Pith. sign in

REVIEW 4 major objections 3 minor 10 cited by

The nucleon's axial form factor falls slower with momentum transfer than deuterium-based fits have claimed, so quasielastic neutrino cross sections are 30–40% larger than previously assumed.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 16:14 UTC pith:JEDGUYVC

load-bearing objection The hydrogen-vs-deuterium tension in FA is real and the analysis is careful, but the compatibility p-values use 1 degree of freedom when they should use 2-3, and the final recommendation leans on an unpublished sister paper. the 4 major comments →

arxiv 2512.14097 v4 pith:JEDGUYVC submitted 2025-12-16 hep-ex hep-ph

The Nucleon Axial Form Factor from Elementary Target Data

A.S. Meyer , T. Cai , M. Moore , S. Akhter , Z. Ahmad Dar , M. Sajjad Athar , M. Betancourt , H. Budd
show 35 more authors
G. Caceres D.S. Correia G.A. D\'iaz J. Felix A.M. Gago H. Gallagher P.K. Gaur S.M. Gilligan R. Gran E. Granados D.A. Harris A.L. Hart R.J. Hill J. Kleykamp A. Klustov\'a M. Kordosky D. Last A. Lozano S. Manly W.A. Mann K.S. McFarland O. Moreno J.K. Nelson A. Olivier V. Paolone G.N. Perdue C. Pernas M.A. Ram\'irez R.D. Ransome D. Ruterbories H. Schellman C.J. Solano Salinas N.H. Vaughan M.O. Wascko L. Zazueta (the MINERvA collaboration)
This is my paper
classification hep-ex hep-ph PACS 13.15.+g14.20.Dh12.38.Gc
keywords nucleon axial form factorquasielastic neutrino scatteringz expansiondeuterium targethydrogen targetlattice QCDaxial radiusMINERvA
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.

This paper argues that the standard deuterium-target measurements of the nucleon axial form factor, FA(Q²), are biased low. A new antineutrino-hydrogen cross-section measurement and lattice QCD predictions agree with each other but disagree with all four deuterium datasets at moderate and high momentum transfer. The paper concludes that deuterium-based extractions underestimate both the central value and the uncertainty of FA, and it recommends replacing them with the LQCD or LQCD-plus-hydrogen z-expansion fits. If correct, neutrino quasielastic cross sections used in long-baseline oscillation analyses would be 30–40% higher at the relevant energies.

Core claim

The central claim is that the axial form factor FA(Q²) has a slower falloff with Q² than deuterium bubble-chamber data had indicated. Through Δχ² compatibility tests, the paper shows that the hydrogen-target data are inconsistent with the combined deuterium datasets—at the Q²≥0.2 GeV² cut, the compatibility p-value is about 4×10⁻⁴—while the hydrogen data and lattice QCD are compatible (p≈0.10–0.15). The paper therefore rejects the deuterium-based result from a 2016 analysis, provides z-expansion parameterizations for the MINERvA hydrogen fit, the LQCD fit, and a combined hydrogen–LQCD fit, and recommends the kmax=6, λ=0 fits as the new best form-factor parameterizations.

What carries the argument

The z expansion: a conformal mapping that transforms Q² into a variable z with |z|<1, expressing FA as a truncated power series in z. Coefficients are constrained by derivative sum rules and the axial coupling gA, and the truncation order and regularization strength are chosen through an L-curve heuristic. This machinery exposes a degeneracy between floating normalizations and form-factor shape in the deuterium fits once the regularization is relaxed, which is how the paper isolates the hydrogen–deuterium tension.

Load-bearing premise

The conclusion that deuterium data are biased rests on assuming the MINERvA hydrogen cross-section measurement is accurate and its uncertainties fully understood; if hidden flux or efficiency systematics inflated FA at moderate Q², the tension would not indicate a deuterium problem.

What would settle it

A future high-statistics measurement of neutrino or antineutrino quasielastic scattering on a free proton target, using a different beam and detector with independent flux determination, would settle the point: if it lands near the deuterium-based form factor rather than the hydrogen/LQCD one, the tension is an experimental artifact. Alternatively, a lattice QCD calculation of the deuterium correction R(Eν,Q²) would test whether unknown nuclear effects explain the discrepancy.

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

If this is right

  • If the deuterium results are replaced, neutrino quasielastic cross sections increase by 30–40% at relevant energies, directly affecting event-rate predictions in long-baseline oscillation experiments.
  • The z-expansion parameterizations with uncertainties are provided for LQCD and LQCD+MINERvA fits, allowing Monte Carlo generators to use flexible form factors instead of the single-parameter dipole.
  • Uncertainties on FA at Q²=0.5 GeV² shrink to about 2% when LQCD results are included, compared with the precision previously assumed from deuterium fits.
  • Future oscillation analyses should treat deuterium-based axial form factors with caution and use models flexible enough to accommodate the slower falloff.
  • The paper recommends the kmax=6 fits to LQCD or LQCD+MINERvA as the new default, citing agreement between two genuinely free-nucleon constraints.

