Assessing the accuracy of the GENIE event generator with electron scattering data: Reduced cross section and nuclear transparency

A. V. Butkevich; S. V. Luchuk

REVIEW 3 major objections 6 minor 1 cited by

Assessing the accuracy of the GENIE event generator with electron scattering data: Reduced cross section and nuclear transparency

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper shows that electron reduced cross sections can benchmark neutrino generators, and finds GENIE overestimates carbon data below missing momentum 80 MeV/c.

desk verdict A useful and honest GENIE benchmark against semi-exclusive (e,e'p) data with a visible low-pm discrepancy, though the approximate event-to-(pm, εm) mapping and thin quantitative details mean the size of the effect should be treated with caution. read the letter →

arxiv 2506.19355 v1 pith:C5HWEVZG submitted 2025-06-24 hep-ph hep-th

A. V. Butkevich , S. V. Luchuk This is my paper · ORCID

classification hep-phhep-th PACS 25.30.-c25.30.Bf25.30.Pt13.15.+g

keywords GENIEeventgeneratorreducedcrosssectionnucleartransparencyquasi-elasticneutrinoscatteringelectronbenchmarkdistortedspectralfunctionmissingmomentumRDWIA

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

Electron and neutrino scattering off nuclei share the same nuclear-physics content: once the lepton vertex and phase space are divided out, the remaining reduced cross section is a distorted spectral function of the target, so precise electron data can test the nuclear models that neutrino event generators rely on. This paper uses that identity to benchmark five GENIE v3 model configurations against four published 12C(e,e'p) reduced-cross-section datasets spanning beam energies from about 0.5 to 2.5 GeV. Across those datasets the paper reports a persistent disagreement: below missing momentum |pm| ≈ 80 MeV/c—the inferred initial momentum of the knocked-out proton—the GENIE models built on a local Fermi gas momentum distribution (G18_10a and G21_11) overestimate the data significantly, while a relativistic distorted-wave impulse approximation (RDWIA) calculation describes the measured cross sections well. If correct, the result means that neutrino energy reconstruction, which depends on these nuclear models, carries an extra systematic uncertainty in exactly the low-missing-momentum region.

What carries the argument

The load-bearing object is the reduced cross section $\sigma_{\mathrm{red}}(p_m) = (d\sigma/dp_m)/(K\,\sigma_{\ell N})$, the measured or simulated fivefold cross section divided by phase space and by the elementary electron- or neutrino-nucleon cross section; in the nonrelativistic plane-wave limit it becomes the bound-nucleon momentum distribution, and with final-state interactions it is the distorted spectral function. Because this object is nearly independent of the lepton probe, electron data can be used to test the nuclear parts of a neutrino event generator in isolation. The practical machinery is the mapping of generator events onto $(p_m,\varepsilon_m)$: GENIE's nuclear models only provide one-dimensional $d\sigma/dp_m$ with fixed binding energies, so the paper selects $1\mu1p$ events, defines $\tilde{\varepsilon}_m = \omega - T_p$, and uses the Jacobian $J(\theta_p)$ of Eq. (22) to convert the lepton-proton kinematics into missing momentum and missing energy.

What would settle it

Run the same five GENIE model configurations but reconstruct missing energy with the full recoil term, $\varepsilon_m = \omega - T_p - \varepsilon_B$, instead of $\tilde{\varepsilon}_m = \omega - T_p$, and repeat the comparison; if the low-$p_m$ overestimate disappears or moves to another kinematic region, the central claim fails as stated. A complementary check is to compare generator predictions against shell-tagged $(e,e'p)$ data selected in the $1p_{3/2}$ ($10<\varepsilon_m<25$ MeV) and $1s_{1/2}$ ($30<\varepsilon_m<50$ MeV) missing-energy windows, which GENIE's one-dimensional models cannot currently reproduce.

