Pith. sign in

REVIEW 4 major objections 4 minor 248 references

This paper argues that few-GeV electron and positron beams can measure tiny charged-current weak processes off protons, and that the Q2-shape of those reactions provides a clean, nuclear-model-free route to the long-disputed axial dipole ma

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2026-08-02 04:56 UTC pith:GU6XGCWH

load-bearing objection A competent, honest review-style benchmark paper; the QE numbers are usable for the stated inputs, but the 'determine the axial dipole mass' promise is contingent on the dipole ansatz the authors themselves show to be questionable. the 4 major comments →

arxiv 2607.13523 v1 pith:GU6XGCWH submitted 2026-07-15 hep-ph hep-exnucl-exnucl-th

Weak charged current induced electron and positron scattering off proton at JLab and MAMI energies

A. Fatima , M. Sajjad Athar , S. K. Singh This is my paper
classification hep-ph hep-exnucl-exnucl-th PACS 13.15.+g13.60.-r12.15.-y13.88.+e
keywords weak charged-current processesaxial-vector form factoraxial dipole masselectron-proton scatteringquasielastic neutrino productionpolarization observablessecond-class currentstime-reversal violation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper develops a comprehensive theoretical framework for weak charged-current electron and positron scattering on protons, covering quasielastic channels, resonance production, and meson production. Its central claim is that the Q2 dependence of cross sections and spin observables is sharply sensitive to the axial-vector form factor, making these measurements a new way to determine the axial dipole mass that has been debated for two decades. It also shows how final-baryon polarization probes time-reversal and second-class-current effects. A sympathetic reader would care because the proposed kinematics combine high luminosity, monochromatic beams, and simple final states, avoiding many nuclear and flux uncertainties that complicate neutrino experiments.

Core claim

Working in the standard V-A framework, with vector and axial form factors constrained by CVC, PCAC, and SU(3), the paper computes total and differential cross sections plus target spin asymmetries and final-baryon polarizations for e-p -> nu_e + n/Lambda/Sigma0, along with resonance and meson channels. Its central claim is that the Q2 dependence of these observables is sharply sensitive to the axial-vector form factor g1(Q2), while being only mildly sensitive to the weak-electric form factor g2; in particular, the dipole with MA=1.026 GeV, z-expansion fits, and lattice-based g1 differ by 20-45% in dsigma/dQ2. The paper therefore proposes the electron-scattering channel as a new, independent

What carries the argument

The axial-vector form factor g1(Q2), parametrized as gA(0)(1+Q2/MA^2)^-2, together with covariant density-matrix spin formalisms for target asymmetries and final-baryon polarizations; these convert W-exchange amplitudes into Q2-dependent observables whose shape distinguishes between parametrizations of the axial form factor.

Load-bearing premise

The entire benchmark program assumes g1(Q2) is a dipole with MA=1.026 GeV; if the actual axial form factor has a different shape, all quoted cross-section benchmarks and the proposed MA extraction shift by tens of percent.

What would settle it

Measure dsigma/dQ2 for e-p -> nu_e n at E_e about 1.1 GeV over Q2=0-1.4 GeV2. If the normalized Q2 shape matches the z-expansion or lattice parametrizations rather than the MA=1.026 dipole across the 20-45% differences shown here, the paper's default benchmark is falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • At the proposed 2.2 GeV, 100 microA, 500 h setup, roughly 10^6 events are expected, making the weak charged-current channel measurable despite its tiny cross section.
  • The Q2 shape of dsigma/dQ2 for e-p -> nu_e n discriminates dipole, z-expansion, and lattice g1 at the 20-45% level, allowing MA to be extracted without nuclear-target uncertainties.
  • Final-baryon transverse polarization PT is predicted to vanish under T-invariance and grow with Im[g2(0)], giving a direct test of T-violation.
  • For Delta(1232) production, electron and positron beams probe the axial N-Delta transition form factors while avoiding pion-background uncertainties common in neutrino experiments.
  • Polarization and asymmetry observables are largely insensitive to MA, so they provide independent cross-checks on the axial sector.