Where Pith is reading between the lines

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

  • Going beyond the paper: if the hydrogen–LQCD tension with deuterium persists, it would point to missing energy-transfer dependence in the deuterium correction (e.g., two-particle–two-hole contributions), which would also affect neutrino–nucleus cross-section modeling beyond the axial form factor.
  • An editorial caveat: the argument leans on the unpublished LQCD sister paper, so the quoted combined-fit precision should be treated as tentative until that result is independently reviewed.
  • A testable extension: re-fit the deuterium event distributions with a deuterium correction R(Eν,Q²) that depends on energy transfer; if the tension disappears, the problem is the nuclear correction rather than FA itself.
  • The consistency of the axial radius r_A² between hydrogen and deuterium at low Q² implies that low-Q² measurements alone cannot distinguish the competing form-factor shapes; future high-precision pion electroproduction data could help pin the slope.

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 / 3 minor

Summary. The paper reanalyzes constraints on the nucleon axial form factor F_A(Q^2) from neutrino scattering on elementary targets: the ANL, BNL, and FNAL deuterium bubble-chamber event distributions, the BEBC deuterium differential cross section, the MINERvA antineutrino-hydrogen differential cross section, and LQCD results from a companion paper (Ref. [16]). The analysis uses a z-expansion parameterization with derivative sum rules, an L-curve heuristic to set the regularization strength λ, floating normalizations for the historical deuterium event distributions, and Δχ² compatibility tests to compare datasets. The paper reports significant tension between hydrogen and deuterium target data, concludes that deuterium-based extractions underestimate both the central value and uncertainty of F_A at moderate/high Q^2, and recommends replacing deuterium-based results with the LQCD or LQCD+MINERvA z-expansion fits. Explicit fit coefficients, covariance matrices, axial radii, and predicted quasielastic cross sections are provided.

Significance. If the central claim holds, the result is significant for neutrino oscillation experiments: the slower Q^2 falloff preferred by MINERvA and LQCD increases quasielastic cross sections by 30–40% relative to previous deuterium-based predictions. The paper is transparent in providing explicit parameterizations, covariance matrices, and a systematic account of regularization and normalization choices. Its main strengths are the use of genuinely elementary-target hydrogen data and the concrete, reproducible fit outputs. However, the headline incompatibility is quantified by Δχ² tests that use an incorrect number of degrees of freedom, and the recommended LQCD-based parameterizations rely on an unpublished companion paper. Both issues are load-bearing and require revision before the conclusions can be accepted.

major comments (4)
  1. [Sec. III B, Eq. (29), Tables III–VIII] The compatibility tests are evaluated as χ² with 1 degree of freedom, but the only parameters shared between datasets are the z-expansion coefficients: 2 for kmax=6 and 3 for kmax=7. All nuisance parameters (normalizations, efficiencies, flux bin shifts, BEBC flux normalization) are dataset-specific and remain free in both the separate and combined fits. By Wilks’ theorem, the asymptotic DoF for Δχ² = χ²_{A+B} − χ²_A − χ²_B is the number of shared parameters, i.e., 2 or 3. Recomputing the reported p-values: Table V, Q²_min=0.20 GeV², kmax=6: p≈0.002 (not 4×10⁻⁴); Table V, Q²_min=0.06 GeV²: p≈0.11; Table VI, Q²_min=0.20 GeV²: p≈0.007; Table VII, 10% flux, kmax=6: p≈0.052 and kmax=7: p≈0.13; Table VIII: p≈0.11 (kmax=6) and p≈0.25 (kmax=7). The high-Q² tension between all deuterium data and MINERvA remains significant, but the blanket statement that all deuterium datasets are incompatible w
  2. [Sec. III C 4 and Sec. V (Recommendations)] The inference from the statistical tension to the conclusion that deuterium data are biased and underestimate F_A is not derived. The argument that the MINERvA dataset is the more accurate estimate is qualitative (Sec. III C 4: “lend credence”) and assumes that the MINERvA flux and efficiency systematics are fully understood and unbiased. A concrete sensitivity test is needed: for example, what global normalization or shape shift in the MINERvA cross section would remove the high-Q² incompatibility? Without such a test, omitting all four deuterium datasets is a modeling judgment, not a result demonstrated by the analysis. This is load-bearing because the paper’s central recommendation replaces deuterium-based parameterizations with the LQCD and LQCD+MINERvA results.
  3. [Sec. IV B and IV D; Ref. [16]] The LQCD results used for the recommended LQCD and LQCD+MINERvA fits are taken from an unpublished companion paper (Ref. [16]). The covariance derating procedure is described, but the actual LQCD data, systematic uncertainties, and correlation structure are not available in this manuscript. Since these fits are the paper’s recommended best parameterizations, the essential LQCD input should be included in an appendix or supplementary material, or the recommendations should be explicitly marked as preliminary pending Ref. [16]. As written, an independent reader cannot reproduce or assess the dominant input.
  4. [Sec. III C 3 and Fig. 10] The “Deuterium+BEBC (envelope)” uncertainty band is constructed from the extreme bounds of the two Q²_min cuts. This is not a statistical uncertainty and is used to support the claim that the deuterium result underestimates the uncertainty (“extreme bounds fall significantly below the other results at larger Q²”). This envelope should be labeled as a systematic model-dependence envelope, and claims about “underestimation of uncertainty” should be separated from the statistical compatibility tests. Otherwise the figure implicitly inflates the evidential weight of the envelope.
minor comments (3)
  1. [Fig. 8 caption] The caption says “The same as Fig. 8, but fit to different choices of t0”; it should refer to Fig. 7.
  2. [Tables III–VIII] The header “p ∆χ²” is confusing; recommend labeling the p-value column explicitly (e.g., “p(Δχ²)”). Also specify the DoF used for each p-value in the table caption.
  3. [Sec. III C 1] The statement that the Hulthén wavefunction underpredicts high-momentum spectator protons “is attributed to final state interactions in the literature” lacks a specific citation. Please provide a reference or soften the claim.

