Neutrinos exist in one of three types or ‘flavours’—electron, muon and tau neutrinos—and oscillate from one flavour to another when propagating through space. This phenomena is one of the few that cannot be described using the standard model of particle physics (reviewed in ref. 1), and so its experimental study can provide new insight into the nature of our Universe (reviewed in ref. 2). Neutrinos oscillate as a function of their propagation distance (L) divided by their energy (E). Therefore, experiments extract oscillation parameters by measuring their energy distribution at different locations. As accelerator-based oscillation experiments cannot directly measure E, the interpretation of these experiments relies heavily on phenomenological models of neutrino–nucleus interactions to infer E. Here we exploit the similarity of electron–nucleus and neutrino–nucleus interactions, and use electron scattering data with known beam energies to test energy reconstruction methods and interaction models. We find that even in simple interactions where no pions are detected, only a small fraction of events reconstruct to the correct incident energy. More importantly, widely used interaction models reproduce the reconstructed energy distribution only qualitatively and the quality of the reproduction varies strongly with beam energy. This shows both the need and the pathway to improve current models to meet the requirements of next-generation, high-precision experiments such as Hyper-Kamiokande (Japan)3 and DUNE (USA)4.
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The raw data from this experiment are archived in the Jefferson Lab’s mass storage silo under the CLAS E2 run-period dataset. Access to these data can be facilitated by contacting either the corresponding authors or the Jefferson Lab computing centre at firstname.lastname@example.org.
Particle Data Group. Review of particle physics. Phys. Rev. D 98, 030001 (2018).
Mohapatra, R. N. et al. Theory of neutrinos: a white paper. Rep. Prog. Phys. 70, 1757–1867 (2007).
Hyper-Kamiokande Proto-Collaboration. Hyper-Kamiokande design report. Preprint at https://arxiv.org/abs/1805.04163 (2018).
DUNE Collaboration. The DUNE Far Detector interim design report. Volume 1: physics, technology and strategies. Preprint at https://arxiv.org/abs/1807.10334 (2018).
Gonzalez-Garcia, M. C. & Nir, Y. Neutrino masses and mixing: evidence and implications. Rev. Mod. Phys. 75, 345–402 (2003).
Fukugita, M. & Yanagida, T. Baryogenesis without grand unification. Phys. Lett. B 174, 45–47 (1986).
The T2K Collaboration. Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations. Nature 580, 339–344 (2020).
T2K Collaboration. Search for CP violation in neutrino and antineutrino oscillations by the T2K Experiment with 2.2 × 1021 protons on target. Phys. Rev. Lett. 121, 171802 (2018).
Alvarez-Ruso, L. et al. NuSTEC White Paper: status and challenges of neutrino nucleus scattering. Prog. Part. Nucl. Phys. 100, 1–68 (2018).
NOνA Collaboration. New constraints on oscillation parameters from νe appearance and νμ disappearance in the NOνA experiment. Phys. Rev. D 98, 032012 (2018).
Ankowski, A. et al. Missing energy and the measurement of the CP-violating phase in neutrino oscillations. Phys. Rev. D 92, 091301 (2015).
Rocco, N. Ab initio calculations of lepton–nucleus scattering. Front. Phys. 8, 00116 (2020).
Dolan, S., Megias, G. D. & Bolognesi, S. Implementation of the SuSAv2-meson exchange current 1p1h and 2p2h models in GENIE and analysis of nuclear effects in T2K measurements. Phys. Rev. D 101, 033003 (2020).
Rocco, N., Lovato, A. & Benhar, O. Unified description of electron–nucleus scattering within the spectral function formalism. Phys. Rev. Lett. 116, 192501 (2016).
MINERνA Collaboration. Neutrino flux predictions for the NuMI beam. Phys. Rev. D 94, 092005 (2016).