Where Pith is reading between the lines

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

  • If the true axial form factor is not dipole, the extracted MA will be an effective parameter tied to the assumed ansatz; comparing dipole and z-expansion extractions could reveal the underlying shape of g1(Q2).
  • Electron-positron comparisons could isolate vector/axial interference terms, potentially separating g1 from g2 more cleanly than either beam alone.
  • A multi-energy run across 0.855, 1.1, and 2.2 GeV would map the Q2 shape over different kinematic ranges and test the predicted energy dependence of the MA sensitivity.
  • The same formalism can be extended to inelastic channels and nuclear targets, turning these benchmarks into inputs for neutrino-nucleus event generators.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This paper presents a comprehensive theoretical study of charged-current weak processes induced by electrons and positrons on protons at JLab/MAMI energies. The core content is a set of calculations for the quasielastic channels e⁻p→νₑn/Λ/Σ⁰, including total and differential cross sections, target spin asymmetries, and final-baryon polarization observables, with and without time-reversal violation. These are complemented by calculations of Δ(1232), P₁₁(1440), and S₁₁(1535) resonance excitation, η and K/Λ production, and associated strange-particle production. The manuscript claims that these results provide essential theoretical benchmarks for upcoming JLab/MAMI experiments and, in particular, that the quasielastic channel offers an independent way to determine the axial dipole mass M_A and to test G- and T-invariance. The calculations use a standard formalism: leptonic and hadronic tensors, CVC/SU(3) for vector form factors, a dipole axial form factor as the default, and external parametrizations (Bradford electromagnetic form factors, Meyer z-expansion fits, lattice and phenomenological axial inputs).

Significance. If the central claims are taken at face value, the paper would be a valuable reference for a future experimental program: it maps out many observables across a wide kinematic range, identifies channels with significant sensitivity to the axial-vector sector and to second-class currents, and provides a convenient summary of the relevant form-factor inputs. The quasielastic part is internally consistent and builds on standard, well-tested weak-interaction formalism. The paper also gives quantitative sensitivity studies for M_A, g₂(0), C₅ᴬ(0), and alternative g₁(Q²) parametrizations, which is useful for experimental planning. However, the headline claim that the kinematics offers a unique opportunity to determine M_A is load-bearing and, as discussed below, is not supported once the dipole-shape assumption is relaxed; the manuscript itself shows that alternative g₁(Q²) forms change the predictions by tens of percent. The resonance benchmarks are also strongly W_max-dependent. The value of the paper lies more in the systematic calculation machinery and the explicit sensitivity maps than in the specific benchmark numbers, which should be reframed accordingly.