Circularity Check

0 steps flagged

No circular reduction; hydrogen–deuterium tension is an empirical fit comparison, with self-citation and statistical caveats noted.

full rationale

The central derivation is a set of fits of independent datasets (MINERvA hydrogen; ANL/BNL/FNAL/BEBC deuterium) to a z-expansion axial form factor. The FA(Q2) curves and their uncertainties are fit outputs; no parameter is defined in terms of the conclusion. The deuterium-underestimate claim rests on Δχ² compatibility tests (Eq. 29, Tables III–VIII), which are empirical comparisons between disjoint datasets, not a construction that forces the answer. The high-Q²min tension (e.g., Δχ²=12.4 with kmax=6/λ=0) persists even if the reported 1-dof p-values are re-evaluated with the 2–3 shared z-expansion coefficients; I therefore do not view the central tension as circular. Two caveats are worth stating, but neither is a circular reduction. First, the Δχ² p-values in Tables III–VIII are quoted with 1 degree of freedom although a simultaneous fit of two disjoint datasets shares 2 (kmax=6) or 3 (kmax=7) free z-expansion coefficients; some marginal incompatibilities (e.g., MINERvA–BEBC Δχ²=5.9) become non-significant at df=2–3. That is a statistical correctness issue, not a self-referential definition. Second, the LQCD fit used in the final recommendation is imported from Ref. [16], a sister paper 'in preparation' by the same first author; however, the underlying lattice-QCD results are published and cited [33–37], and the MINERvA-vs-deuterium comparison does not depend on Ref. [16]. The z-expansion coefficient translation in Sec. IV C (Eq. 47) is a mathematical identity for re-expressing a known curve, not a prediction generated from its own fit. No step in the paper exhibits Eq. X = Eq. Y by construction or a fitted parameter renamed as a prediction. Overall: no significant circularity; score 2 reflects the self-citation/availability caveat.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The paper's central output is a fit, so most free parameters are z-expansion coefficients and normalizations. It introduces no new entities. Main load-bearing external assumption is the unpublished LQCD sister-paper result.

free parameters (6)
  • z-expansion coefficients a1, a2 (kmax=6 fits) = MINERvA: a1=-1.65(24), a2=0.94(30); LQCD: -1.721(52), 0.31(13); Combined: -1.743(49), 0.38(12); Deuterium+BEBC: see Eqns
    Fitted to cross-section data; these are the shape parameters of FA(Q2).
  • Floating normalizations for ANL, BNL, FNAL event distributions = not quoted in text
    Flux uncertainties poorly constrained; normalizations allowed to float freely, causing degeneracy with FA shape (Sect II D3).
  • BEBC flux normalization nuisance = 10% (tested 20%)
    Single normalization multiplier with Gaussian penalty; affects absolute scale of deuterium cross sections.
  • Efficiency correction nuisance parameters ξ = not quoted
    One per bubble-chamber dataset; from Figure 1 of Ref [44] uncertainty.
  • Regularization strength λ = 0 for kmax=6; 0.1 for kmax=7
    Selected by L-curve heuristic; a data-driven choice rather than a fitted parameter, but affects uncertainties.
  • z-expansion kinematic parameter t0 = -0.50 GeV^2
    Chosen to minimize |z| over experimental range; not fitted, but affects coefficient values.
axioms (6)
  • domain assumption PCAC and pion pole dominance: FP = 2 M_N^2/(M_pi^2+Q^2) FA
    Used to eliminate induced pseudoscalar; justified by LQCD citations and m_l^2 suppression.
  • domain assumption Deuterium correction R(Q2) depends only on Q2 (Eq. 17), using Singh correction
    Paper acknowledges R should depend on Eν/ω; 2p2h and FSI not included; central to deuterium fits.
  • domain assumption Vector form factors are precisely known from BBBA05/Borah et al.
    Uncertainty assessed via PCA and found small relative to axial uncertainty.
  • standard math z-expansion unitarity bounds and sum rules at z=1 (Eq. 10) justify truncation and regularization
    Standard conformal mapping; sum rules regulate Q^2->infinity behavior.
  • ad hoc to paper LQCD results from sister paper Ref [16] are valid and their unknown correlations bounded by covariance derating
    The combined recommended fit is dominated by these not-yet-published results.
  • domain assumption gA fixed exactly to PDG 1.2754
    Axial coupling at Q2=0 pinned; uncertainty negligible for this analysis.

pith-pipeline@v1.3.0-alltime-deepseek · 30774 in / 11378 out tokens · 90311 ms · 2026-08-03T16:14:35.027080+00:00 · methodology

0 comments
read the original abstract

Precise neutrino-nucleon amplitudes are essential ingredients for predicting neutrino event rates in current and upcoming long-baseline neutrino oscillation experiments. A common neutrino interaction with a low reaction threshold and with most of the energy carried by two final state particles is quasielastic scattering, for which the nucleon axial form factor, $F_{A}(Q^{2})$, is a dominant source of uncertainty. Improvements to the nucleon axial form factor rely on neutrino scattering data with elementary targets to reduce or eliminate the need for nuclear modeling systematics. This work examines constraints on the nucleon axial form factor that can be achieved from datasets of neutrino scattering on deuterium targets, Lattice QCD predictions, and from the recent hydrogen target data from the MINERvA Collaboration. Significant tension is found between hydrogen and deuterium target data, suggesting that extractions from deuterium underestimate both the central value and uncertainty of the form factor. Parameterizations for and uncertainties of the nucleon axial form factor using the $z$ expansion are provided.