Maan, K. K. on behalf of the NOνA Collaboration. Constraints on the neutrino flux in NOνA using the near-detector data. In Proc. Sci. 38th Intl Conf. High Energy Physics (ICHEP2016) Vol. 282 931 (Sissa, 2016).
T2K Collaboration. T2K near detector constraints for oscillation results. In 18th Intl Workshop on Neutrino Factories and Future Neutrino Facilities Search 2 (2017); https://arxiv.org/abs/1701.02559
Ankowski, A. & Friedland, A. Assessing the accuracy of the GENIE event generator with electron-scattering data. Phys. Rev. D 102, 053001 (2020).
Papadopolou, A. et al. Inclusive electron scattering and the GENIE neutrino event generator. Phys. Rev. D 103, 113003 (2021).
Mecking, B. A. et al. The CEBAF large acceptance spectrometer (CLAS). Nucl. Instrum. Meth. A 503, 513–553 (2003).
MINERνA Collaboration. Direct measurement of nuclear dependence of charged current quasielastic-like neutrino interactions using MINERνA Phys. Rev. Lett. 119, 082001 (2017).
Aliaga, L. et al. Design, calibration, and performance of the MINERνA detector. Nucl. Instrum. Meth. A 743 130–159 (2014).
Acciarri, R. et al. Design and construction of the MicroBooNE detector. J. Instrum. 12, P02017 (2017).
The ICARUS-WA104 Collaboration, The LAr1-ND Collaboration, The MicroBooNE Collaboration & additional Fermilab contributors. A proposal for a three detector short-baseline neutrino oscillation program in the Fermilab Booster Neutrino Beam. Preprint at https://arxiv.org/abs/1503.01520
The DUNE Collaboration. Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) conceptual design report. Volume 2: The physics program for DUNE at LBNF. Preprint at https://arxiv.org/abs/1512.06148 (2016).
Katori, T. & Martini, M. Neutrino–nucleus cross sections for oscillation experiments. J. Phys. G 45, 013001 (2018).
Andreopoulos, C. et al. The GENIE neutrino Monte Carlo generator. Nucl. Instrum. Meth. A 614, 87–104 (2010).
MicroBooNE Collaboration. First measurement of inclusive muon neutrino charged current differential cross sections on argon at Eν ~ 0.8 GeV with the MicroBooNE detector. Phys. Rev. Lett. 123, 131801 (2019).
Lu, X.-G. et al. Measurement of nuclear effects in neutrino interactions with minimal dependence on neutrino energy. Phys. Rev. C 94, 015503 (2016).
The T2K Collaboration. Characterization of nuclear effects in muon–neutrino scattering on hydrocarbon with a measurement of final-state kinematics and correlations in charged-current pionless interactions at T2K. Phys. Rev. D 98, 032003 (2018).
MINERνA Collaboration. Measurement of final-state correlations in neutrino muon–proton mesonless production on hydrocarbon at ⟨Eν⟩ = 3 GeV. Phys. Rev. Lett. 121, 022504 (2018).
Freund, M. Analytic approximations for three neutrino oscillation parameters and probabilities in matter. Phys. Rev. D 64, 053003 (2001).
Cervera, A. et al. Golden measurements at a neutrino factory. Nucl. Phys. B 579, 17–55 (2000).
Cervera, A. et al. Erratum to: “Golden measurements at a neutrino factory”: [Nucl. Phys. B 579 (2000) 17]. Nucl. Phys. B 593, 731–732 (2001).
Osipenko, M. et al. Measurement of the nucleon structure function F2 in the nuclear medium and evaluation of its moments. Nucl. Phys. A 845, 1–32 (2010).
CLAS Collaboration. Measurement of two- and three-nucleon short-range correlation probabilities in nuclei. Phys. Rev. Lett. 96, 082501 (2006).
CLAS Collaboration. Survey of ALT′ asymmetries in semi-exclusive electron scattering on 4He and 12C. Nucl. Phys. A 748, 357–373 (2005).