major comments (4)
  1. [§II.A.1(d), Eq. (28), Figs. 2, 4-6] The central claim of an independent determination of the axial dipole mass M_A rests on the dipole ansatz g₁(Q²)=g_A(0)(1+Q²/M_A²)⁻² with M_A=1.026 GeV. The manuscript itself shows this assumption is not neutral: Fig. 2 shows the combined MINERvA+LQCD z-expansion fit exceeds the dipole by ~30% over the full Q² range, and Fig. 6 shows dσ/dQ² changes by 20-45% at Q²=1 GeV² (about 80% for the Chen-Roberts lattice form). The text also notes that M_A≈1.3-1.35 GeV within the dipole reproduces these alternative parameterizations. Therefore an 'extracted M_A' from these observables is an effective parameter that depends on the assumed functional shape and on the fitted Q² range. To support the stated opportunity claim, the paper should (i) explicitly frame M_A as defined within the dipole ansatz, and (ii) provide a quantitative analysis of how well the proposed JLab/MAMI setup can distinguish th
  2. [§III.B.5, Figs. 50-51] The resonance cross sections are not robust benchmarks because they depend strongly on the arbitrary choice of W_max. For P₁₁(1440), increasing W_max from 1.4 GeV to ~1.6 GeV raises σ(Eₑ) by about 65% at 1 GeV and ~100% at 2 GeV; for S₁₁(1535), dσ/dQ² in the peak region changes by ~70% when W_max is varied from 1.7 to 1.5 GeV. The manuscript does not provide a physical criterion for choosing W_max or a range of predictions covering this uncertainty. At minimum, the reported cross sections should be accompanied by a W_max-uncertainty band, and the text should state that the resonance-channel benchmarks are only indicative, not quantitative predictions. This is a load-bearing issue because the resonance sections are presented as part of the same 'essential theoretical benchmark' deliverable.
  3. [§II.C.2, Eq. (51), Figs. 14,17,28,31,40,43] The T-violation predictions scan the free parameter Im g₂(0) over 0-3 (or 1-3) with essentially no experimental input. Since P_T(Q²) is linear in Im g₂(0), the paper is effectively offering a proportionality curve, not a falsifiable prediction. The statement that an experimental observation of P_T 'can be used to probe T-noninvariance' requires either (i) a concrete sensitivity analysis for the proposed JLab/MAMI luminosities, including expected statistical and systematic uncertainties on P_T, or (ii) an explicit statement that the results are templates to be used once an experimental limit on P_T exists. As written, the prominence given to these T-violation predictions exceeds what the current input information justifies.
  4. [§II.D.1, Fig. 4 (right), §II.D.4, Fig. 18] The total-cross-section correlation plots for g₂^R(0) versus M_A (Figs. 5 and 19) show that for the Λ channel, positive and negative values of g₂^R(0) shift σ(Eₑ) by comparable amounts to M_A variations. The text acknowledges that a nonzero g₂^R(0) can bias the extraction of M_A. This degeneracy is not quantified in terms of a fit or a covariance analysis. Given that the paper aims to provide benchmarks for extracting M_A, the degeneracy between g₂(0) and M_A should be included in the extraction discussion, otherwise the M_A-determination claim is incomplete even within the dipole assumption.
minor comments (4)
  1. [Introduction] Typo: 'felicitated' should read 'facilitated'. Also, several captions label positron processes as e⁺+p→νₑ+Δ⁺⁺ (e.g., Figs. 47-49) but the final-state neutrino should be \barνₑ; similarly Fig. 51 shows 'e⁺+p→νₑ+N⋆(1535)' although the text discusses electron-induced excitation.
  2. [Table IV and Section II.A.1] The notation alternates between 'Λ0' and 'Λ' and 'Σ⁰'/'Σ0'; the table header uses 'Λ0' while the text uses 'Λ'. Please unify the notation.
  3. [§II.A.1(d), Fig. 2] The z-expansion coefficients in Table V are quoted to many digits but no corresponding uncertainties or covariance matrix are given. Since the paper emphasizes sensitivity to different g₁ forms, the reader cannot assess whether the differences between fits are statistically significant. Adding uncertainties would increase the usefulness of these benchmark calculations.
  4. [§III.B.5, Figs. 50-51] The captions say 'Lines and points have the same meaning as in Fig. 50' but the legends are not fully described in the captions. Please spell out the line styles for each W_max choice in the captions or in the figures themselves.

Circularity Check

0 steps flagged

No significant circularity: the paper's observables are explicit functions of externally anchored form-factor inputs, and the MA-determination claim is a proposed experimental extraction, not a fitted prediction.

