattice QCD, Phys

    H.-W. Lin,Nucleon helicity generalized parton distribution at physical pion mass from lattice QCD, Phys. Lett. B824 (2022) 136821 [2112.07519]

    2022 arXiv

  45. [52]

    Alexandrou,Nucleon axial form factors from lattice QCD, SciPost Phys

    C. Alexandrou,Nucleon axial form factors from lattice QCD, SciPost Phys. Proc.6 (2022) 006

    2022

  46. [53]

    Djukanovic, G

    D. Djukanovic, G. von Hippel, J. Koponen, H.B. Meyer, K. Ottnad, T. Schulz et al., Isovector axial form factor of the nucleon from lattice QCD, Phys. Rev. D106 (2022) 074503 [2207.03440]

    2022 arXiv

  47. [54]

    Lin,Hadron Spectroscopy and Structure from Lattice QCD, Few Body Syst.63 (2022) 65

    H.-W. Lin,Hadron Spectroscopy and Structure from Lattice QCD, Few Body Syst.63 (2022) 65

    2022

  48. [55]

    Koponen, D

    J. Koponen, D. Djukanovic, G. von Hippel, H.B. Meyer, K. Ottnad, T. Schulz et al., Isovector Axial Form Factor of the Nucleon from Lattice QCD, PoS LA TTICE2022 (2023) 113

    2023

  49. [56]

    Precision Neutron Decay Matrix Elements (PNDME) collaboration, Nucleon isovector axial form factors, Phys. Rev. D109 (2024) 014503 [2305.11330]

    2024 arXiv

  50. [57]

    Extended Twisted Mass collaboration, Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point, Phys. Rev. D109 (2024) 034503 [2309.05774]

    2024 arXiv

  51. [58]

    Meissner and N

    U.G. Meissner and N. Kaiser,U(2)-V Yang-Mills Approach to Skyrmions With Vector Mesons: Axial Properties of Nucleons, Phys. Lett. B180 (1986) 129

    1986

  52. [59]

    Meissner, N

    U.G. Meissner, N. Kaiser and W. Weise,Nucleons as Skyrme Solitons with Vector Mesons: Electromagnetic and Axial Properties, Nucl. Phys. A466 (1987) 685

    1987

  53. [60]

    Bernard, N

    V. Bernard, N. Kaiser and U.G. Meissner,QCD accurately predicts the induced pseudoscalar coupling constant, Phys. Rev. D50 (1994) 6899 [hep-ph/9403351]

    1994 arXiv

  54. [61]

    Ohlsson and H

    T. Ohlsson and H. Snellman,Weak form-factors for semileptonic octet baryon decays in the chiral quark model, Eur. Phys. J. C6 (1999) 285 [hep-ph/9803490]. – 31 –

    1999 arXiv

  55. [62]

    Barquilla-Cano, A.J

    D. Barquilla-Cano, A.J. Buchmann and E. Hernandez,Partial conservation of axial current and axial exchange currents in the nucleon, Nucl. Phys. A714 (2003) 611 [nucl-th/0204067]

    2003 arXiv

  56. [63]

    Silva, H.-C

    A. Silva, H.-C. Kim, D. Urbano and K. Goeke,Axial-vector form-factors of the nucleon within the chiral quark-soliton model and their strange components, Phys. Rev. D72 (2005) 094011 [hep-ph/0509281]

    2005 arXiv

  57. [64]

    Schindler and S

    M.R. Schindler and S. Scherer,Nucleon Form Factors of the Isovector Axial-Vector Current: Situation of Experiments and Theory, Eur. Phys. J. A32 (2007) 429 [hep-ph/0608325]

    2007 arXiv

  58. [65]

    Aliev and M

    T.M. Aliev and M. Savci,Nucleon form-factors induced by isovector and isoscalar axial-vector currents in QCD, Phys. Lett. B656 (2007) 56 [0711.1757]

    2007 arXiv

  59. [66]

    Sharma, H

    N. Sharma, H. Dahiya, P.K. Chatley and M. Gupta,Weak vector and axial-vector form factors in the chiral constituent quark model with configuration mixing, Phys. Rev. D79 (2009) 077503 [0904.2246]

    2009 arXiv

  60. [67]

    Eichmann and C.S

    G. Eichmann and C.S. Fischer,Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation, Eur. Phys. J. A48 (2012) 9 [1111.2614]

    2012 arXiv

  61. [68]

    X.Y. Liu, K. Khosonthongkee, A. Limphirat, P. Suebka and Y. Yan,Meson cloud contributions to baryon axial form factors, Phys. Rev. D91 (2015) 034022 [1406.7633]

    2015 arXiv

  62. [69]

    Dahiya and M

    H. Dahiya and M. Randhawa,Axial-vector form factors for the low lying octet baryons in the chiral quark constituent model, Phys. Rev. D90 (2014) 074001 [1409.4943]