CLAS Collaboration. Proton source size measurements in the eA → e′ppX reaction. Phys. Rev. Lett. 93, 192301 (2004).
CLAS Collaboration. Two-nucleon momentum distributions measured in 3He(e, e′pp)n. Phys. Rev. Lett. 92, 052303 (2004).
CLAS Collaboration. Observation of nuclear scaling in the A(e, e′) reaction at xB > 1. Phys. Rev. C 68, 014313 (2003).
Hen, O. et al. Momentum sharing in imbalanced Fermi systems. Science 346, 614–617 (2014).
Sealock, R. M. et al. Electroexcitation of the Δ(1232) in nuclei. Phys. Rev. Lett. 62, 1350–1353 (1989).
Gonzaléz-Jiménez, R. et al. Extensions of superscaling from relativistic mean field theory: the SuSAv2 model. Phys. Rev. C 90, 035501 (2014).
Megias, G. D. et al. Inclusive electron scattering within the SuSAv2 meson-exchange current approach. Phys. Rev. D 94, 013012 (2016).
De Pace, A., Nardi, M., Alberico, W. M., Donnelly, T.W. & Molinaria, A. The 2p–2h electromagnetic response in the quasielastic peak and beyond. Nucl. Phys. A 726, 303–326 (2003).
Katori, T. Meson exchange current (MEC) models in neutrino interaction generators. In NuINT12: 8th Intl Workshop On Neutrino–Nucleus Interactions in the Few-GeV Region (eds. Da Motta, H. et al.) https://doi.org/10.1063/1.4919465 (AIP, 2015).
GENIE Collaboration. Neutrino–nucleon cross-section model tuning in GENIE v3. Phys. Rev. D 104, 072009 (2021).
Berger, Ch. & Sehgal, L. M. Lepton mass effects in single pion production by neutrinos. Phys. Rev. D 76, 113004 (2007).
Feynman, R. P., Kislinger, M. & Ravndal, F. Current matrix elements from a relativistic quark model. Phys. Rev. D 3, 2706 (1971).
Bodek, A. & Yang, U. K. Higher twist, ξw scaling, and effective LO PDFs for lepton scattering in the few GeV region. J. Phys. G 29, 1899–1905 (2003).
Yang, T., Andreopoulos, C., Gallagher, H., Hofmann, K. & Kehayias, P. A hadronization model for few-GeV neutrino interactions. Eur. Phys. J. C 63, 1–10 (2009).
Sjostrand, T., Mrenna, S. & Skands, P. Z. PYTHIA 6.4 physics and manual. J. High Energy Phys. 2006, 026 (2006).
Andreopoulos, C. et al. The GENIE neutrino Monte Carlo generator: physics and user manual. Preprint at https://arxiv.org/abs/1510.05494 (2015).
Dytman, S. A. & Meyer, A. S. Final state interactions in GENIE. AIP Conf. Proc. 1405, 213 (2011).
Merenyi, R. et al. Determination of pion intranuclear rescattering rates in νμ–Ne versus νμ–D interactions for the atmospheric ν flux. Phys. Rev. D 45, 743–751 (1992).
Mashnik, S. G., Sierk, A. J., Gudima, K. K. & Baznat, M. I. CEM03 and LAQGSM03—new modeling tools for nuclear applications. Phys. Conf. Ser. 41, https://doi.org/10.1088/1742-6596/41/1/037 (2006).
Mo, L. W. & Tsai, Y.-S. Radiative corrections to elastic and inelastic ep and μp scattering. Rev. Mod. Phys. 41, 205–235 (1969).
The T2K Collaboration. Measurement of the muon neutrino charged-current single π+ production on hydrocarbon using the T2K off-axis near detector ND280. Phys. Rev. D 101, 012007 (2020).
The T2K Collaboration. Exclusive π0p electroproduction off protons in the resonance region at photon virtualities 0.4 GeV2 ≤ Q2 ≤ 1 GeV2. Phys. Rev. C 101, 015208 (2020).