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Extended reading notes

Core claim

The paper's central claim is that the reduced cross section $\sigma_{\mathrm{red}}(p_m)$ of semi-exclusive $(l,l'p)$ scattering is, up to small Coulomb corrections, the same object for electron and neutrino probes: after dividing out phase space and the elementary lepton-nucleon cross section, what remains is a distorted nuclear spectral function determined by the target and by the ejected nucleon's interaction with the residual nucleus. Using this identity, the paper generates $10^8$ charged-current quasielastic neutrino events per GENIE model configuration, keeps events that end as one muon plus one proton after the intranuclear cascade, maps them to $(p_m,\varepsilon_m)$ using the approximate missing-energy definition $\tilde{\varepsilon}_m = \omega - T_p$ and the Jacobian of Eq. (22), and compares the resulting $d\sigma/dp_m$ with four published $^{12}\mathrm{C}(e,e'p)$ datasets. On that comparison the paper reports persistent disagreements: at missing momenta below about 80 MeV/$c$, the GENIE models based on a local Fermi gas momentum distribution (G18_10a and G21_11) and also the spectral-function-based sf1d and effsf models overestimate the data, while at higher $p_m$ they tend to underestimate; the G18_02a Fermi-gas model shows the opposite pattern at low beam energy. A relativistic distorted-wave impulse approximation (RDWIA) treatment of the same kinematics is found to describe the measured reduced cross sections well, and GENIE's nuclear transparency for carbon is found to be roughly consistent with the transparency data, though the paper concludes that both GENIE and RDWIA need additional strength beyond single-nucleon knockout.

Load-bearing premise

The comparison assumes that GENIE events selected as one muon plus one proton and mapped to missing momentum/energy via the approximate formula $\tilde{\varepsilon}_m = \omega - T_p$ and the Jacobian of Eq. (22) reproduce the experimental $(e,e'p)$ reduced cross section; if that kinematic mapping distorts the low-$p_m$ region, the reported overestimate would be an artifact rather than a property of the nuclear models.

Editorial extensions

If this is right

Neutrino energy reconstruction in experiments that rely on GENIE will inherit a systematic error in the low-missing-momentum region, where the ejected proton carries little recoil momentum.
The electron-scattering datasets used here provide an out-of-sample test, since they were not used to tune the GENIE configurations; the reported disagreement therefore counts against those nuclear models rather than being a fit artifact.
RDWIA-style unfactorized calculations, which include the distortion of the outgoing nucleon wave function, reproduce the data better and are a natural starting point for improving event-generator nuclear models.
Because GENIE's nuclear transparency predictions agree roughly with data, the failure appears concentrated in the ground-state momentum distribution or quasielastic vertex rather than in the whole intranuclear-cascade description.
The same reduced-cross-section benchmark can be applied to other targets and to other generators, turning precise electron data into a routine validation step for neutrino interaction models.

Reading between the lines

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

If the reported low-momentum overestimate is real, its likely origin is that the LFG and effective spectral-function distributions put too much probability at small initial nucleon momenta; testing the generator's pre-FSI momentum distribution against measured spectral functions would separate that cause from distortions introduced by the cascade.
The paper's comparison discards shell-resolved missing-energy information because GENIE's models are one-dimensional; implementing two-dimensional spectral functions in generators would make the low-$p_m$ comparison much sharper and might resolve whether part of the discrepancy is an artifact of the kinematic mapping.
A practical extension would be to quantify how much the low-$p_m$ overestimate shifts the reconstructed neutrino energy in a simulated oscillation analysis; that number would translate this physics disagreement directly into a systematic uncertainty.
Repeating the benchmark on a heavier target such as argon would show whether the failure is specific to carbon or generic to the momentum-distribution parametrizations used in current generators.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a useful and honest benchmark paper. Butkevich and Luchuk compare five GENIE v3.04 CCQE model configurations (RFG, LFG, SuSAv2, sf1d, effsf) against four semi-exclusive (e,e'p) reduced-cross-section data sets for carbon, using external data that weren't part of GENIE's tuning. The main finding — LFG-based models overestimate the reduced cross section at missing momentum below ~80 MeV/c, while their own RDWIA tracks the data — is visible in the figures and consistent across kinematics. That's a genuinely useful result for the neutrino community, since GENIE is what all the Fermilab experiments use for energy reconstruction, and a persistent low-pm discrepancy in the nuclear model feeds directly into oscillation systematics.