    2014 arXiv

  63. [70]

    Ramalho and K

    G. Ramalho and K. Tsushima,Axial form factors of the octet baryons in a covariant quark model, Phys. Rev. D94 (2016) 014001 [1512.01167]

    2016 arXiv

  64. [71]

    Anikin, V.M

    I.V. Anikin, V.M. Braun and N. Offen,Axial form factor of the nucleon at large momentum transfers, Phys. Rev. D94 (2016) 034011 [1607.01504]

    2016 arXiv

  65. [72]

    Mamedov, B.B

    S. Mamedov, B.B. Sirvanli, I. Atayev and N. Huseynova,Nucleon’s axial-vector form factor in the hard-wall AdS/QCD model, Int. J. Theor. Phys.56 (2017) 1861 [1609.00167]

    2017 arXiv

  66. [73]

    Hashamipour, M

    H. Hashamipour, M. Goharipour and S.S. Gousheh,Nucleon axial form factor from generalized parton distributions, Phys. Rev. D100 (2019) 016001 [1903.05542]

    2019 arXiv

  67. [74]

    Mondal, S

    C. Mondal, S. Xu, J. Lan, X. Zhao, Y. Li, D. Chakrabarti et al.,Proton structure from a light-front Hamiltonian, Phys. Rev. D102 (2020) 016008 [1911.10913]

    2020 arXiv

  68. [75]

    Zhang, T.J

    X. Zhang, T.J. Hobbs and G.A. Miller,Unified model of nucleon elastic form factors and implications for neutrino-oscillation experiments, Phys. Rev. D102 (2020) 074026 [1912.07797]

    2020 arXiv

  69. [76]

    Jun, J.-M

    Y.-S. Jun, J.-M. Suh and H.-C. Kim,Axial-vector form factors of the baryon decuplet with flavor SU(3) symmetry breaking, Phys. Rev. D102 (2020) 054011 [2005.06824]

    2020 arXiv

  70. [77]

    Chen, C.S

    C. Chen, C.S. Fischer, C.D. Roberts and J. Segovia,Form Factors of the Nucleon Axial Current, Phys. Lett. B815 (2021) 136150 [2011.14026]

    2021 arXiv

  71. [78]

    Chen, C.S

    C. Chen, C.S. Fischer, C.D. Roberts and J. Segovia,Nucleon axial-vector and pseudoscalar form factors and PCAC relations, Phys. Rev. D105 (2022) 094022 [2103.02054]

    2022 arXiv

  72. [79]

    Ahmady, D

    M. Ahmady, D. Chakrabarti, C. Mondal and R. Sandapen,Nucleon electroweak form factors using spin-improved holographic light-front wavefunctions, Nucl. Phys. A1016 (2021) 122334 [2105.02213]. – 32 –

    2021 arXiv

  73. [80]

    Sauerwein, M.F.M

    U. Sauerwein, M.F.M. Lutz and R.G.E. Timmermans,Axial-vector form factors of the baryon octet and chiral symmetry, Phys. Rev. D105 (2022) 054005 [2105.06755]

    2022 arXiv

  74. [81]

    BLFQ collaboration, Nucleon structure from basis light-front quantization, Phys. Rev. D 104 (2021) 094036 [2108.03909]

    2021 arXiv

  75. [82]

    Atayev and S

    I. Atayev and S. Mamedov,Axial-Vector Form Factor of Nucleons in the Isospin Medium from the Hard-Wall AdS/QCD Model, Int. J. Theor. Phys.61 (2022) 250 [2205.14958]

    2022 arXiv

  76. [83]

    Chen and C.D

    C. Chen and C.D. Roberts,Nucleon axial form factor at large momentum transfers, Eur. Phys. J. A58 (2022) 206 [2206.12518]

    2022 arXiv

  77. [84]

    Cheng, F.E

    P. Cheng, F.E. Serna, Z.-Q. Yao, C. Chen, Z.-F. Cui and C.D. Roberts,Contact interaction analysis of octet baryon axial-vector and pseudoscalar form factors, Phys. Rev. D106 (2022) 054031 [2207.13811]

    2022 arXiv

  78. [85]

    X.Y. Liu, A. Limphirat, K. Xu, Z. Zhao, K. Khosonthongkee and Y. Yan,Axial transition form factors of octet baryons in the perturbative chiral quark model, Phys. Rev. D107 (2023) 074006 [2209.00808]

    2023 arXiv

  79. [86]

    Irani, M

    F. Irani, M. Goharipour, H. Hashamipour and K. Azizi,Impact of recent MINERvA measurement of the antineutrino-proton scattering cross section on the generalized parton distributions, Phys. Rev. D108 (2023) 074018 [2306.13060]

    2023 arXiv

  80. [87]