full rationale

The derivation chain is a standard weak-interaction calculation: Eq. (8) gives dσ/dQ² directly in terms of the leptonic and hadronic tensors, with the hadronic current built from vector form factors (Bradford et al.), the axial form factor g1(Q²) taken as input — Eq. (28), the dipole with MA = 1.026 GeV, or z-expansion/lattice alternatives — Eq. (32) for g2(Q²), and SU(3) coefficients for the strangeness-changing channels. The computed cross sections, asymmetries, and polarizations are explicit functions of these inputs; no quantity is fitted to a subset of the presented observables and then renamed as a prediction. The abstract's claim of 'alternative ways to determine the axial dipole mass' is a proposal for future experimental extraction, not a claim that this paper itself determines MA from its own outputs. The paper's own Figs. 2 and 6 quantify the dependence on the g1 parametrization and on MA; this is model dependence and caveat, not circularity. Self-citations occur for the covariant density-matrix formalism and for resonance helicity/cut-off parameters fitted in earlier work to external CLAS photoproduction data; these are methodology citations or externally anchored fits, not a self-referential chain that assumes the present benchmark results. Thus no circular step satisfying the quoted-evidence standard can be identified.

Axiom & Free-Parameter Ledger

11 free parameters · 8 axioms · 0 invented entities

Eleven free parameters, mostly external fits or manual cut choices; the only ad-hoc modeling choice local to this paper is the dipole ansatz in the axial sector. Several inputs (helicity amplitudes, ΛB, CA3/CA4) were fitted by the authors in prior papers to external electromagnetic data — legitimate as independent support but not author-independent. No invented entities.

free parameters (11)
  • MA (axial dipole mass) = 1.026 GeV (world average [11]); varied to 1.35 GeV
    Central input of the dipole form g1(Q²)=gA(0)(1+Q²/MA²)⁻², Eq. (28); the entire MA-determination proposal rests on this parameter.
  • M2 (dipole mass of weak electric form factor g2) = 1.026 GeV (M2 = MA)
    Sec. II A 1 (e): "no experimental information on M2 ... set M2 = MA = 1.026 GeV".
  • g2R(0)/g2I(0) (second-class current strength) = scanned: real ±2 (n), ±3 (Λ, Σ⁰); imaginary 0-3
    Sec. II A 1 (e): ranges from old β-decay/muon-capture/neutrino analyses; for Im g2Λ(0) the upper bound is essentially unconstrained; drives all G/T-violation observables.
  • x1, x2 (SU(3) axial ratios) = x1 = 0.364; x2 assumed constant
    Sec. II A 1 (c): from hyperon semileptonic decay analysis [81]; assumed Q²-independent — an ad-hoc simplification.
  • CA5(0) (N-Δ axial coupling) = 1.2 (GT relation with fπ=0.97mπ, gΔNπ=28.6)
    Eq. (70); varied 0.87-1.4 to produce bands in Figs. 44, 47.
  • z-expansion coefficients a0-a6 = Table V (MINERvA H, LQCD, deuterium, combined)
    Eqs. (29)-(30); taken from fits in refs. [96, 97]; the paper notes the spread across fits (e.g., a4, a5 differ in sign between deuterium and LQCD fits).
  • Helicity amplitude parameters Aα(0), a1, b1 = Tables VIII & X (fitted to CLAS electroproduction)
    Eq. (98); "obtained by fitting the meson electroproduction data ... as measured in the CLAS experiment" (Sec. III B 2), in the authors' earlier works.
  • Strong form-factor cut-offs ΛB = ΛR = 0.75 GeV (proton), 0.72 GeV (neutron)
    Sec. IV C 1-2: fitted to η photoproduction data [224, 225] in Ref. [215]; used for Born and resonance terms.
  • CA3/CA4 parametrization constants = a3=-4.61, b3=2.8 GeV², MA3=1.67 GeV; x3=1, x4=0.74, MAS=1 GeV
    Eqs. (78)-(79): the Q² dependence "has been given numerically ... in the form of plots. We have fitted them assuming dipole forms" (Sec. III A 3 (b)) — digitization of figures.
  • Wmax (invariant-mass upper cut) = 1.4 GeV (P11), 1.5 GeV (S11), 1.8 GeV (η), 1.4 GeV (Δ)
    Manual kinematic cuts; changing Wmax by ~0.2-0.3 GeV changes resonance σ by 40-100% (Sec. III B 5) — the largest sensitivity in the paper.
  • α (form-factor scale in Dl(x)) = 400 MeV
    Eq. (108), from Ref. [216]; shapes the energy-dependent decay widths of P11/S11.
axioms (8)
  • domain assumption CVC hypothesis: f3 = 0 and weak vector form factors equal electromagnetic ones via isospin
    Sec. II A 1 (ii): used to build f1,2 for n, Λ, Σ⁰ and to fix N-Δ vector form factors (Eq. 65).
  • domain assumption PCAC + pion/kaon pole dominance
    Sec. II A 1 (v), III A 3 (a): relates g3, CA6, g1CC(0) to couplings; the paper sets g3 ≈ 0 for electrons.
  • domain assumption SU(3) octet symmetry for ΔS=1 transitions with Q²-independent x1,2
    Sec. II A 1 (c): gpΛ1,2 and gpΣ01,2 built from gpn1,2 via x1,2 = const; paper admits SU(3) breaking in nature.
  • domain assumption G-invariance (absence of second-class currents) in the baseline set: f3 = g2 = 0
    Sec. II A 1 (iv): baseline calculations assume it; the paper then relaxes it to study G/T violation.
  • domain assumption T-invariance: all form factors real
    Sec. II A 1 (i): baseline; relaxed via imaginary g2(0).
  • ad hoc to paper Dipole ansatz for g1(Q²) (Eq. 28) and g2 (Eq. 32)
    Default axial form factors; alternatives (z-expansion, lattice) are shown as comparisons, but the central benchmark tables use the dipole.
  • standard math Rarita-Schwinger formalism for spin-3/2 with off-shell ambiguities accepted
    Sec. III A: the paper chooses RS over Pascalutsa-Timmermans for Δ(1232), justified by the phenomenological availability of form factors.
  • domain assumption Bradford et al. electromagnetic form factors
    Sec. II A 1 (b): external parametrization used for the vector sector.