What's actually new here is the systematic comparison itself. Earlier generator-electron comparisons used inclusive (e,e') cross sections; this uses the semi-exclusive reduced cross section, which is a stricter test of the nuclear ground state and FSI. The authors also deserve credit for stating plainly that GENIE's nuclear models are one-dimensional in pm with fixed binding energies and cannot reproduce the shell-resolved missing-energy structure in the electron data. That's the right kind of honesty.

The soft spots are real but mostly don't kill the qualitative conclusion. The kinematic mapping from GENIE events to (pm, εm) — Eq. (17) for missing energy, the Jacobian in Eq. (22), and the window integration — is approximate and, as the stress test notes, unvalidated. The low-pm region is exactly where the 1/pm Jacobian and the experimental acceptance cuts are least benign. I'd push back on one part of the stress test: the flatness concern about Eq. (24) is probably overstated. Read in context, 'integrated over range Δεm' means the density is the window average, so multiplying by Δεm is just the integral — not an assumption of flatness, though the notation is sloppy and should be clarified. The 1p+Nn vs 1p+0n choice is also defensible: electron (e,e'p) experiments don't detect neutrons, so allowing extra neutrons matches the experimental selection.

More legitimate concerns: χ2/DOF values are quoted without the number of points or the definition of χ2; no configuration files or code are shipped, so reproducing the five model settings is harder than it should be; and the 'RDWIA does better' conclusion rests on the authors' own earlier RDWIA calculations, which are not independently reproduced here.

Who's this for? Anyone working on GENIE validation or neutrino energy reconstruction. It deserves a serious referee — not a desk reject. The referee should push for a validation of the event-to-(pm, εm) mapping (e.g., a closure test against a model with a known spectral function) and for the χ2 details, but the qualitative finding will likely survive.

Referee Report

3 major / 6 minor

Summary. The paper proposes using semi-exclusive electron-carbon scattering data—reduced cross sections and nuclear transparency—as a benchmark for the nuclear models implemented in the GENIE neutrino event generator. The authors simulate charged-current quasielastic neutrino-carbon events with five GENIE model configurations (RFG, LFG, SuSAv2-MEC, spectral function, and effective spectral function), convert the final-state kinematics into a reduced cross section as a function of missing momentum via an approximate missing-energy definition, and compare the results with (e,e'p) data from Tokyo, Saclay, SLAC, and JLab. They report that GENIE models based on the local Fermi gas overestimate the measured reduced cross sections for missing momenta below about 80 MeV/c, while RDWIA calculations agree better. They also compare GENIE nuclear transparency predictions with electron-scattering transparency data and find satisfactory agreement, with some shortcomings attributed to missing multinucleon strength.

Significance. If the comparison is valid, the paper offers a novel, externally grounded test of the nuclear models in a widely used neutrino event generator, using electron-scattering data that were not used to tune those models. The low-missing-momentum region is directly relevant to neutrino energy reconstruction in oscillation experiments, so the claimed discrepancy would be of practical importance. The transparency comparison adds a second, independent validation channel. The paper also demonstrates a general methodology for converting generator events into spectral-function-like observables. However, the central claim depends entirely on the event-to-(pm, epsilon_m) mapping and on matching the missing-energy windows of the experimental data, and the quantitative evidence is reported without a complete goodness-of-fit treatment.

major comments (3)