Figures

Figures reproduced from arXiv: 2512.14097 by A. Klustov\'a, A.L. Hart, A. Lozano, A.M. Gago, A. Olivier, A.S. Meyer, C.J. Solano Salinas, C. Pernas, D.A. Harris, D. Last, D. Ruterbories, D.S. Correia, E. Granados, G.A. D\'iaz, G. Caceres, G.N. Perdue, H. Budd, H. Gallagher, H. Schellman, J. Felix, J. Kleykamp, J.K. Nelson, K.S. McFarland, L. Zazueta (The MINERvA Collaboration), M.A. Ram\'irez, M. Betancourt, M. Kordosky, M. Moore, M.O. Wascko, M. Sajjad Athar, N.H. Vaughan, O. Moreno, P.K. Gaur, R.D. Ransome, R. Gran, R.J. Hill, S. Akhter, S. Manly, S.M. Gilligan, T. Cai, V. Paolone, W.A. Mann, Z. Ahmad Dar.

Figure 1
Figure 1. Figure 1: FIG. 1. L-curve obtained from fitting only the MINERvA dataset. The left plot shows the full range [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. L-curve obtained from fitting all of the deuterium datasets together. The left plot shows the [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Plots of the axial form factor as a function of the 4-momentum transfer [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The fit axial form factors both before and after the addition of the BEBC dataset to the other event distributions. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The fit axial form factors for the BEBC dataset [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Axial form factor results for fits comparing the complete set of deuterium data versus the MINERvA dataset. In [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The MINERvA dataset fit to different choices of [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The MINERvA dataset fit to both the BBBA05 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The same as the top panel of Fig. [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The top panel shows the final choices for the [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The quasielastic cross section for the interaction [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Extraction of the nucleon axial form factor from Lattice QCD using NNLO chiral perturbation theory

    hep-ph 2026-06 conditional novelty 6.0

    A global NNLO chiral-perturbation-theory fit with explicit Delta to lattice-QCD axial form factors gives g_A = 1.257 ± 0.011 and r_A² = 0.312 ± 0.037 fm².

  2. Measurement of muon (anti-)neutrino charged-current quasielastic-like cross section using off-axis NuMI beam at ICARUS

    hep-ex 2026-04 conditional novelty 6.0

    First ICARUS off-axis NuMI measurement of muon-neutrino CCQE-like cross sections on argon yields four flux-averaged differential distributions that agree with all tested event generators.

  3. Measurement of muon (anti-)neutrino charged-current quasielastic-like cross section using off-axis NuMI beam at ICARUS

    hep-ex 2026-04 accept novelty 5.0

    ICARUS measures flux-averaged differential CCQE-like cross sections in lepton angle, lepton-proton opening angle, and transverse kinematic imbalance variables, finding agreement with event generator predictions within...

  4. Nucleon axial-vector form factor and radius from radiatively-corrected antineutrino scattering data

    hep-ph 2026-01 unverdicted novelty 5.0

    Radiative corrections applied to MINERvA antineutrino data yield updated values for the nucleon axial-vector form factor G_A and axial radius.

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

    hep-ph 2026-07 conditional novelty 4.0

    Calculated cross sections and spin observables for weak charged-current e±+p scattering at JLab-MAMI energies, presented as benchmarks to extract the axial dipole mass and test G- and T-invariance.

  6. Extraction of the nucleon axial form factor from Lattice QCD using NNLO chiral perturbation theory

    hep-ph 2026-06 unverdicted novelty 4.0

    NNLO ChPT with explicit Delta fits lattice data to extract g_A = 1.257 ± 0.011 and axial radius squared 0.312 ± 0.037 fm² at the physical point.

  7. Benchmarking State-of-the-Art Theory and Empirical Models of Pionless Neutrino-Argon Scattering in GENIE

    hep-ph 2026-05 unverdicted novelty 4.0

    GENIE model components for pionless neutrino-argon scattering are swapped and tested against MicroBooNE data to compare sophisticated theory-based options with empirical alternatives.

  8. Benchmarking State-of-the-Art Theory and Empirical Models of Pionless Neutrino-Argon Scattering in GENIE

    hep-ph 2026-05 unverdicted novelty 4.0

    The study evaluates and contrasts sophisticated and empirical model components in GENIE for pionless neutrino-argon interactions using recent MicroBooNE measurements.

  9. Two-body current and axial form factor effects in charged-current quasielastic neutrino-nucleus scattering within the NEUT event generator

    nucl-th 2026-05 unverdicted novelty 4.0

    Adding two-body currents and updated axial form factors to a relativistic spectral function model increases predicted cross sections for neutrino-carbon scattering, with the LQCD+MINERvA fit overestimating data while ...

  10. Measurement of muon (anti-)neutrino charged-current quasielastic-like cross section using off-axis NuMI beam at ICARUS

    hep-ex 2026-04 unverdicted novelty 4.0

    ICARUS measures flux-averaged differential CCQE-like cross sections in lepton angle, opening angle, and transverse imbalance variables, finding general agreement with event generators but insufficient power to discrim...