Osipenko, M. A Kinematically Complete Measurement of the Proton Structure Function F2 in the Resonance Region and Evaluation of its Moments. PhD thesis, Moscow State Univ. (2002); https://www.jlab.org/Hall-B/general/thesis/Osipenko_thesis.ps.gz
The T2K Collaboration. Improved constraints on neutrino mixing from the T2K experiment with 3.13 × 1021 protons on target. Phys. Rev. D 103, 112008 (2021).
DUNE Collaboration. Long-baseline neutrino oscillation physics potential of the DUNE experiment. Eur. Phys. J. C 80, 978 (2020).
We acknowledge the efforts of the staff of the Accelerator and Physics Divisions at Jefferson Lab that made this experiment possible. We thank L. Pickering for useful discussions. The analysis presented here was carried out as part of the Jefferson Lab Hall B Data-Mining project supported by the US Department of Energy (DOE). The research was supported also by DOE, the US National Science Foundation, the Israel Science Foundation, the Chilean Comisión Nacional de Investigación Científica y Tecnológica, the French Centre national de la recherche scientifique and Commissariat à l'Energie Atomique et aux Energies Alternatives, the French–American Cultural Exchange, the Italian Istituto Nazionale di Fisica Nucleare, the National Research Foundation of Korea, and the UK Science and Technology Facilities Council. P. Coloma acknowledges support from project PROMETEO/2019/083. This project has been supported by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 674896 (Elusives, H2020-MSCA-ITN- 2015-674896). G.D.M. acknowledges support from the Spanish Ministerio de Economía y Competitividad and ERDF (European Regional Development Fund) under contract FIS2017-88410-P, by the University of Tokyo ICRRs Inter-University Research Program FY2020 & 2021, refs no. A07 and A06; by the Junta de Andalucia (grant no. FQM160); and by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 839481. This document was prepared by the e4ν Collaboration using the resources of the Fermi National Accelerator Laboratory (Fermilab), a US Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under contract no. DE-AC02-07CH11359. Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility for the DOE, Office of Science, Office of Nuclear Physics under contract DE-AC05-06OR23177. The raw data from this experiment are archived in Jefferson Lab’s mass storage silo.
The authors declare no competing interests.
Peer review information Nature thanks Tingjun Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
Left, Before oscillation at the near detector; and right, after oscillation at the far detector61,62. The vertical lines show the three electron beam energies of this measurement. The NOνA far-detector beam flux is calculated using the near-detector flux and the neutrino oscillation parameters from the Particle Data Group. arb., arbitrary units.
Left, The ratio of e-GENIE to data for the fraction of the weighted cross-section that reconstructs to the correct incident energy, plotted versus incident energy; and right, the e-GENIE–data weighted cross-section ratio for events that reconstruct to the correct incident energy, plotted versus incident energy. The triangles and dashed lines indicate the G2018/data ratios and the squares and solid lines indicate the SuSAv2/data ratios. SuSAv2 is not intended to model nuclei lighter than 12C. Yellow shows the carbon, blue shows helium and green shows iron. Error bars show the 68% (1σ) confidence limits for the statistical and point-to-point systematic uncertainties added in quadrature. Error bars are not shown when they are smaller than the size of the data point. Normalization uncertainties of 3% not shown.
Left, The proton (black) and charged pion (blue) multiplicities for data (points), SuSAv2 (solid histogram) and G2018 (dashed histogram) for 2.257-GeV carbon. Right, Comparison between the inclusive C(e, e′) cross-sections measured at 37.5° for data (points) and SuSAv2 (lines) for the 0.961- and 1.299-GeV SLAC data42 and our 1.159-GeV CLAS data. Error bars show the 68% (1σ) confidence limits for the statistical and point-to-point systematic uncertainties added in quadrature. Error bars are not shown when they are smaller than the size of the data point. Normalization uncertainties of 3% not shown.
a–d, (Erec – Etrue)/Etrue for data (points) and SuSAv2 (lines) for 1.159 GeV (red triangles and dotted lines), 2.257 GeV (green squares and solid lines) and 4.453 GeV (blue dots and solid lines) for C Ecal (a), C EQE (b), Fe Ecal (c), and Fe EQE (d). The plots are area-normalized and each bin has been scaled by the bin width. Error bars show the 68% (1σ) confidence limits for the statistical and point-to-point systematic uncertainties added in quadrature. Error bars are not shown when they are smaller than the size of the data point. Normalization uncertainties of 3% not shown.