[III, Eqs. (17)-(24)] The conversion from GENIE events to the reduced cross section is not sufficiently justified. The paper states in Sec. III that the GENIE nuclear models provide only one-dimensional dsigma/dpm distributions with fixed binding energies, so they cannot produce the shell-resolved d²sigma/dpm/depsilon_m. Nevertheless, Eq. (24) defines dsigma/dpm = Deltaepsilon_m d²sigma/dpm/depsilon_m, which is only correct if d²sigma/dpm/depsilon_m is flat over the window Deltaepsilon_m; for a fixed-binding model the epsilon_m distribution is a narrow peak, not a flat density. Please show explicitly how the event counts are binned and integrated over epsilon_m (for example, by counting events in the full Deltaepsilon_m window and dividing by Delta pm), and state which missing-energy window the electron data actually correspond to. If the data are the shell-separated bins 10-25 MeV and 30-50 MeV mentioned in Sec. III while the GENIE curves are integrated over 80 MeV, the comparison is not apples-to-apples and the reported low-pm overestimate could be an artifact of the window mismatch.
[V, chi-squared paragraph] The quantitative support for the central claim is incomplete. After Fig. 7 the paper reports chi2/DOF approximately 12.6 for the effsf model with SLAC data and approximately 17.5 for the sf1d model with JLab data, but it never gives the number of degrees of freedom, the definition of chi2, the error treatment (statistical errors of the data, normalization uncertainties, or any uncertainty bands on the GENIE predictions), or the pm range used in the comparison. Without this information the phrase "persistent disagreements" is not quantitatively established; please provide a defined goodness-of-fit statistic with all components and show the sensitivity of the conclusion to the treatment of data normalization uncertainties.
[III, event selection (1p+Nn vs 1p+0n)] The choice of the 1p+Nn event set as the analogue of the proton-only final state in (e,e'p) needs justification. Figure 2 shows that for the G21_11 and spectral-function models the missing-energy distributions of 1p+Nn and 1p+0n events differ noticeably, and the text notes that inelastic FSI changes proton energies and pushes events to higher missing energy. Since the electron data select a knocked-out proton with no associated neutron emission, including events with additional neutrons in the GENIE comparison may bias sigma_red(pm), and the paper does not quantify this bias. Please show the effect of the two selections on the final reduced cross sections, especially at pm below 80 MeV/c, or justify why the 1p+Nn selection is equivalent to the experimental proton-only selection for this observable.

minor comments (6)

[Abstract] The sentence "The approach presented in this paper provide a great opportunity" should read "provides a great opportunity".
[Fig. 7 caption] The caption says "Same as Fig. 3 but for the sf1d (SF) model calculation," but the text and figure content describe the effsf model; the caption should be corrected.
[Introduction, section numbering] The Introduction states that results are presented in Sec. IV, but the results actually appear in Sec. V; the cross-reference should be corrected.
[Eq. (22)] "Jacobin" should be "Jacobian," and the sign convention in the second term of the Jacobian expression should be checked for consistency with the definition of pm in Eq. (20).
[Introduction] "Femilab" should be "Fermilab."
[Fig. 9 caption] "transparensy" should be "transparency."

Circularity Check

1 steps flagged · score 2.0 of 10

Minor fitted-input overlap for the sf1d comparison; the central LFG-model benchmark is external and non-circular.

fitted input called prediction [Sec. IV (model descriptions) and Sec. V (Fig. 6, sf1d comparison)]
"The mean field piece has been fitted to the (e,e’p) scattering data ... In Fig. 6 we compare the GENIE sf1d model calculations with the data for reduced cross sections of electron scattering on carbon."

The input to the sf1d model, its mean-field spectral function, was previously fitted to (e,e'p) scattering data. Since the paper's Eq. (25) identifies the reduced cross section with the (distorted) spectral function, the Fig. 6 comparison of GENIE sf1d predictions with 12C(e,e'p) reduced-cross-section data is in part a comparison of a fitted quantity with its training data. This is a partial reduction by construction for the sf1d configuration only. The paper's central conclusion about the LFG-based G18_10a and G21_11 models does not rest on this fitted input, so the circularity is minor.

full rationale

The core benchmark is external and non-circular: GENIE v3.04.00 predictions for five model configurations are generated from the generator and compared with published 12C(e,e'p) reduced-cross-section data (Saclay, Tokyo, SLAC, JLab), none of which are fitted in this paper. The headline low-pm overestimate concerns the LFG-based G18_10a and G21_11 models, whose GENIE implementations are not tuned to these data. The RDWIA comparisons cited from Refs. [23-26] are prior parameter-free calculations by the same authors; they were not fitted to the data used here and are externally falsifiable, so invoking them is legitimate independent support rather than circularity. The kinematic mapping in Eqs. (17)-(25), including the approximate missing-energy definition, the Jacobian, and the flatness assumption behind Eq. (24), is an approximation that could bias the low-pm region, but it is a validation/correctness concern rather than a circular definition. The only mild circular element is the sf1d model comparison, since that model's mean-field spectral function was previously fitted to (e,e'p) data; this does not affect the LFG-based central conclusion. Overall circularity is minor, with a score of 2.