    BLFQ collaboration, Spatial imaging of proton via leading-twist nonskewed GPDs with basis light-front quantization, Phys. Rev. D109 (2024) 014015 [2307.09869]

    2024 arXiv

  81. [88]

    Ramalho, K

    G. Ramalho, K. Tsushima and M.-K. Cheoun,Weak interaction axial form factors of the octet baryons in nuclear medium, Phys. Rev. D111 (2025) 013002 [2406.07958]

    2025 arXiv

  82. [89]

    Tomalak, Q

    O. Tomalak, Q. Chen, R.J. Hill, K.S. McFarland and C. Wret,Theory of QED radiative corrections to neutrino scattering at accelerator energies, Phys. Rev. D106 (2022) 093006 [2204.11379]

    2022 arXiv

  83. [90]

    Sobczyk and J

    J.E. Sobczyk and J. Nieves,Neutrino and antineutrino charged-current multinucleon cross sections reexamined, Phys. Rev. C 111 (2025) 025502 [2407.21587]

    2025 arXiv

  84. [91]

    Sajjad Athar, A

    M. Sajjad Athar, A. Fatima, S.K. Singh and F. Zaidi,Charged current neutrino scattering from nucleons, 2409.14732

    arXiv

  85. [92]

    Llewellyn Smith,Neutrino Reactions at Accelerator Energies, Phys

    C.H. Llewellyn Smith,Neutrino Reactions at Accelerator Energies, Phys. Rept.3 (1972) 261

    1972

  86. [93]

    Gourdin,Weak and Electromagnetic Form-Factors of Hadrons, Phys

    M. Gourdin,Weak and Electromagnetic Form-Factors of Hadrons, Phys. Rept.11 (1974) 29

    1974

  87. [94]

    Bernard, N

    V. Bernard, N. Kaiser and U.-G. Meissner,Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E4 (1995) 193 [hep-ph/9501384]

    1995 arXiv

  88. [95]

    Bernard, L

    V. Bernard, L. Elouadrhiri and U.-G. Meissner,Axial structure of the nucleon: topical review, J. Phys. G 28 (2002) R1 [hep-ph/0107088]

    2002 arXiv

  89. [96]

    Gorringe and H.W

    T. Gorringe and H.W. Fearing,Induced pseudoscalar coupling of the proton weak interaction, Rev. Mod. Phys.76 (2004) 31 [nucl-th/0206039]

    2004 arXiv

  90. [97]

    Beise, M.L

    E.J. Beise, M.L. Pitt and D.T. Spayde,The SAMPLE experiment and weak nucleon structure, Prog. Part. Nucl. Phys.54 (2005) 289 [nucl-ex/0412054]

    2005 arXiv

  91. [98]

    Gallagher, G

    H. Gallagher, G. Garvey and G.P. Zeller,Neutrino-nucleus interactions, Ann. Rev. Nucl. Part. Sci. 61 (2011) 355. – 33 –

    2011

  92. [99]

    Formaggio and G.P

    J.A. Formaggio and G.P. Zeller,From eV to EeV: neutrino cross sections ccross energy scales, Rev. Mod. Phys.84 (2012) 1307 [1305.7513]

    2012 arXiv

  93. [100]

    Morfin, J

    J.G. Morfin, J. Nieves and J.T. Sobczyk,Recent developments in neutrino/antineutrino - nucleus interactions, Adv. High Energy Phys.2012 (2012) 934597 [1209.6586]

    2012 arXiv

  94. [101]

    Gonzalez-Jimenez, J.A

    R. Gonzalez-Jimenez, J.A. Caballero and T.W. Donnelly,Parity violation in elastic electron-nucleon scattering: strangeness content in the nucleon, Phys. Rept. 524 (2013) 1 [1111.6918]

    2013 arXiv

  95. [102]

    Alvarez-Ruso, Y

    L. Alvarez-Ruso, Y. Hayato and J. Nieves,Progress and open questions in the physics of neutrino cross sections at intermediate energies, New J. Phys.16 (2014) 075015 [1403.2673]

    2014 arXiv

  96. [103]

    Mosel,Neutrino Interactions with Nucleons and Nuclei: Importance for Long-Baseline Experiments, Ann

    U. Mosel,Neutrino Interactions with Nucleons and Nuclei: Importance for Long-Baseline Experiments, Ann. Rev. Nucl. Part. Sci.66 (2016) 171 [1602.00696]

    2016 arXiv

  97. [104]

    Krebs, E

    H. Krebs, E. Epelbaum and U.G. Meißner,Nuclear axial current operators to fourth order in chiral effective field theory, Annals Phys. 378 (2017) 317 [1610.03569]

    2017 arXiv

  98. [105]

    NuSTEC collaboration, NuSTEC White Paper: Status and challenges of neutrino–nucleus scattering, Prog. Part. Nucl. Phys.100 (2018) 1 [1706.03621]

