arxiv: 2604.15724 · v1 · submitted 2026-04-17 · ✦ hep-ph · hep-ex· nucl-th

Recognition: unknown

Theoretical modeling of charged current ν_μ(barν_μ)-⁴⁰Ar DIS at DUNE energies

F. Zaidi , S. Akther , M. Sajjad Athar , S.K. Singh

Authors on Pith no claims yet

Pith reviewed 2026-05-10 08:54 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-th

keywords neutrino deep inelastic scatteringargon-40 targetnuclear structure functionsspectral functioncharged current interactionsDUNE experiment

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The pith

Nuclear structure functions for argon-40 are built from spectral functions and applied to charged-current neutrino DIS cross sections at 4-6 GeV.

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

The paper calculates charged-current muon neutrino and antineutrino deep inelastic scattering on an argon-40 target by first determining the nuclear structure functions F1A, F2A and F3A. These functions are obtained by embedding free-nucleon structure functions, derived from MMHT 2014 parton distributions with NNLO corrections and target-mass corrections, into a relativistic nucleon spectral function treated in the local density approximation. Nuclear medium effects from Fermi motion, binding energy, nucleon correlations, mesonic pion and rho contributions, and nuclear shadowing are included explicitly. The resulting structure functions are then used to compute the differential cross sections d²σ/dx dy and dσ/dx at beam energies of 4 GeV and 6 GeV. A sympathetic reader would care because liquid-argon detectors are central to the DUNE experiment and accurate interaction rates are required to interpret oscillation data.

Core claim

The charged current νμ(¯νμ)-induced DIS from 40Ar is modeled by evaluating the nuclear structure functions F_iA(x,Q²) (i=1-3) via a relativistic nucleon spectral function within the local density approximation; the free-nucleon inputs F_iN(x,Q²) are taken from MMHT 2014 PDFs supplemented by NNLO perturbative QCD corrections and target-mass corrections, with additional explicit contributions from Fermi motion, binding, correlations, mesonic π and ρ clouds, and nuclear shadowing and antishadowing; these structure functions are then folded into the differential cross sections at neutrino energies of 4 GeV and 6 GeV.

What carries the argument

The relativistic nucleon spectral function inside the local density approximation, which supplies the momentum and removal-energy distribution of bound nucleons and thereby folds nuclear medium corrections into the free-nucleon structure functions.

If this is right

Differential cross sections d²σ/dx dy and dσ/dx are obtained for both neutrinos and antineutrinos at 4 GeV and 6 GeV.
The results incorporate the full set of nuclear corrections and are intended for use in liquid-argon time-projection-chamber simulations.
Mesonic contributions and shadowing modify the structure functions most strongly at low and moderate values of Bjorken x.
The same framework supplies the input needed for event generators in ongoing and future argon-based neutrino programs.

Where Pith is reading between the lines

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

The calculated cross sections could serve as a benchmark for testing how well nuclear effects are captured in Monte Carlo generators used by DUNE.
Repeating the calculation at higher beam energies would show whether the same spectral-function treatment continues to hold above the resonance region.
Direct comparison with data from the Short-Baseline Neutrino program would isolate the size of the mesonic and shadowing corrections for argon.

Load-bearing premise

Free-nucleon parton distributions from MMHT 2014 remain valid inside the nuclear spectral function once the explicit mesonic and shadowing corrections have been added, with no further medium-induced changes to the parton distributions themselves.

What would settle it

A precision measurement of the differential cross section d²σ/dx dy in a liquid-argon detector at 4-6 GeV neutrino energy that deviates from the predicted curves by more than the combined experimental and theoretical uncertainties.

Figures

Figures reproduced from arXiv: 2604.15724 by F. Zaidi, M. Sajjad Athar, S. Akther, S.K. Singh.

**Figure 2.** Figure 2: FIG. 2: Feynman diagram representing the deep inelastic sca [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Feynman diagram showing the deep inelastic scatteri [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: and 6); however, there are quantitative differences. For example, the reduction in the cross section due to effect of nuclear structure, relative to the free nucleon case, is about 13% at y = 0.45 for 0.35 ≤ x ≤ 0.65 at E = 4 GeV. The inclusion of mesonic cloud contributions leads to an enhancement in the differential cross sections for x ≤ 0.45, while the effect is very small for x > 0.45. For instance, t… view at source ↗