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

The paper introduces no new fitted parameters or invented entities. All model inputs are inherited from GENIE configurations calibrated to other data. The main burden is domain assumptions connecting electron and neutrino observables and the factorized definition of the reduced cross section.

free parameters (4)

Fermi momentum and binding energy for 12C in GENIE RFG (G18_02a) = GENIE defaults, not stated in paper
Sets the dP/dpm shape that controls the reduced cross section; inherited from Bodek-Ritchie model fits to electron scattering.
Local Fermi gas and RPA parameters (G18_10a, G21_11a) = Not stated in paper
The LFG momentum distribution and RPA screening parameters determine the low-missing-momentum behavior that drives the reported overestimate.
Spectral function mean-field normalization (sf1d) = Fitted to (e,e'p) data in Refs. [46,47]
The model's mean-field part is already calibrated to electron knockout data, so the benchmark partly checks how GENIE encodes that fit.
Effective spectral function transverse enhancement (eﬀsf) = Not stated in paper
The enhancement term was introduced to reproduce transverse e-C scattering; the value is inherited from the GENIE implementation.

assumptions (4)

domain assumption The factorized form d5sigma = K x sigma_lN x sigma_red (Eq. 14) is accurate enough for the kinematics used.
The reduced cross section is defined through this factorization; the text admits it is not strictly valid relativistically (Ref. [29]).
domain assumption Electron and neutrino reduced cross sections for the same nucleus agree up to Coulomb corrections.
This is the bridge that lets neutrino generator output be compared with electron data; established in Refs. [23-26] and assumed here.
domain assumption Coulomb corrections can be represented by an effective momentum transfer qeff and are about 10% at low beam energy.
Used to interpret Saclay and Tokyo discrepancies; no dedicated calculation is performed in this paper.
domain assumption The INTRANUKE hA cascade models proton final-state interactions well enough for reduced cross section and transparency comparisons.
The simulated FSI is what converts the initial nucleon momentum distribution into the distorted spectral function; this is exactly what is being tested.

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Cite this review

Pith. "Pith review of Assessing the accuracy of the GENIE event generator with electron scattering data: Reduced cross section and nuclear transparency." pith.science (2026). https://pith.science/paper/C5HWEVZG

@misc{pith2026250619355,
  author       = {Pith},
  title        = {Pith review of: Assessing the accuracy of the GENIE event generator with electron scattering data: Reduced cross section and nuclear transparency},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C5HWEVZG}},
  note         = {Machine review of arXiv:2506.19355}
}

abstract

The reduced cross sections of the semi-exclusive $(l,l'p)$ lepton scattering process can be identified with distorted nuclear spectral functions. Irrespective of the type of interaction the distorted spectral function is determined mainly by intrinsic properties of the target and the ejected nucleon interaction with residual nucleus. Thus the reduced cross sections of the neutrino and electron scattering on nuclei as functions of nucleon missing momentum and energy are similar up to Coulomb corrections. Here we demonstrate the utility of this approach by benchmarking the GENIE neutrino event generator against a broad set of semi-exclusive electron scattering data for carbon target. We observe persistent disagreements between the generator predictions and data in the range of nucleon missing momenta less than 80 MeV/c. The approach presented in this paper provide a great opportunity to test better the accuracy of nuclear models of quasi-elastic neutrino-nucleus scattering, employed in neutrino event generators.

Figures

Figures reproduced from arXiv: 2506.19355 by the authors.

**Figure 2.** FIG. 2. Probability density distribution vs missing energy [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** FIG. 3. Comparison of the GENIE G18 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4. Same as Fig. 3 but for the G18 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

**Figure 5.** Figure 5: FIG. 5. Same as Fig. 3 but for the G21 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

**Figure 6.** Figure 6: FIG. 6. Same as Fig. 3 but for the sf1d (SF) model calculation. [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]

**Figure 7.** Figure 7: FIG. 7. Same as Fig. 3 but for the sf1d (SF) model calculation. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

**Figure 8.** Figure 8: FIG. 8. Same as Fig. 3 but for the RDWIA model calculation. [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]

**Figure 9.** Figure 9: FIG. 9. Nuclear transparency as a function of proton kinetic [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]

**Figure 10.** Figure 10: FIG. 10. Nuclear transparency as a function of proton kineti [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]

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