    2018 arXiv

  99. [106]

    R.J. Hill, P. Kammel, W.J. Marciano and A. Sirlin,Nucleon axial radius and muonic hydrogen — a new analysis and review, Rept. Prog. Phys.81 (2018) 096301 [1708.08462]

    2018 arXiv

  100. [107]

    Meyer, A

    A.S. Meyer, A. Walker-Loud and C. Wilkinson,Status of Lattice QCD Determination of Nucleon Form Factors and their Relevance for the Few-GeV Neutrino Program, Ann. Rev. Nucl. Part. Sci.72 (2022) 205 [2201.01839]

    2022 arXiv

  101. [108]

    Sajjad Athar, A

    M. Sajjad Athar, A. Fatima and S.K. Singh,Neutrinos and their interactions with matter, Prog. Part. Nucl. Phys.129 (2023) 104019 [2206.13792]

    2023 arXiv

  102. [109]

    Ernst, R.G

    F.J. Ernst, R.G. Sachs and K.C. Wali,Electromagnetic form factors of the nucleon, Phys. Rev. 119 (1960) 1105

    1960

  103. [110]

    Sachs,High-Energy Behavior of Nucleon Electromagnetic Form Factors, Phys

    R.G. Sachs,High-Energy Behavior of Nucleon Electromagnetic Form Factors, Phys. Rev. 126 (1962) 2256

    1962

  104. [111]

    Yennie, M.M

    D.R. Yennie, M.M. Lévy and D.G. Ravenhall,Electromagnetic Structure of Nucleons, Rev. Mod. Phys. 29 (1957) 144

    1957

  105. [112]

    G. Breit,Limitations on the interpretation of electromagnetic form-factors of nucleons, in Proceedings of the XII International Conference on High Energy Physics (ICHEP 1964), (Moscow), pp. 985–987, Atomizdat, 1966, https://inspirehep.net/literature/1670085

    1964

  106. [113]

    Kelly,Nucleon charge and magnetization densities from Sachs form-factors, Phys

    J.J. Kelly,Nucleon charge and magnetization densities from Sachs form-factors, Phys. Rev. C 66 (2002) 065203 [hep-ph/0204239]

    2002 arXiv

  107. [114]

    Burkardt,Impact parameter dependent parton distributions and off forward parton distributions for ζ → 0, Phys

    M. Burkardt,Impact parameter dependent parton distributions and off forward parton distributions for ζ → 0, Phys. Rev. D62 (2000) 071503 [hep-ph/0005108]

    2000 arXiv

  108. [115]

    Belitsky, X.-d

    A.V. Belitsky, X.-d. Ji and F. Yuan,Quark imaging in the proton via quantum phase space distributions, Phys. Rev. D69 (2004) 074014 [hep-ph/0307383]

    2004 arXiv

  109. [116]

    Jaffe,Ambiguities in the definition of local spatial densities in light hadrons, Phys

    R.L. Jaffe,Ambiguities in the definition of local spatial densities in light hadrons, Phys. Rev. D 103 (2021) 016017 [2010.15887]

    2021 arXiv

  110. [117]

    Brodsky, H.-C

    S.J. Brodsky, H.-C. Pauli and S.S. Pinsky,Quantum chromodynamics and other field theories on the light cone, Phys. Rept. 301 (1998) 299 [hep-ph/9705477]. – 34 –

    1998 arXiv

  111. [118]

    Susskind,Model of selfinduced strong interactions, Phys

    L. Susskind,Model of selfinduced strong interactions, Phys. Rev. 165 (1968) 1535

    1968

  112. [119]

    Kogut and D.E

    J.B. Kogut and D.E. Soper,Quantum Electrodynamics in the Infinite Momentum Frame, Phys. Rev. D1 (1970) 2901

    1970

  113. [120]

    Burkardt,Impact parameter space interpretation for generalized parton distributions, Int

    M. Burkardt,Impact parameter space interpretation for generalized parton distributions, Int. J. Mod. Phys. A18 (2003) 173 [hep-ph/0207047]

    2003 arXiv

  114. [121]

    Miller,Charge Density of the Neutron, Phys

    G.A. Miller,Charge Density of the Neutron, Phys. Rev. Lett.99 (2007) 112001 [0705.2409]

    2007 arXiv

  115. [122]

    Carlson and M

    C.E. Carlson and M. Vanderhaeghen,Empirical transverse charge densities in the nucleon and the nucleon-to-Delta transition, Phys. Rev. Lett.100 (2008) 032004 [0710.0835]

    2008 arXiv

  116. [123]

    Alexandrou, T

    C. Alexandrou, T. Korzec, G. Koutsou, T. Leontiou, C. Lorce, J.W. Negele et al., Delta-baryon electromagnetic form factors in lattice QCD, Phys. Rev. D79 (2009) 014507 [0810.3976]

