Precision semi-exclusive electron scattering, (e,e′p)(e,e'p), exposes persistent failures of the nuclear models used in the GENIE neutrino event generator: below missing momentum pm≈80p_m\approx 80 MeV/c the generator's quasielastic reduced cross sections overpredict carbon data, roughly 12% of the spectral strength at missing energy εm≤80\varepsilon_m \le 80 MeV is missing from single-nucleon knockout descriptions, and transparency predictions disagree with data at low ejectile momenta. The open problem, posed by Butkevich and Luchuk (Phys. Rev. D 112, 093005 (2025)) and reconfirmed by follow-up work through 2026, is to bring the generator description of quasielastic lepton-nucleus scattering into quantitative agreement with (e,e′p)(e,e'p) data by implementing the missing multinucleon and continuum strength and upgrading to two-dimensional distorted spectral functions.

Background

Accelerator neutrino oscillation experiments (DUNE, T2K, Hyper-Kamiokande) infer oscillation parameters from event rates that depend on simulated neutrino-nucleus interactions. At GeV energies the dominant charged-current quasielastic (CCQE) channel — a neutrino converts to a charged lepton while knocking a single nucleon out of the target nucleus — is modeled inside event generators such as GENIE, which describe (i) the nuclear ground state, (ii) the primary vertex, and (iii) final-state interactions (FSI), the rescattering of the knocked-out nucleon on its way out of the nucleus. Semi-exclusive electron scattering, in which an electron of known energy ejects a detected proton, provides a precision test of exactly these ingredients: dividing the measured fivefold differential cross section by the kinematic factor and the off-shell electron-proton cross section yields the reduced cross section, which can be identified with the distorted spectral function — the probability of finding a proton with missing momentum pmp_m (the momentum unaccounted for by the detected proton and momentum transfer) and missing energy εm\varepsilon_m (the energy needed to separate that proton from the nucleus), modified by FSI distortion. Nuclear transparency, the probability that the knocked-out nucleon escapes without significant rescattering, isolates the FSI component. Because the vector current probed by electrons is shared with the weak interaction, the distorted spectral function is, up to Coulomb corrections, the same for electron and neutrino scattering, so electron data benchmark neutrino generators directly. The relativistic distorted-wave impulse approximation (RDWIA), which describes the ejectile's interaction with the residual nucleus through an optical potential, describes these observables well, whereas phenomenological generator models do not. Butkevich and Luchuk (Phys. Rev. D 112, 093005 (2025)) compared five GENIE v3 model configurations — the relativistic and local Fermi gas models G18_02a and G18_10a, the SuSAv2-MEC superscaling model G21_11a, and the spectral-function-based sf1d and effsf models, all with the INTRANUKE hA intranuclear-cascade FSI (an empirical, data-driven rescattering model; the alternative hN variant is a full step-by-step cascade) — against the Tokyo, Saclay, SLAC, and Jefferson Lab carbon (e,e′p)(e,e'p) datasets. They found that the local-Fermi-gas-based models significantly overpredict the reduced cross sections below pm≈80p_m\approx 80 MeV/c, that transparency agreement is only satisfactory, and — following earlier Jefferson Lab transparency analyses (Dutta et al., Phys. Rev. C 68, 064603 (2003), where scaling the RDWIA calculation by 1.12 described the data) — that roughly 12% of the strength at εm≤80\varepsilon_m\le 80 MeV must arise from multinucleon knockout (reactions in which two or more nucleons share the energy transfer, e.g. two-particle-two-hole meson-exchange-current contributions) and continuum channels absent from the generators. A further structural limitation is that the generator spectral-function implementations use one-dimensional dσ/dpmd\sigma/dp_m distributions with fixed binding energies, so they cannot be compared with data in narrow (pm,εm)(p_m, \varepsilon_m) windows. Since these electron data have not been used to tune the generators, they provide an unbiased test whose current outcome is failure, and the residual FSI-modeling uncertainty has been shown (Liu, Munteanu, and Dolan, Phys. Rev. Lett. 136, 201801 (2026)) to distort reconstructed neutrino-energy spectra at DUNE at levels comparable to the target oscillation-parameter precision.