The cross-section plotted versus transverse missing momentum PT for data (black points), SuSAv2 (black solid curve) and G2018 (black dotted curve). Different panels show results for different beam energy and target nucleus combinations: a–c, Carbon target at 1.159 GeV (a), 2.257 GeV (b) and 4.453 GeV (c). d, e, Iron target at 2.257 GeV (d) and 4.453 GeV (e). The 4.453-GeV yields have been scaled by four to have the same vertical scale. Coloured lines show the contributions of different processes to the SuSAv2 GENIE simulation: QE (blue), MEC (red), RES (green) and DIS (orange). Error bars show the 68% (1σ) confidence limits for the statistical and point-to-point systematic uncertainties added in quadrature. Error bars are not shown when they are smaller than the size of the data point. Normalization uncertainties of 3% not shown.
a–j, The cross-section plotted versus δαT (a–e) and versus δϕT (f–j) for data (black points), SuSAv2 (black solid curve) and G2018 (black dotted curve). Different panels show results for different beam energy and target nucleus combinations: a–c, Carbon target at 1.159 GeV (a), 2.257 GeV (b) and 4.453 GeV (c). d, e, Iron target at 2.257 GeV (d) and 4.453 GeV (e). The 4.453-GeV yields have been scaled by two to have the same vertical scale. Coloured lines show the contributions of different processes to the SuSAv2 GENIE simulation: QE (blue), MEC (red), RES (green) and DIS (orange). Error bars show the 68% (1σ) confidence limits for the statistical and point-to-point systematic uncertainties added in quadrature. Error bars are not shown when they are smaller than the size of the data point. Normalization uncertainties of 3% not shown.
The number of weighted events as a function of reconstructed energy EQE for 4.453-GeV Fe(e, e′) events for: left, events with a detected π± or photon (blue), events with one (red) or two (light brown) undetected π± or photons; and right, all (e, e′X) events with detected or undetected π± or photon (blue), (e, e′) events with no detected π± or photon (red), and (e, e′) events after subtraction for undetected π± or photon (light brown). The uncertainties are statistical only and are shown at the 1σ or 68% confidence level. Error bars are not shown when they are smaller than the size of the data point.
a–c, Acceptance correction factors; d–f, acceptance correction factor uncertainties; and g–i, electron radiation correction factors plotted versus Ecal for the three incident beam energies. Results for carbon are shown in black, helium in green and iron in magenta. The left column (a, d, g) shows the 1.159-GeV results, the middle column (b, e, h) shows the 2.257-GeV results and the right column (c, f, i) shows the 4.453-GeV results.
a, Cutaway drawing of CLAS showing the sector structure and the different detectors. Yellow, toroidal magnet; blue, drift chambers; magenta, Cherenkov counter; red, scintillation counters (time of flight); green, electromagnetic calorimeter. The beam enters from the upper left and the target is in the center of CLAS. CLAS detector image reproduced with permission of the CLAS Collaboration. b, The 2.257-GeV 3He(e, e′pp)X missing mass for data (solid histogram) and simulation (dashed histogram). c, The H(e, e′π+)X missing mass for data (black) and fit to data (red).
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Khachatryan, M., Papadopoulou, A., Ashkenazi, A. et al. Electron-beam energy reconstruction for neutrino oscillation measurements. Nature 599, 565–570 (2021). https://doi.org/10.1038/s41586-021-04046-5