    2009 arXiv

  117. [124]

    Alexandrou, T

    C. Alexandrou, T. Korzec, G. Koutsou, C. Lorce, J.W. Negele, V. Pascalutsa et al.,Quark transverse charge densities in the Delta(1232) from lattice QCD, Nucl. Phys. A825 (2009) 115 [0901.3457]

    2009 arXiv

  118. [125]

    Carlson and M

    C.E. Carlson and M. Vanderhaeghen,Empirical transverse charge densities in the deuteron, Eur. Phys. J. A41 (2009) 1 [0807.4537]

    2009 arXiv

  119. [126]

    Gorchtein, C

    M. Gorchtein, C. Lorce, B. Pasquini and M. Vanderhaeghen,Light-front interpretation of Proton Generalized Polarizabilities, Phys. Rev. Lett.104 (2010) 112001 [0911.2882]

    2010 arXiv

  120. [127]

    Miller,Transverse Charge Densities, Ann

    G.A. Miller,Transverse Charge Densities, Ann. Rev. Nucl. Part. Sci.60 (2010) 1 [1002.0355]

    2010 arXiv

  121. [128]

    Miller,Defining the proton radius: A unified treatment, Phys

    G.A. Miller,Defining the proton radius: A unified treatment, Phys. Rev. C 99 (2019) 035202 [1812.02714]

    2019 arXiv

  122. [129]

    Freese and G.A

    A. Freese and G.A. Miller,Light front synchronization and rest frame densities of the proton: Electromagnetic densities, Phys. Rev. D107 (2023) 074036 [2302.09171]

    2023 arXiv

  123. [130]

    Freese and G.A

    A. Freese and G.A. Miller,Synchronization effects on rest frame energy and momentum densities in the proton, Phys. Rev. D108 (2023) 094026 [2307.11165]

    2023 arXiv

  124. [131]

    Miller and S.J

    G.A. Miller and S.J. Brodsky,Frame-independent spatial coordinate˜z: Implications for light-front wave functions, deep inelastic scattering, light-front holography, and lattice QCD calculations, Phys. Rev. C 102 (2020) 022201 [1912.08911]

    2020 arXiv

  125. [132]

    Jacob and G.C

    M. Jacob and G.C. Wick,On the General Theory of Collisions for Particles with Spin, Annals Phys. 7 (1959) 404

    1959

  126. [133]

    Durand, P.C

    L. Durand, P.C. DeCelles and R.B. Marr,Lorentz Invariance and the Kinematic Structure of Vertex Functions, Phys. Rev. 126 (1962) 1882

    1962

  127. [134]

    Melosh,Quarks: Currents and constituents, Phys

    H.J. Melosh,Quarks: Currents and constituents, Phys. Rev. D9 (1974) 1095

    1974

  128. [135]

    Lorce and B

    C. Lorce and B. Pasquini,On the Origin of Model Relations among Transverse-Momentum Dependent Parton Distributions, Phys. Rev. D84 (2011) 034039 [1104.5651]

    2011 arXiv

  129. [136]

    Polyzou, W

    W.N. Polyzou, W. Glöckle and H. Witala,Spin in relativistic quantum theory, Few Body Syst. 54 (2013) 1667 [1208.5840]

    2013 arXiv

  130. [137]

    Z. Li, M. An and C.-R. Ji,Interpolating Helicity Spinors Between the Instant Form and the Light-front Form, Phys. Rev. D92 (2015) 105014 [1509.00431]. – 35 –

    2015 arXiv

  131. [138]

    Wigner,On the quantum correction for thermodynamic equilibrium, Phys

    E.P. Wigner,On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40 (1932) 749

    1932

  132. [139]

    Hillery, R.F

    M. Hillery, R.F. O’Connell, M.O. Scully and E.P. Wigner,Distribution functions in physics: Fundamentals, Phys. Rept. 106 (1984) 121

    1984

  133. [140]

    Bialynicki-Birula, P

    I. Bialynicki-Birula, P. Gornicki and J. Rafelski,Phase space structure of the Dirac vacuum, Phys. Rev. D44 (1991) 1825

    1991

  134. [141]

    Lorcé, L

    C. Lorcé, L. Mantovani and B. Pasquini,Spatial distribution of angular momentum inside the nucleon, Phys. Lett. B776 (2018) 38 [1704.08557]

    2018 arXiv

  135. [142]

    Lorcé,The relativistic center of mass in field theory with spin, Eur

    C. Lorcé,The relativistic center of mass in field theory with spin, Eur. Phys. J. C78 (2018) 785 [1805.05284]

    2018 arXiv

  136. [143]

    Lorcé, H

    C. Lorcé, H. Moutarde and A.P. Trawiński,Revisiting the mechanical properties of the nucleon, Eur. Phys. J. C79 (2019) 89 [1810.09837]