Problem Statement

Bring the nuclear-physics description of quasielastic lepton-nucleus scattering employed in the GENIE event generator (and generators of its class) into quantitative agreement with precision semi-exclusive electron-scattering data. The single objective — a generator whose predictions of (e,e′p)(e,e'p) observables match data — decomposes into two jointly necessary, mutually supporting deliverables: (1) implement the multinucleon-knockout and continuum contributions accounting for the approximately 12% of spectral strength at missing energy εm≤80\varepsilon_m\le 80 MeV that is missing from single-nucleon knockout descriptions, so that both generator and RDWIA predictions of the reduced cross sections and nuclear transparency converge to the measured data; (2) replace the one-dimensional dσ/dpmd\sigma/dp_m treatments with fixed binding energies by two-dimensional distorted spectral functions d2σ/dpm dεmd^2\sigma/dp_m\,d\varepsilon_m with consistent εm\varepsilon_m dependence and shell structure, enabling direct comparison with (e,e′p)(e,e'p) data in narrow missing-energy windows. Completion is achieved when generator predictions are brought into quantitative agreement with the benchmark (e,e′p)(e,e'p) reduced-cross-section and transparency datasets (carbon is required; oxygen and argon are extensions) over the measured kinematic range, with quantitative agreement meaning predictions within the quoted experimental uncertainties of the data — in particular removing the overprediction below pm≈80p_m\approx 80 MeV/c and supplying the missing low-εm\varepsilon_m strength.

References

  1. A. V. Butkevich and S. V. Luchuk, "Assessing the accuracy of the GENIE event generator with electron scattering data: Reduced cross section and nuclear transparency", Phys. Rev. D 112, 093005 (2025), doi:10.1103/jrnx-r49l, arXiv:2506.19355, https://arxiv.org/abs/2506.19355
  2. A. V. Butkevich and S. V. Luchuk, "Test of the GENIE neutrino event generator against reduced cross sections extracted from 16{}^{16}O (e,e′p)(e,e'p) data", Phys. Rev. D 113, 053006 (2026), doi:10.1103/326r-sr5s, arXiv:2511.03274, https://arxiv.org/abs/2511.03274
  3. S. Dytman, M. Betancourt, N. Steinberg, L. B. Weinstein, A. Ashkenazi, J. Tena-Vidal, A. Papadopoulou, G. Chambers-Wall, J. Smith et al. (CLAS and e4nu Collaborations), "Proton transparency and neutrino physics: New methods and modeling", Phys. Rev. D 113, 092007 (2026), doi:10.1103/7xct-5jcp, arXiv:2508.01905, https://arxiv.org/abs/2508.01905
  4. Y. Liu, L. Munteanu, and S. Dolan, "Role of Final-State Interaction Modeling in Neutrino-Energy Reconstruction and Oscillation Measurements", Phys. Rev. Lett. 136, 201801 (2026), doi:10.1103/5ckv-2hpk, arXiv:2511.03964, https://arxiv.org/abs/2511.03964
  5. L. Liu, S. Gardiner, and S. Dytman, "Benchmarking State-of-the-Art Theory and Empirical Models of Pionless Neutrino-Argon Scattering in GENIE", arXiv:2605.14196 (2026), https://arxiv.org/abs/2605.14196
  6. S. Dolan, L. Pickering, P. Stowell, C. Wilkinson, and C. Wret, "CP-violation or Nuclear Excitation: Reviewing the Role of Neutrino Interaction Model Uncertainties on Accelerator-Based Neutrino Oscillation Measurements", arXiv:2605.28671 (2026), https://arxiv.org/abs/2605.28671
  7. M. Betancourt, S. Gardiner, N. Rocco, and N. Steinberg, "Interfacing electron and neutrino quasielastic scattering cross sections with the spectral function in GENIE", Phys. Rev. D 108, 113009 (2023), doi:10.1103/PhysRevD.108.113009, arXiv:2308.15524, https://arxiv.org/abs/2308.15524
  8. D. Dutta, D. van Westrum, D. Abbott, A. Ahmidouch, Ts. A. Amatuoni, C. Armstrong, J. Arrington, K. A. Assamagan, K. Bailey, O. K. Baker, S. Barrow et al., "Quasielastic (e,e'p) reaction on 12{}^{12}C, 56{}^{56}Fe, and 197{}^{197}Au", Phys. Rev. C 68, 064603 (2003), doi:10.1103/PhysRevC.68.064603, arXiv:nucl-ex/0303011, https://arxiv.org/abs/nucl-ex/0303011
  9. A. V. Butkevich and S. V. Luchuk, "Flux-integrated inclusive and pionless cross sections for charged-current neutrino scattering off 40{}^{40}Ar at energies available in the MicroBooNE experiment", arXiv:2607.06241 (2026), https://arxiv.org/abs/2607.06241