pith-pipeline@v1.3.0-alltime-deepseek · 76274 in / 21751 out tokens · 214175 ms · 2026-08-02T04:56:48.809082+00:00 · methodology

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read the original abstract

The development of next-generation, high-luminosity, and high-precision charged lepton beam facilities at JLab and MAMI has opened, in recent years, a new frontier in the exploration of weak interaction processes induced by electrons and positrons in the neutral current sector, which can also be used to study weak interaction processes induced by charged currents. In particular, these processes in the intermediate energy regime, spanning from a few hundred MeV to a few GeV, play a crucial role in understanding electroweak dynamics, nucleon structure, and hadronic response functions. This review presents a comprehensive theoretical study of weak charged-current interactions of electrons and positrons with free protons, encompassing quasielastic scattering in both the strangeness conserving and strangeness changing channels, together with inelastic production of the $P_{33}$(1232), $P_{11}$(1440), $S_{11}$(1535) resonances, $\eta$ and $K$ mesons, and associated production of strange particles. We analyse differential and total cross sections, polarization observables of the final baryons, and spin asymmetries of the proton target, demonstrating their sensitivity to the underlying weak interaction dynamics and to possible second class currents, thereby enabling stringent tests of G- and T- invariance. The explored kinematic region also offers a unique and independent opportunity to constrain the axial vector sector of the weak interaction, and it provides a discussion of alternative ways to determine the axial dipole mass in the quasielastic scattering region, a fundamental parameter that is in debate for nearly two decades. It also focuses on the study of the axial-vector form factors associated with the excitation of the $P_{33}(1232)$ resonance in a manner that is free from the uncertainties inherent in their determination from studies of (anti)neutrino-induced weak processes.

Figures

Figures reproduced from arXiv: 2607.13523 by A. Fatima, M. Sajjad Athar, S. K. Singh.