Reference graph

Works this paper leans on

81 extracted references · 33 linked inside Pith · cited by 6 Pith papers

  1. [1]

    There are a few considerations to be conscious of:

    Event Distribution Datasets In the ANL, BNL, and FNAL deuterium datasets, the low-Q2 region requires the most care due to its sensitivity to systematic effects. There are a few considerations to be conscious of:

  2. [2]

    dN dEν (⃗ η) # i =

    Flux Uncertainty The last column of Tab. I is the method that was ap- plied to capture the uncertainty due to the neutrino flux. There are three options listed. For the ANL, BNL, and FNAL datasets, labeled with “dN/dE,” the flux uncer- tainty is applied to the bins of the neutrino energy event distribution. Each bin in the energy event distribution is all...

  3. [3]

    The available distributions lack correlations be- tween the eventE ν andQ 2

    Normalizations The ANL, BNL, and FNAL datasets, lack sufficient information to absolutely normalize the event distribu- tions. The available distributions lack correlations be- tween the eventE ν andQ 2. Without this information, there is a complicated interplay between the appliedQ 2 cut, the differential cross section with its deuterium cor- rection, an...

  4. [4]

    acceptance

    Efficiency Corrections The deuterium bubble chamber experiments suffered from reduced efficiency – referred to as “acceptance” in Ref. [44] – when tracks were not prominent enough to measure accurately. This reduced efficiency primarily af- fected the low-Q2 region and was accounted for with the efficiency correction f(Q 2;ξ) = ϵ(Q2) +ξδϵ(Q 2) −1 = 1 ϵ(Q2...

  5. [5]

    dND dQ2 # i =N Z bini dQ2 Z dEν

    Deuterium Corrections For experiments with a deuterium target, a correction is needed to relate the free nucleon quasielastic cross sec- tion (σN ) to the deuterium cross section (σ D). This cor- rection is typically assumed (as is the case in the present 6 work) to be characterized by a ratio that depends only onQ 2, dσD dQ2 (Eν, Q2)≈R(Q 2) dσN dQ2 (Eν, ...

  6. [6]

    Bernard, L

    V. Bernard, L. Elouadrhiri, and U.-G. Meissner, J. Phys. G28, R1 (2002), arXiv:hep-ph/0107088

    Pith/arXiv arXiv 2002

  7. [7]

    theory-free

    However, the uncertainties ofk max = 7 are generally large enough that the shift remains less than 1σ. The only exception is the combined MINERvA+LQCD fit, which gives a mild 1.6σshift. The trend might argue 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Q2/GeV2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 FA(Q2) LQCD average MINERvA Deuterium + BEBC (envelope) Axia...

    2016

  8. [8]

    Reference [44] estimates that the track re- construction efficiency is about 89±7% for events in the range 0.05≤Q 2 ≤0.10 GeV 2

    The tracks from the struck proton can be too short to reconstruct reliably at lowQ2, leading to poor ef- ficiency and inaccurate characterization of the kine- matics. Reference [44] estimates that the track re- construction efficiency is about 89±7% for events in the range 0.05≤Q 2 ≤0.10 GeV 2. The effi- ciency correction has been added to alleviate some ...

  9. [9]

    two-prong

    The spectator proton also cannot be reliably mea- 10 sured when it has small outgoing momentum. For momenta below 0.1 GeV/c, nearly all of the spec- tator protons are missed. Fits are employed to extract spectator momenta for these “two-prong” events assuming values centered at 0 and prior widths of around±50 MeV/c. The distributions are typically compare...

  10. [10]

    The corresponding deuterium effect essen- tially turns off aboveQ 2 ≳0.15 GeV 2 in corrections applied to the data

    The corrections due to deuterium effects are as- sumed to be largest at lowQ 2, due to Pauli ex- clusion principle for the low-momentum outgoing protons. The corresponding deuterium effect essen- tially turns off aboveQ 2 ≳0.15 GeV 2 in corrections applied to the data

  11. [11]

    To test the dependence on systematics due to the in- clusion of low-Q 2 region, two different ranges ofQ 2 are considered for the ANL, BNL, and FNAL deuterium datasets, as in Ref

    Even with the corrections discussed here, the dif- ferential cross section data still exhibit a turnover at low-Q2 that is too sharp to be well-described by the fits. To test the dependence on systematics due to the in- clusion of low-Q 2 region, two different ranges ofQ 2 are considered for the ANL, BNL, and FNAL deuterium datasets, as in Ref. [8]. The t...

  12. [12]

    A solution that does not appeal to introduction of a reg- ularization would be preferable to one that does

    Addition of BEBC Dataset A solution is needed for the degeneracy between the floating normalization and the axial form factor shape. A solution that does not appeal to introduction of a reg- ularization would be preferable to one that does. For- tunately, the datasets with a flux-integrated differential cross section are absolutely normalized to within th...

    2016

  13. [13]

    All Deuterium

    All Deuterium versus MINERvA The ∆χ2 tests from Sect. III C 2 demonstrate that the complete set of four deuterium results are sufficiently compatible that they can be averaged together. How- 12 Q2 min = 0.06 GeV 2 Q2 min = 0.20 GeV 2 Fit χ2/DoFp ∆χ2 χ2/DoFp ∆χ2 All Deuterium 116.8/108 99.5/102 MINERvA 9.2/ 11 9.2/ 11 All 130.4/120 121.1/114 ∆χ2 4.4/ 1 0.0...