**Figure 10.** Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗

read the original abstract

The charged current $\nu_\mu(\bar{\nu}_\mu)$-induced deep inelastic scattering (DIS) from an $^{40}\mathrm{Ar}$ target is studied using a microscopic framework that incorporates nuclear medium effects due to Fermi motion, binding energy, nucleon correlations, mesonic ($\pi$ and $\rho$) contributions, and nuclear shadowing and antishadowing across the relevant Bjorken-$x$ region. The nuclear structure functions $F_{iA}(x,Q^2)$ $(i=1\text{-}3)$ are evaluated using a relativistic nucleon spectral function ($S_h$) within the local density approximation employing the free nucleon structure functions, $F_{iN}(x,Q^2)$ $(i=1\text{-}3)$. These $F_{iN}(x,Q^2)$ $(i=1\text{-}3)$ are calculated using parton distribution functions (PDFs) from MMHT 2014 parameterization, including higher-order perturbative QCD corrections up to next-to-next-to-leading order (NNLO), along with nonperturbative target mass corrections (TMC). The resulting nuclear structure functions $F_{iA}(x,Q^2)$ $(i=1\text{-}3)$ are subsequently used to compute the differential DIS cross sections for $^{40}Ar$ nucleus. Numerical results are presented for $\nu_\mu(\bar\nu_\mu)$ beam energies $E=4$ GeV and $E=6$ GeV for the differential scattering cross sections $\frac{d^2\sigma}{dx dy}$ and $\frac{d\sigma}{dx}$, relevant to ongoing and upcoming liquid-argon neutrino experiments such as DUNE and the Fermilab Short-Baseline Neutrino program.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper supplies numerical DIS cross sections for argon-40 at 4-6 GeV with standard nuclear corrections, but adds no new methods or derivations.

read the letter

The main point is that Zaidi et al. have produced differential cross sections for charged-current muon neutrino and antineutrino DIS on 40Ar at beam energies of 4 and 6 GeV. They use a relativistic spectral function in the local density approximation to fold in Fermi motion, binding, nucleon correlations, mesonic contributions from pions and rhos, and shadowing plus antishadowing. Free-nucleon inputs come from MMHT 2014 NNLO PDFs with NNLO QCD corrections and target mass corrections, then the nuclear structure functions F1A, F2A, F3A are computed and turned into d2sigma/dxdy and dsigma/dx distributions. These specific numbers for the DUNE target and energy range are the concrete new output. The framework is taken from earlier literature, so the work is an application rather than a fresh derivation. It does a reasonable job of including the main nuclear effects in one place and presents results in a form that experiments can directly use. The soft spots are proportionate to the incremental nature of the paper. Nothing in the setup shows internal contradictions, but the central assumption that free PDFs plus the listed corrections suffice without further medium modifications to the partons is standard yet open to debate at the low Q2 values here. Numerical implementation details of the matching between spectral function and corrections would need checking in the full text. This is aimed at neutrino experimentalists running simulations or analyses for DUNE and the Short-Baseline program who need argon-specific inputs. A reader hunting for new nuclear physics or first-principles advances will not find them. The calculation is grounded enough and the topic timely enough that it deserves peer review rather than a desk reject. I would send it out.

Referee Report

1 major / 2 minor

Summary. The manuscript presents a microscopic calculation of charged-current deep inelastic scattering cross sections for muon neutrinos and antineutrinos on a 40Ar target at beam energies of 4 and 6 GeV. Nuclear structure functions F_iA(x,Q²) (i=1-3) are obtained by folding free-nucleon structure functions (computed from MMHT 2014 PDFs at NNLO with target-mass corrections) with a relativistic nucleon spectral function in the local density approximation; additional nuclear effects from Fermi motion, binding, correlations, π/ρ mesonic contributions, and shadowing/antishadowing are included. The resulting structure functions are used to evaluate the differential cross sections d²σ/dx dy and dσ/dx.

Significance. If the implementation is accurate, the work supplies concrete predictions for neutrino DIS on argon at DUNE-relevant energies, where nuclear effects are sizable. The consistent microscopic treatment combining spectral functions, mesonic currents, and shadowing offers a useful benchmark for liquid-argon neutrino experiments and can help quantify uncertainties in oscillation analyses.

major comments (1)

The central results rest on the assumption that free-nucleon PDFs (MMHT 2014) can be embedded directly into the spectral function without further medium modifications to the parton distributions themselves beyond the explicit mesonic and shadowing terms. At the moderate Q² values accessed at E=4–6 GeV this assumption is load-bearing; a quantitative estimate of the uncertainty arising from possible additional nuclear PDF modifications would be required to support the claimed accuracy of the cross sections.

minor comments (2)