    2019 arXiv

  137. [144]

    Lorcé,Charge Distributions of Moving Nucleons, Phys

    C. Lorcé,Charge Distributions of Moving Nucleons, Phys. Rev. Lett.125 (2020) 232002 [2007.05318]

    2020 arXiv

  138. [145]

    Lorcé,Relativistic spin sum rules and the role of the pivot, Eur

    C. Lorcé,Relativistic spin sum rules and the role of the pivot, Eur. Phys. J. C81 (2021) 413 [2103.10100]

    2021 arXiv

  139. [146]

    Lorcé and P

    C. Lorcé and P. Wang,Deuteron relativistic charge distributions, Phys. Rev. D105 (2022) 096032 [2204.01465]

    2022 arXiv

  140. [147]

    Lorcé, P

    C. Lorcé, P. Schweitzer and K. Tezgin,2D energy-momentum tensor distributions of nucleon in a large-Nc quark model from ultrarelativistic to nonrelativistic limit, Phys. Rev. D 106 (2022) 014012 [2202.01192]

    2022 arXiv

  141. [148]

    Chen and C

    Y. Chen and C. Lorcé,Pion and nucleon relativistic electromagnetic four-current distributions, Phys. Rev. D106 (2022) 116024 [2210.02908]

    2022 arXiv

  142. [149]

    Chen and C

    Y. Chen and C. Lorcé,Nucleon relativistic polarization and magnetization distributions, Phys. Rev. D107 (2023) 096003 [2302.04672]

    2023 arXiv

  143. [151]

    Lorcé,Electromagnetic and gravitational form factors of the nucleon, PoS SPIN2023 (2024) 010 [2402.00429]

    C. Lorcé,Electromagnetic and gravitational form factors of the nucleon, PoS SPIN2023 (2024) 010 [2402.00429]

    2024 arXiv

  144. [152]

    Lorcé,3D structure of hadrons and energy-momentum tensor, PoS DIS2024 (2025) 003 [2407.10496]

    C. Lorcé,3D structure of hadrons and energy-momentum tensor, PoS DIS2024 (2025) 003 [2407.10496]

    2025 arXiv

  145. [153]

    Kim and H.-C

    J.-Y. Kim and H.-C. Kim,Transverse charge distributions of the nucleon and their Abel images, Phys. Rev. D104 (2021) 074003 [2106.10986]

    2021 arXiv

  146. [154]

    Kim,Electromagnetic multipole structure of a spin-one particle: Abel tomography case, Phys

    J.-Y. Kim,Electromagnetic multipole structure of a spin-one particle: Abel tomography case, Phys. Rev. D106 (2022) 014022 [2204.08248]

    2022 arXiv

  147. [155]

    Hong, J.-Y

    K.-H. Hong, J.-Y. Kim and H.-C. Kim,Two-dimensional transverse charge distributions of the ∆ baryon: Interpolation between the nonrelativistic and ultrarelativistic limits, Phys. Rev. D 107 (2023) 074004 [2301.09267]

    2023 arXiv

  148. [156]

    Castelli, A

    I. Castelli, A. Freese, C. Lorcé, A. Metz, B. Pasquini and S. Rodini,Perturbative results of matrix elements of the axial current and their relation with the axial anomaly, Phys. Lett. B 857 (2024) 138999 [2408.00554]. – 36 –

    2024 arXiv

  149. [157]

    Bhattacharya, Y

    S. Bhattacharya, Y. Hatta and J. Schoenleber,Nonlocal chiral anomaly and generalized parton distributions, Phys. Rev. D111 (2025) 014013 [2411.07024]

    2025 arXiv

  150. [158]

    Weinberg,Charge symmetry of weak interactions, Phys

    S. Weinberg,Charge symmetry of weak interactions, Phys. Rev. 112 (1958) 1375

    1958

  151. [159]

    Fatima, M

    A. Fatima, M. Sajjad Athar and S.K. Singh,Second class currents and T violation in quasielastic neutrino and antineutrino scattering from nucleons, Phys. Rev. D98 (2018) 033005 [1806.08597]

    2018 arXiv

  152. [160]

    Shiomi,Second class current in QCD sum rules, Nucl

    H. Shiomi,Second class current in QCD sum rules, Nucl. Phys. A603 (1996) 281 [hep-ph/9601329]

    1996 arXiv

  153. [161]

    Lorcé and P

    C. Lorcé and P. Schweitzer,Pressure inside hadrons: criticism, conjectures, and all that, 2501.04622

    arXiv

  154. [162]

    Polyakov and P

    M.V. Polyakov and P. Schweitzer,D-term, strong forces in the nucleon, and their applications, 1801.05858

    arXiv

  155. [163]

    Polyakov and P

    M.V. Polyakov and P. Schweitzer,Forces inside hadrons: pressure, surface tension, mechanical radius, and all that, Int. J. Mod. Phys. A33 (2018) 1830025 [1805.06596]

