Abstract
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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Data availability
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 helpdesk@jlab.org.
Change history
25 November 2021
The linking to some of the Source Data files was originally incorrect and has now been amended.
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Acknowledgements
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.
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The CEBAF Large Acceptance Spectrometer was designed and constructed by the CLAS Collaboration and Jefferson Lab. Data acquisition, processing and calibration, Monte Carlo simulations of the detector and data analyses were performed by a large number of CLAS Collaboration members, who also discussed and approved the scientific results. The analysis presented here was performed by M. Khachatryan, A.P., A.A., A. Hrnjic and A.N. with guidance from A.A., F.H., O.H., E. Piasetzky and L.B.W., and was reviewed by the CLAS Collaboration. S. Dytman., M. Betancourt and K.M. provided expertise on neutrino scattering. S. Dytman, G.M., S. Dolan and S.G. helped develop e-GENIE. P. Coloma performed a simulation of the DUNE sensitivity to the oscillation parameters, and determined the impact of our results on the fit.
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Extended data figures and tables
Extended Data Fig. 1 Energy distributions of different νμ beams.
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.
Extended Data Fig. 2 Peak energy reconstruction fraction and width.
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.
Extended Data Fig. 3 Particle multiplicities and include cross-section extraction.
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.
Extended Data Fig. 4 Energy feed-down cross-sections.
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.
Extended Data Fig. 5 Transverse missing-momentum-dependent differential cross-section.
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.
Extended Data Fig. 6 δαT-dependent differential cross-section.
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.
Extended Data Fig. 7 The effect of undetected pion subtraction.
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.
Extended Data Fig. 8 Acceptance and radiation corrections.
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.
Extended Data Fig. 9 CLAS detector and its calibration performance.
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
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DOI: https://doi.org/10.1038/s41586-021-04046-5
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