The abstract and introduction should explicitly state the kinematic range in Q² and x that is covered by the calculation, as this determines the applicability of the DIS formalism and the validity of the PDFs.
Notation for the nuclear structure functions F_iA and the spectral function S_h should be introduced once and used consistently; a short table summarizing the nuclear corrections included (Fermi motion, binding, mesonic, shadowing) would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript, the positive assessment of its significance, and the constructive comment. We address the major comment below and have revised the manuscript to strengthen the discussion of model assumptions and limitations.

read point-by-point responses

Referee: The central results rest on the assumption that free-nucleon PDFs (MMHT 2014) can be embedded directly into the spectral function without further medium modifications to the parton distributions themselves beyond the explicit mesonic and shadowing terms. At the moderate Q² values accessed at E=4–6 GeV this assumption is load-bearing; a quantitative estimate of the uncertainty arising from possible additional nuclear PDF modifications would be required to support the claimed accuracy of the cross sections.

Authors: We appreciate the referee drawing attention to this key aspect of our framework. The nuclear structure functions are constructed by convolving free-nucleon structure functions (computed from MMHT2014 PDFs at NNLO with target-mass corrections) with a relativistic spectral function in the local density approximation; this incorporates Fermi motion, binding, and correlations. Mesonic (π and ρ) contributions and shadowing/antishadowing are added explicitly to capture additional nuclear modifications to the parton distributions. This microscopic approach follows standard practice in the field for neutrino-nucleus DIS calculations. We agree that at the moderate Q² values relevant to 4–6 GeV beams, further medium modifications to the PDFs could exist beyond those included. In the revised manuscript we have added a dedicated paragraph in Section III discussing this modeling assumption, its kinematic relevance, and the associated limitations, with references to global nuclear PDF analyses. A full quantitative uncertainty band derived from a separate nPDF fit lies outside the scope of the present work, but the added discussion clarifies the robustness of the results within the stated model. revision: partial

Circularity Check

0 steps flagged

Standard folding of external MMHT PDFs and published spectral-function formalism; no derivation reduces to self-defined or fitted input

full rationale

The paper evaluates nuclear structure functions F_iA by embedding free-nucleon F_iN (from MMHT 2014 PDFs plus NNLO and TMC) inside a relativistic nucleon spectral function in the local density approximation, then folds the result into differential cross sections. No equation equates an output quantity to a parameter fitted inside this work, and no uniqueness theorem or ansatz is smuggled via self-citation. The cited PDFs and nuclear model are independent external inputs; the calculation is a standard convolution whose results remain falsifiable against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The calculation rests on standard QCD factorization, the validity of the local-density approximation for the spectral function, and the assumption that nuclear modifications beyond Fermi motion, binding, mesons, and shadowing can be neglected. No new free parameters are introduced by the authors; all inputs are taken from cited external sources.

axioms (2)

standard math QCD factorization holds for the free-nucleon structure functions at the relevant Q^2 and x
Invoked when using MMHT 2014 PDFs with NNLO corrections and target-mass corrections
domain assumption The relativistic nucleon spectral function in local density approximation correctly captures Fermi motion, binding, and correlations in 40Ar
Central modeling choice stated in the abstract

pith-pipeline@v0.9.0 · 5642 in / 1659 out tokens · 31208 ms · 2026-05-10T08:54:27.600205+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

49 extracted references · 19 canonical work pages

[1]

3 ≤ x ≤ 0. 8. Furthermore, an enhancement is observed when mesonic contr ibutions are included in the low-to- intermediate x (≲ 0. 5) region; for example, it is about 10 − 12% at x = 0. 3, 4 − 5% at x = 0. 4 and about 1% at x = 0. 5 for 4 ≤ E ≤ 6 GeV, in the absence of any W cut. We ﬁnd that, due to the inclusion of nuclear medium eﬀects, the re is an enh...

2023
[2]

Abiet al.(DUNE), (2018), arXiv:1807.10334 [physics.ins-det]

B. Abi et al. [DUNE], [arXiv:1807.10334 [physics.ins-det]]

work page arXiv
[3]

Cicero [DUNE], Nucl

V. Cicero [DUNE], Nucl. Instrum. Meth. A 1080, 170801 (2025)

2025
[4]

Abe, et al., Sensitivity of the Hyper-Kamiokande exper- iment to neutrino oscillation parameters using accelerator neutrinos, Eur

K. Abe et al. [Hyper-Kamiokande], Eur. Phys. J. C 86, no.2, 170 (2026) doi:10.1140/epjc/s10052-025-14938-9 [arXiv:2505.15019 [hep-ex]]

work page doi:10.1140/epjc/s10052-025-14938-9 2026
[5]