    2018 arXiv

  156. [164]

    Burkert, L

    V.D. Burkert, L. Elouadrhiri, F.X. Girod, C. Lorcé, P. Schweitzer and P.E. Shanahan, Colloquium: Gravitational form factors of the proton, Rev. Mod. Phys.95 (2023) 041002 [2303.08347]

    2023 arXiv

  157. [165]

    Hackett, D.A

    D.C. Hackett, D.A. Pefkou and P.E. Shanahan,Gravitational Form Factors of the Proton from Lattice QCD, Phys. Rev. Lett.132 (2024) 251904 [2310.08484]

    2024 arXiv

  158. [166]

    Leader and C

    E. Leader and C. Lorcé,The angular momentum controversy: What’s it all about and does it matter?, Phys. Rept. 541 (2014) 163 [1309.4235]

    2014 arXiv

  159. [167]

    Repko, P.G

    A. Repko, P.G. Reinhard, V.O. Nesterenko and J. Kvasil,Toroidal nature of the low-energy E1 mode, Phys. Rev. C 87 (2013) 024305 [1212.2088]

    2013 arXiv

  160. [168]

    von Neumann-Cosel et al.,Candidate Toroidal Electric Dipole Mode in the Spherical Nucleus Ni58, Phys

    P. von Neumann-Cosel et al.,Candidate Toroidal Electric Dipole Mode in the Spherical Nucleus Ni58, Phys. Rev. Lett.133 (2024) 232502 [2310.04736]

    2024

  161. [169]

    Day and K.S

    M. Day and K.S. McFarland,Differences in Quasi-Elastic Cross-Sections of Muon and Electron Neutrinos, Phys. Rev. D86 (2012) 053003 [1206.6745]

    2012 arXiv

  162. [170]

    Bernard, N

    V. Bernard, N. Kaiser and U.G. Meissner,Measuring the axial radius of the nucleon in pion electroproduction, Phys. Rev. Lett.69 (1992) 1877

    1992

  163. [171]

    A1 collaboration, A Measurement of the axial form-factor of the nucleon by the p(e, e′π+)n reaction at W = 1125 MeV, Phys. Lett. B468 (1999) 20 [nucl-ex/9911003]

    1999 arXiv

  164. [172]

    Petti, R.J

    R. Petti, R.J. Hill and O. Tomalak,Nucleon axial-vector form factor and radius from future neutrino experiments, Phys. Rev. D109 (2024) L051301 [2309.02509]

    2024 arXiv

  165. [173]

    Kaiser and W

    N. Kaiser and W. Weise,Sizes of the nucleon, Phys. Rev. C 110 (2024) 015202 [2404.11292]

    2024 arXiv

  166. [174]

    Chen,Nucleon relativistic weak-neutral axial-vector four-current distributions, 2411.12521v2

    Y. Chen,Nucleon relativistic weak-neutral axial-vector four-current distributions, 2411.12521v2

    arXiv

  167. [175]

    Freese and G.A

    A. Freese and G.A. Miller,Forces within hadrons on the light front, Phys. Rev. D103 (2021) 094023 [2102.01683]

    2021 arXiv

  168. [176]

    Freese and G.A

    A. Freese and G.A. Miller,Convolution formalism for defining densities of hadrons, Phys. Rev. D 108 (2023) 034008 [2210.03807]. – 37 –

    2023 arXiv

  169. [177]

    Soper,The Parton Model and the Bethe-Salpeter Wave Function, Phys

    D.E. Soper,The Parton Model and the Bethe-Salpeter Wave Function, Phys. Rev. D15 (1977) 1141

    1977

  170. [178]

    Diehl and P

    M. Diehl and P. Hagler,Spin densities in the transverse plane and generalized transversity distributions, Eur. Phys. J. C44 (2005) 87 [hep-ph/0504175]

    2005 arXiv

  171. [179]

    Particle Data Group collaboration, Review of particle physics, Phys. Rev. D110 (2024) 030001

    2024

  172. [180]

    Weinberg,Effects of a neutral intermediate boson in semileptonic processes, Phys

    S. Weinberg,Effects of a neutral intermediate boson in semileptonic processes, Phys. Rev. D 5 (1972) 1412

    1972

  173. [181]

    Garvey, W.C

    G.T. Garvey, W.C. Louis and D.H. White,Determination of proton strange form-factors from neutrino p elastic scattering, Phys. Rev. C 48 (1993) 761

    1993

  174. [182]

    Garvey, E

    G. Garvey, E. Kolbe, K. Langanke and S. Krewald,Role of strange quarks in quasielastic neutrino scattering, Phys. Rev. C 48 (1993) 1919

    1993

  175. [183]