Figure 1
Figure 1. Figure 1: FIG. 1: Feynman diagram for the process [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Diagrammatic representation of the process [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Total cross section [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
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Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
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Figure 38. Figure 38: FIG. 38 [PITH_FULL_IMAGE:figures/full_fig_p035_38.png] view at source ↗
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Figure 39. Figure 39: FIG. 39 [PITH_FULL_IMAGE:figures/full_fig_p036_39.png] view at source ↗
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Figure 42. Figure 42: FIG. 42 [PITH_FULL_IMAGE:figures/full_fig_p038_42.png] view at source ↗
Figure 43
Figure 43. Figure 43: FIG. 43 [PITH_FULL_IMAGE:figures/full_fig_p039_43.png] view at source ↗
Figure 44
Figure 44. Figure 44: FIG. 44: Total scattering cross section ( [PITH_FULL_IMAGE:figures/full_fig_p047_44.png] view at source ↗
Figure 45
Figure 45. Figure 45: FIG. 45: Total scattering cross section ( [PITH_FULL_IMAGE:figures/full_fig_p048_45.png] view at source ↗
Figure 46
Figure 46. Figure 46: FIG. 46: Total scattering cross section ( [PITH_FULL_IMAGE:figures/full_fig_p048_46.png] view at source ↗
Figure 47
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Figure 49. Figure 49: FIG. 49 [PITH_FULL_IMAGE:figures/full_fig_p051_49.png] view at source ↗
Figure 50
Figure 50. Figure 50: FIG. 50: Total scattering cross section ( [PITH_FULL_IMAGE:figures/full_fig_p055_50.png] view at source ↗
Figure 51
Figure 51. Figure 51: FIG. 51 [PITH_FULL_IMAGE:figures/full_fig_p056_51.png] view at source ↗
Figure 52
Figure 52. Figure 52: FIG. 52: Electron and positron scattering and reaction plan [PITH_FULL_IMAGE:figures/full_fig_p058_52.png] view at source ↗
Figure 53
Figure 53. Figure 53: FIG. 53: Feynman diagrams corresponding to the nonresonant [PITH_FULL_IMAGE:figures/full_fig_p062_53.png] view at source ↗
Figure 54
Figure 54. Figure 54: FIG. 54: (Left panel) Total scattering cross section [PITH_FULL_IMAGE:figures/full_fig_p064_54.png] view at source ↗
Figure 55
Figure 55. Figure 55: FIG. 55: Feynman diagrams corresponding to the nonresonant [PITH_FULL_IMAGE:figures/full_fig_p065_55.png] view at source ↗
Figure 56
Figure 56. Figure 56: FIG. 56: (Left panel) Total scattering cross section ( [PITH_FULL_IMAGE:figures/full_fig_p070_56.png] view at source ↗
Figure 57
Figure 57. Figure 57: FIG. 57: Feynman diagrams for the processes [PITH_FULL_IMAGE:figures/full_fig_p071_57.png] view at source ↗
Figure 58
Figure 58. Figure 58: FIG. 58: The total scattering cross section ( [PITH_FULL_IMAGE:figures/full_fig_p073_58.png] view at source ↗
Figure 59
Figure 59. Figure 59: FIG. 59: The differential scattering cross section [PITH_FULL_IMAGE:figures/full_fig_p073_59.png] view at source ↗
Figure 60
Figure 60. Figure 60: FIG. 60: Total scattering cross section [PITH_FULL_IMAGE:figures/full_fig_p074_60.png] view at source ↗

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Works this paper leans on

248 extracted references · 51 canonical work pages

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    Nonresonant contribution: The expression for the hadronic current jµ corresponding to the various nonresonant diagrams for electron and positron induced single kaon production, as depicted in Fig. 57, are o btained using the nonlinear sigma model discussed 71 (A) W (q) N (p) Λ , Σ(p + q) N (p′) K(pK) (B) W (q) N (p) N (p′) K(pK) π, η(p − p′) (C) W (q) N (...

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