Abratenko, et al., ICARUS at the Fermilab Short-Baseline Neutrino program: initial operation, Eur

P. Abratenko et al. [ICARUS], Eur. Phys. J. C 83, no.6, 467 (2023) doi:10.1140/epjc/s10052-023-11610-y [ arXiv:2301.08634 [hep-ex]]

work page doi:10.1140/epjc/s10052-023-11610-y 2023
[6]

A. P. Wood, [arXiv:2504.08950 [hep-ex]]

work page arXiv
[7]

Acciarriet al.(SBND), (2025), arXiv:2504.00245 [hep-ex]

R. Acciarri et al. [SBND], [arXiv:2504.00245 [hep-ex]]

work page arXiv
[8]

H. M. Freire [SBND], FERMILAB-MASTERS-2025-02

2025
[9]

Abratenko et al

P. Abratenko et al. [MicroBooNE], doi:10.1103/lwrr-98vx [arXiv:2511.17342 [hep-ex]]

work page doi:10.1103/lwrr-98vx
[10]

Sajjad Athar, A

M. Sajjad Athar, A. Fatima and S. K. Singh, Prog. Part. Nuc l. Phys. 129, 104019 (2023)

2023
[11]

Choudhary et al

B. Choudhary et al. [NOvA], Springer Proc. Phys. 432, 46-51 (2026) doi:10.1007/978-981-95-1513-4 8

work page doi:10.1007/978-981-95-1513-4 2026
[12]

Kalitkina [NOvA], Phys

A. Kalitkina [NOvA], Phys. Atom. Nucl. 88, no.3, 443-447 (2025) doi:10.1134/S1063778825600654

work page doi:10.1134/s1063778825600654 2025
[13]

Lozanoet al., Measurement of charged-currentν µ and ¯νµ cross sections on hydrocarbon in a shallow inelastic scattering region (2025), arXiv:2503.20043 [hep-ex]

A. Lozano et al. [MINERvA], [arXiv:2503.20043 [hep-ex]]

work page arXiv
[14]

Henry et al

S. Henry et al. [MINERvA], Phys. Rev. D 109, no.9, 092008 (2024) doi:10.1103/PhysRevD.109.092008 [a rXiv:2312.16631 [hep-ex]]

work page doi:10.1103/physrevd.109.092008 2024
[15]

K. E. Duﬀy et al. [MicroBooNE and ArgoNeuT], Eur. Phys. J. ST 230, no.24, 4275-4291 (2021) doi:10.1140/epjs/s11734- 021-00297-5

work page doi:10.1140/epjs/s11734- 2021
[16]

Acciarri et al

R. Acciarri et al. [ArgoNeuT], Phys. Rev. D 102, no.1, 011101 (2020) doi:10.1103/PhysRevD.102.011101 [a rXiv:2004.01956 [hep-ex]]

work page doi:10.1103/physrevd.102.011101 2020
[17]

Sajjad Athar and J

M. Sajjad Athar and J. G. Morf ´ ın, J. Phys. G 48, no.3, 034001 (2021)

2021
[18]

Alvarez-Ruso et al

L. Alvarez-Ruso et al. [GENIE], Eur. Phys. J. ST 230, no.24, 4449-4467 (2021) doi:10.1140/epjs/s11734-021-0 0295-7 [arXiv:2106.09381 [hep-ph]]. 17

work page doi:10.1140/epjs/s11734-021-0 2021
[19]

Bodek and U

A. Bodek and U. K. Yang, arXiv:1011.6592 [hep-ph]; Nucl . Phys. Proc. Suppl. 112, 70 (2002)

work page arXiv 2002
[20]

J. J. Aubert et al. [European Muon], Phys. Lett. B 123, 275-278 (1983)

1983
[21]

Arneodo, Phys

M. Arneodo, Phys. Rept. 240, 301-393 (1994)

1994
[22]

Gomez, R

J. Gomez, R. G. Arnold, P. E. Bosted, C. C. Chang, A. T. Kat ramatou, G. G. Petratos, A. A. Rahbar, S. E. Rock, A. F. Sill and Z. M. Szalata, et al. Phys. Rev. D 49, 4348-4372 (1994)

1994
[23]

Sajjad Athar, Springer Proc

M. Sajjad Athar, Springer Proc. Phys. 432, 20-26 (2026)

2026
[24]

Hirai, S

M. Hirai, S. Kumano and T. H. Nagai, Phys. Rev. C 76, 065207 (2007) doi:10.1103/PhysRevC.76.065207 [arXiv:0 709.3038 [hep-ph]]

work page doi:10.1103/physrevc.76.065207 2007
[25]