    Pate,Determination of the strange form-factors of the nucleon from nu p, anti-nu p, and parity violating polarized-e p elastic scattering, Phys

    S.F. Pate,Determination of the strange form-factors of the nucleon from nu p, anti-nu p, and parity violating polarized-e p elastic scattering, Phys. Rev. Lett.92 (2004) 082002 [hep-ex/0310052]

    2004 arXiv

  176. [184]

    Sufian, K.-F

    R.S. Sufian, K.-F. Liu and D.G. Richards,Weak neutral current axial form factor using (ν) ν-nucleon scattering and lattice QCD inputs, JHEP 01 (2020) 136 [1809.03509]

    2020 arXiv

  177. [185]

    Ji,Gauge-Invariant Decomposition of Nucleon Spin, Phys

    X.-D. Ji,Gauge-Invariant Decomposition of Nucleon Spin, Phys. Rev. Lett.78 (1997) 610 [hep-ph/9603249]

    1997 arXiv

  178. [186]

    Diehl,Generalized parton distributions, Phys

    M. Diehl,Generalized parton distributions, Phys. Rept. 388 (2003) 41 [hep-ph/0307382]

    2003 arXiv

  179. [187]

    Jefferson Lab Hall A collaboration, Deeply Virtual Compton Scattering Cross Section at High Bjorken xB, Phys. Rev. Lett.128 (2022) 252002 [2201.03714]

    2022 arXiv

  180. [188]

    χQCD collaboration, Quark spins and Anomalous Ward Identity, Phys. Rev. D98 (2018) 074505 [1806.08366]

    2018 arXiv

  181. [189]

    Reinert, H

    P. Reinert, H. Krebs and E. Epelbaum,Precision determination of pion-nucleon coupling constants using effective field theory, Phys. Rev. Lett.126 (2021) 092501 [2006.15360]

    2021 arXiv

  182. [190]

    Goldberger and S.B

    M.L. Goldberger and S.B. Treiman,Decay of the pi meson, Phys. Rev. 110 (1958) 1178

    1958

  183. [191]

    Bardin, J

    G. Bardin, J. Duclos, A. Magnon, J. Martino, A. Richter, E. Zavattini et al.,Measurement of the Ortho - Para Transition Rate in thepµp Molecule and Deduction of the Pseudoscalar Coupling Constant, Phys. Lett. B104 (1981) 320

    1981

  184. [192]

    MuCap collaboration, Measurement of Muon Capture on the Proton to 1% Precision and Determination of the Pseudoscalar CouplinggP, Phys. Rev. Lett.110 (2013) 012504 [1210.6545]

    2013 arXiv

  185. [193]

    Choi et al.,Axial and pseudoscalar nucleon form-factors from low-energy pion electroproduction, Phys

    S. Choi et al.,Axial and pseudoscalar nucleon form-factors from low-energy pion electroproduction, Phys. Rev. Lett.71 (1993) 3927

    1993

  186. [194]

    Moiseeva and M.V

    A.M. Moiseeva and M.V. Polyakov,Dual parameterization and Abel transform tomography for twist-3 DVCS, Nucl. Phys. B 832 (2010) 241 [0803.1777]

    2010 arXiv

  187. [195]

    Panteleeva and M.V

    J.Y. Panteleeva and M.V. Polyakov,Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case, Phys. Rev. D104 (2021) 014008 [2102.10902]. – 38 –

    2021 arXiv

  188. [196]

    Kim and H.-C

    J.-Y. Kim and H.-C. Kim,Energy-momentum tensor of the nucleon on the light front: Abel tomography case, Phys. Rev. D104 (2021) 074019 [2105.10279]

    2021 arXiv

  189. [197]

    J.-Y. Kim, U. Yakhshiev and H.-C. Kim,Medium modification of the nucleon mechanical properties: Abel tomography case, Eur. Phys. J. C82 (2022) 719 [2204.10093]

    2022 arXiv

  190. [198]

    Choudhary, B

    P. Choudhary, B. Gurjar, D. Chakrabarti and A. Mukherjee,Gravitational form factors and mechanical properties of the proton: Connections between distributions in 2D and 3D, Phys. Rev. D 106 (2022) 076004 [2206.12206]

    2022 arXiv

  191. [199]

    Freese and G.A

    A. Freese and G.A. Miller,Unified formalism for electromagnetic and gravitational probes: Densities, Phys. Rev. D105 (2022) 014003 [2108.03301]

    2022 arXiv

  192. [200]

    Bracewell,The Fourier Transform and Its Applications, McGraw-Hill, New York (2000)

    R.N. Bracewell,The Fourier Transform and Its Applications, McGraw-Hill, New York (2000)

    2000

  193. [201]

    Panteleeva, E

    J.Y. Panteleeva, E. Epelbaum, J. Gegelia and U.G. Meißner,On the definition of the nucleon axial charge density, 2412.05050. – 39 –

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