  14. [14]

    MINERvA–BEBC Compatibility Since agreement between MINERvA and the other deuterium datasets is contingent on inclusion of the poorly-fit lowQ 2 bins, the MINERvA dataset is con- sidered to be inconsistent with the deuterium datasets. The lost correlations betweenQ 2 andE ν of these his- torical deuterium event data and the absence of nuclear corrections i...

    2016

  15. [15]

    No statistically significant shifts are observed under the different fit choices made in this work

    Parameterization Choices In principle, the parameterization choice should be in- sensitive to the choice of fit parameterst 0,k max, andλ. No statistically significant shifts are observed under the different fit choices made in this work. Fig. 7 shows the effects of choosing between the dif- ferent truncations for the axial form factor power series. The v...

    2016

  16. [16]

    Vector Form Factors This subsection explores the effects of vector form fac- tor parameterizations on the axial form factor shape and uncertainty. In Fig. 9, the result of replacing the BBBA05 parameterization for the vector form factors with thezexpansion parameterization. As expected, no substantial difference is seen between the two choices. The axial ...

  17. [17]

    the L-curve study in Sect. III A for fits to the MINERvA dataset show that moving from an un- regularizedk max = 5 fit to an unregularizedk max = 6 fit decreasesχ 2 aug by only about 0.2, which when considered in isolation is insufficient to justify the increasek max = 6; and

  18. [18]

    ignore unknown

    although the MINERvA fits preferk max = 5, the pvalue is not significantly diminished atk max = 6 and so comparisons with LQCD, which prefer kmax = 6, can be performed without adversely im- pacting the fit quality. For evaluating systematics due to finite truncation of the zexpansion parameterizations, the values fork max = 7 andλ= 0.1 fits (orλ= 0 for LQ...

    2016

  19. [19]

    Bernard, N

    V. Bernard, N. Kaiser, and U. G. Meissner, Phys. Rev. Lett.69, 1877 (1992)

    1992

  20. [20]

    The NOvA Technical Design Report,

    D. S. Ayreset al.(NOvA), “The NOvA Technical Design Report,” (2007), (unpublished)

    2007

  21. [21]

    JUNO Conceptual De- sign Report,

    Z. Djurcicet al.(JUNO), “JUNO Conceptual De- sign Report,” (2015), (unpublished), arXiv:1508.07166 [physics.ins-det]

    Pith/arXiv arXiv 2015

  22. [22]

    Long-Baseline Neutrino Fa- cility (LBNF) and Deep Underground Neutrino Exper- iment (DUNE): Conceptual Design Report, Volume 2: The Physics Program for DUNE at LBNF,

    R. Acciarriet al.(DUNE), “Long-Baseline Neutrino Fa- cility (LBNF) and Deep Underground Neutrino Exper- iment (DUNE): Conceptual Design Report, Volume 2: The Physics Program for DUNE at LBNF,” (2015), (un- published), arXiv:1512.06148 [physics.ins-det]

    arXiv 2015

  23. [23]

    Hyper- Kamiokande Design Report,

    K. Abeet al.(Hyper-Kamiokande), “Hyper- Kamiokande Design Report,” (2018), (unpublished), arXiv:1805.04163 [physics.ins-det]

    Pith/arXiv arXiv 2018

  24. [24]

    Deep Underground Neutrino Ex- periment (DUNE), Far Detector Technical Design Re- port, Volume II: DUNE Physics,

    B. Abiet al.(DUNE), “Deep Underground Neutrino Ex- periment (DUNE), Far Detector Technical Design Re- port, Volume II: DUNE Physics,” (2020), (unpublished), arXiv:2002.03005 [hep-ex]

    arXiv 2020

  25. [25]

    V. A. Andreevet al.(MuCap), Phys. Rev. C91, 055502 (2015), arXiv:1502.00913 [nucl-ex]. 22

    Pith/arXiv arXiv 2015

  26. [26]

    Bodek, S

    A. Bodek, S. Avvakumov, R. Bradford, and H. S. Budd, Eur. Phys. J. C53, 349 (2008), arXiv:0708.1946 [hep-ex]

    Pith/arXiv arXiv 2008

  27. [27]

    A. S. Meyer, M. Betancourt, R. Gran, and R. J. Hill, Phys. Rev. D93, 113015 (2016), arXiv:1603.03048 [hep- ph]

    Pith/arXiv arXiv 2016

  28. [28]

    Abratenkoet al.(MicroBooNE), Phys

    P. Abratenkoet al.(MicroBooNE), Phys. Rev. D105, 072001 (2022), arXiv:2110.14028 [hep-ex]

    Pith/arXiv arXiv 2022

  29. [29]

    Tena-Vidalet al.(GENIE), Phys

    J. Tena-Vidalet al.(GENIE), Phys. Rev. D106, 112001 (2022), arXiv:2206.11050 [hep-ph]

    Pith/arXiv arXiv 2022

  30. [30]

    A. S. Meyer, A. Walker-Loud, and C. Wilkinson, Ann. Rev. Nucl. Part. Sci.72, 205 (2022), arXiv:2201.01839 [hep-lat]

    Pith/arXiv arXiv 2022

  31. [31]

    Neutrino and Muon Fluxes in the CERN 400-gev Proton Beam Dump Experiments,

    H. Wachsmuth, “Neutrino and Muon Fluxes in the CERN 400-gev Proton Beam Dump Experiments,” (1979), (Ph.D. Thesis)

    1979

  32. [32]