K. J. Eskola, H. Paukkunen and C. A. Salgado, JHEP 04, 065 (2009) doi:10.1088/1126-6708/2009/04/065 [arXiv:0 902.4154 [hep-ph]]

work page doi:10.1088/1126-6708/2009/04/065 2009
[26]

de Florian, R

D. de Florian, R. Sassot, P. Zurita and M. Stratmann, Phy s. Rev. D 85, 074028 (2012) doi:10.1103/PhysRevD.85.074028 [arXiv:1112.6324 [hep-ph]]

work page doi:10.1103/physrevd.85.074028 2012
[27]

Kovarik, I

K. Kovarik, I. Schienbein, T. Stavreva, F. I. Olness, J. Y. Yu, C. Keppel, J. G. Morﬁn and J. F. Owens, Few Body Syst. 52, 271-277 (2012) doi:10.1007/s00601-011-0297-7

work page doi:10.1007/s00601-011-0297-7 2012
[28]

Kovarik, A

K. Kovarik, A. Kusina, T. Jezo, D. B. Clark, C. Keppel, F. Lyonnet, J. G. Morﬁn, F. I. Olness, J. F. Owens and I. Schienbein, et al. Phys. Rev. D 93, no.8, 085037 (2016) doi:10.1103/PhysRevD.93.085037 [ar Xiv:1509.00792 [hep-ph]]

work page doi:10.1103/physrevd.93.085037 2016
[29]

J. G. Morﬁn, private communication
[30]

Marco et al

E. Marco et al. , Nucl. Phys. A 611, 484 (1996)

1996
[31]

Fernandez de Cordoba and E

P. Fernandez de Cordoba and E. Oset, Phys. Rev. C 46, 1697 (1992)

1992
[32]

S. A. Kulagin and R. Petti, Nucl. Phys. A 765, 126 (2006)

2006
[33]

L. A. Harland-Lang, A. D. Martin, P. Motylinski and R. S. Thorne, Eur. Phys. J. C 75, no. 5, 204 (2015)

2015
[34]

J. A. M. Vermaseren et al. , Nucl. Phys. B 724, 3 (2005)

2005
[35]

S. Moch, J. A. M. Vermaseren and A. Vogt, Phys. Lett. B 606, 123 (2005)

2005
[36]

S. Moch, J. A. M. Vermaseren and A. Vogt, Nucl. Phys. B 813, 220 (2009)

2009
[37]

Schienbein et al

I. Schienbein et al. , J. Phys. G 35, 053101 (2008)

2008
[38]

Zaidi, H

F. Zaidi, H. Haider, M. Sajjad Athar, S. K. Singh and I. Ru iz Simo, Phys. Rev. D 101, no.3, 033001 (2020)

2020
[39]

Quarks and Leptons: An Introd uctory Course in Modern Particle Physics

F. Halzen and A.D. Martin “Quarks and Leptons: An Introd uctory Course in Modern Particle Physics ”, Pg. no. 207, Ed. John Wiley & Sons, Reprint (2008)

2008
[40]

C. G. Callan, Jr. and D. J. Gross, Phys. Rev. Lett. 22, 156 (1969)

1969
[41]

R. D. Ball et al. [NNPDF], JHEP 04, 040 (2015)

2015
[42]

Bailey, T

S. Bailey, T. Cridge, L. A. Harland-Lang, A. D. Martin an d R. S. Thorne, Eur. Phys. J. C 81, no.4, 341 (2021)

2021
[43]

M. Yan, T. J. Hou, P. Nadolsky and C. P. Yuan, Phys. Rev. D 107, no.11, 116001 (2023)

2023
[44]

Gluck, P

M. Gluck, P. Jimenez-Delgado and E. Reya, Eur. Phys. J. C 53, 355-366 (2008)

2008
[45]

H. L. Lai, J. Huston, S. Mrenna, P. Nadolsky, D. Stump, W. K. Tung and C. P. Yuan, JHEP 04, 035 (2010)

2010
[46]

Alekhin, J

S. Alekhin, J. Bl¨ umlein and S. Moch, Eur. Phys. J. C 78, no.6, 477 (2018)

2018
[47]

Zaidi, H

F. Zaidi, H. Haider, M. Sajjad Athar, S. K. Singh and I. Ru iz Simo, Phys. Rev. D 99, no. 9, 093011 (2019)

2019
[48]

Baym and G

G. Baym and G. E. Brown, Nucl. Phys. A 247, 395 (1975)

1975
[49]

Gluck et al

M. Gluck et al. , Z. Phys. C 53, 651 (1992)

1992