    Quasi-elastic interactions and one-pion production by neutrinos and anti-neutrinos on a deu- terium target,

    S. J. M. Barlag, “Quasi-elastic interactions and one-pion production by neutrinos and anti-neutrinos on a deu- terium target,” (1984), (Ph.D. Thesis)

    1984

  33. [33]

    Allasiaet al., Nucl

    D. Allasiaet al., Nucl. Phys. B343, 285 (1990)

    1990

  34. [34]

    Caiet al.(MINERvA), Nature614, 48 (2023)

    T. Caiet al.(MINERvA), Nature614, 48 (2023)

    2023

  35. [35]

    A. S. Meyer, in preparation (2025)

    2025

  36. [36]

    Bernard, L

    V. Bernard, L. Elouadrhiri, and U.-G. Meißner, Journal of Physics G: Nuclear and Particle Physics28, R1 (2001)

    2001

  37. [37]

    R. J. Hill, P. Kammel, W. J. Marciano, and A. Sirlin, Rept. Prog. Phys.81, 096301 (2018), arXiv:1708.08462 [hep-ph]

    Pith/arXiv arXiv 2018

  38. [38]

    R. J. Hill and G. Paz, Phys. Rev. D82, 113005 (2010), arXiv:1008.4619 [hep-ph]

    Pith/arXiv arXiv 2010

  39. [39]

    K. I. Blomqvistet al., Z. Phys. A353, 415 (1996)

    1996

  40. [40]

    Liesenfeldet al.(A1), Phys

    A. Liesenfeldet al.(A1), Phys. Lett. B468, 20 (1999), arXiv:nucl-ex/9911003

    Pith/arXiv arXiv 1999

  41. [41]

    M. Hilt, B. C. Lehnhart, S. Scherer, and L. Tiator, Phys. Rev. C88, 055207 (2013), arXiv:1309.3385 [nucl-th]

    Pith/arXiv arXiv 2013

  42. [42]

    Czarnecki, W

    A. Czarnecki, W. J. Marciano, and A. Sirlin, Phys. Rev. Lett.99, 032003 (2007), arXiv:0704.3968 [hep-ph]

    Pith/arXiv arXiv 2007

  43. [43]

    V. A. Andreevet al.(MuCap), Phys. Rev. Lett.110, 012504 (2013), arXiv:1210.6545 [nucl-ex]

    Pith/arXiv arXiv 2013

  44. [44]

    K. L. Milleret al., Phys. Rev. D26, 537 (1982)

    1982

  45. [45]

    BNL νµ + D dN/dQ2 Q2 ≥ {0.06,0.20}GeV2 dN/dE

  46. [46]

    The list of datasets considered in this work

    FNAL νµ + D dN/dQ2 Q2 ≥ {0.06,0.20}GeV2 dN/dE [12–14] BEBC νµ + D dσ/dQ2 — Scaled [15, 47] MINERvA ¯νµ +p dσ/dQ2 1.5≤p µ ≤20 GeV,θ µ ≤20 ◦ Covariance TABLE I. The list of datasets considered in this work. The columns of the table indicate the references for the dataset, the label used for the dataset, the scattering interaction considered, the type of dis...

  47. [47]

    C. H. Llewellyn Smith, Phys. Rept.3, 261 (1972)

    1972

  48. [48]

    J. A. Formaggio and G. P. Zeller, Rev. Mod. Phys.84, 1307 (2012), arXiv:1305.7513 [hep-ex]

    Pith/arXiv arXiv 2012

  49. [49]

    Bradford, A

    R. Bradford, A. Bodek, H. S. Budd, and J. Arrington, Nucl. Phys. B Proc. Suppl.159, 127 (2006), arXiv:hep- ex/0602017

    arXiv 2006

  50. [50]

    Borah, R

    K. Borah, R. J. Hill, G. Lee, and O. Tomalak, Phys. Rev. D102, 074012 (2020), arXiv:2003.13640 [hep-ph]

    Pith/arXiv arXiv 2020

  51. [51]

    Z. Ye, J. Arrington, R. J. Hill, and G. Lee, Phys. Lett. B777, 8 (2018), arXiv:1707.09063 [nucl-ex]

    Pith/arXiv arXiv 2018

  52. [52]

    S. L. Adler, Phys. Rev.137, B1022 (1965)

    1965

  53. [53]

    S. L. Adler, Phys. Rev.139, B1638 (1965)

    1965

  54. [54]

    G. S. Bali, L. Barca, S. Collins, M. Gruber, M. L¨ offler, A. Sch¨ afer, W. S¨ oldner, P. Wein, S. Weish¨ aupl, and T. Wurm (RQCD), JHEP05, 126 (2020), arXiv:1911.13150 [hep-lat]

    Pith/arXiv arXiv 2020

  55. [55]

    S. Park, R. Gupta, B. Yoon, S. Mondal, T. Bhattacharya, Y.-C. Jang, B. Jo´ o, and F. Winter (Nucleon Matrix Elements (NME)), Phys. Rev. D105, 054505 (2022), arXiv:2103.05599 [hep-lat]

    Pith/arXiv arXiv 2022

  56. [56]

    Djukanovic, G

    D. Djukanovic, G. von Hippel, J. Koponen, H. B. Meyer, K. Ottnad, T. Schulz, and H. Wittig, Phys. Rev. D106, 074503 (2022), arXiv:2207.03440 [hep-lat]

    Pith/arXiv arXiv 2022

  57. [57]

    Y.-C. Jang, R. Gupta, T. Bhattacharya, B. Yoon, and H.-W. Lin (Precision Neutron Decay Matrix Ele- ments (PNDME)), Phys. Rev. D109, 014503 (2024), arXiv:2305.11330 [hep-lat]

    Pith/arXiv arXiv 2024

  58. [58]

    Alexandrou, S

    C. Alexandrou, S. Bacchio, M. Constantinou, J. Finken- rath, R. Frezzotti, B. Kostrzewa, G. Koutsou, G. Spanoudes, and C. Urbach, PoSLA TTICE2024, 330 (2025), arXiv:2502.07583 [hep-lat]

    Pith/arXiv arXiv 2025

  59. [59]

    Bhattacharya, R

    B. Bhattacharya, R. J. Hill, and G. Paz, Phys. Rev. D 84, 073006 (2011), arXiv:1108.0423 [hep-ph]

    Pith/arXiv arXiv 2011

  60. [60]

    Navaset al.(Particle Data Group), Phys

    S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

    2024

  61. [61]

    W. A. Mannet al., Phys. Rev. Lett.31, 844 (1973)

    1973

  62. [62]

    S. J. Barishet al., Phys. Rev. D16, 3103 (1977)

    1977

  63. [63]

    S. J. Barishet al., Phys. Rev. D19, 2521 (1979)

    1979

  64. [64]

    N. J. Baker, A. M. Cnops, P. L. Connolly, S. A. Kahn, H. G. Kirk, M. J. Murtagh, R. B. Palmer, N. P. Samios, and M. Tanaka, Phys. Rev. D23, 2499 (1981)

    1981

  65. [65]

    Kitagakiet al., Phys

    T. Kitagakiet al., Phys. Rev. D28, 436 (1983)

    1983

  66. [66]

    Zazuetaet al.(MINERvA), Phys

    L. Zazuetaet al.(MINERvA), Phys. Rev. D107, 012001 (2023), arXiv:2209.05540 [hep-ex]

    Pith/arXiv arXiv 2023

  67. [67]

    S. K. Singh, Nucl. Phys. B36, 419 (1972)

    1972

  68. [68]

    G. Shen, L. E. Marcucci, J. Carlson, S. Gandolfi, and R. Schiavilla, Phys. Rev. C86, 035503 (2012), arXiv:1205.4337 [nucl-th]

    Pith/arXiv arXiv 2012

  69. [69]

    P. C. Hansen, SIAM Review34, 561 (1992), https://doi.org/10.1137/1034115

    doi:10.1137/1034115 1992

  70. [70]

    The l-curve and its use in the numerical treatment of inverse problems,

    P. C. Hansen, “The l-curve and its use in the numerical treatment of inverse problems,” (WIT Press, 2001) pp. 119–142

    2001

  71. [71]

    Hulth´ en, Arkiv f¨ or Matematik Astronomi och Fysik A 28(1942)

    L. Hulth´ en, Arkiv f¨ or Matematik Astronomi och Fysik A 28(1942)

    1942

  72. [72]

    Hulth´ en, Arkiv f¨ or Matematik Astronomi och Fysik B 29(1942)

    L. Hulth´ en, Arkiv f¨ or Matematik Astronomi och Fysik B 29(1942)

    1942

  73. [73]

    The two-nucleon prob- lem,

    L. Hulth´ en and M. Sugawara, “The two-nucleon prob- lem,” inStructure of Atomic Nuclei / Bau der Atom- kerne(Springer Berlin Heidelberg, Berlin, Heidelberg,

  74. [74]

    Koch, Phys

    L. Koch, Phys. Rev. D111, 033002 (2025), arXiv:2410.22333 [stat.ME]

    arXiv 2025

  75. [75]

    J. E. Amaro and E. Ruiz Arriola, Phys. Rev. D93, 053002 (2016), arXiv:1510.07532 [nucl-th]

    Pith/arXiv arXiv 2016

  76. [76]

    A. A. Aguilar-Arevaloet al.(MiniBooNE), Phys. Rev. D 81, 092005 (2010), arXiv:1002.2680 [hep-ex]

    Pith/arXiv arXiv 2010

  77. [77]

    Lyubushkinet al.(NOMAD Collaboration), Eur

    V. Lyubushkinet al.(NOMAD Collaboration), Eur. Phys. J. C63, 355 (2009), arXiv:0812.4543 [hep-ex]

    Pith/arXiv arXiv 2009

  78. [78]

    Goharipour, F

    M. Goharipour, F. Irani, M. H. Amiri, H. Fatehi, B. Falahi, A. Moradi, and K. Azizi (MMGPDs), Nucl. Phys. B1017, 116962 (2025), arXiv:2503.08847 [hep-ph]

    Pith/arXiv arXiv 2025

  79. [79]

    C. Chen, C. S. Fischer, C. D. Roberts, and J. Segovia, Phys. Rev. D105, 094022 (2022), arXiv:2103.02054 [hep- ph]

    Pith/arXiv arXiv 2022

  80. [80]

    Chen and C

    C. Chen and C. D. Roberts, Eur. Phys. J. A58, 206 (2022), arXiv:2206.12518 [hep-ph]

    Pith/arXiv arXiv 2022

Showing first 80 references.