Reconstruction of interactions in the ProtoDUNE-SP detector with Pandora

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Reconstruction of interactions in the ProtoDUNE-SP detector with Pandora © 2023 the Authors Published version DUNE Collaboration DUNE Collaboration. (2023). Reconstruction of interactions in the ProtoDUNE-SP detector with Pandora. European Physical Journal C, 83, Article 618. https://doi.org/10.1140/epjc/s10052023-11733-2 2023 Eur. Phys. J. C (2023) 83:618 https://doi.org/10.1140/epjc/s10052-023-11733-2 Regular Article - Experimental Physics Reconstruction of interactions in the ProtoDUNE-SP detector with Pandora DUNE Collaboration A. Abed Abud35,130,B.Abi 158, R. Acciarri67, M. A. Acero11, M. R. Adames195, G. Adamov72, M. Adamowski67, D. Adams20, M. Adinolfi19, C. Adriano30, A. Aduszkiewicz81, J. 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Zuklin48,V.Zutshi 152,R.Zwaska 67 1Abilene Christian University, Abilene, TX 79601, USA 2University of Albany, SUNY, Albany, NY 12222, USA 3University of Amsterdam, 1098 XG Amsterdam, The Netherlands 4Antalya Bilim University, 07190 Dö¸semealtı/Antalya, Turkey 5University of Antananarivo, 101 Antananarivo, Madagascar 6Universidad Antonio Nariño, Bogotá, Colombia 7Argonne National Laboratory, Argonne, IL 60439, USA 8University of Arizona, Tucson, AZ 85721, USA 9Universidad Nacional de Asunción, San Lorenzo, Paraguay 10 University of Athens, 157 84 Zografou, Greece 11 Universidad del Atlántico, Barranquilla, Atlántico, Colombia 12 Augustana University, Sioux Falls, SD 57197, USA 13 University of Basel, 4056 Basel, Switzerland 14 University of Bern, 3012 Bern, Switzerland 15 Beykent University, Istanbul, Turkey 16 University of Birmingham, Birmingham B15 2TT, UK 17 Università del Bologna, 40127 Bologna, Italy 18 Boston University, Boston, MA 02215, USA 19 University of Bristol, Bristol BS8 1TL, UK 20 Brookhaven National Laboratory, Upton, NY 11973, USA 21 University of Bucharest, Bucharest, Romania 22 University of California Berkeley, Berkeley, CA 94720, USA 23 University of California Davis, Davis, CA 95616, USA 24 University of California Irvine, Irvine, CA 92697, USA 25 University of California Los Angeles, Los Angeles, CA 90095, USA 26 University of California Riverside, Riverside, CA 92521, USA 27 University of California Santa Barbara, Santa Barbara, CA 93106, USA 28 California Institute of Technology, Pasadena, CA 91125, USA 29 University of Cambridge, Cambridge CB3 0HE, UK 30 Universidade Estadual de Campinas, Campinas, SP 13083-970, Brazil 31 Università di Catania, 2, 95131 Catania, Italy 32 Universidad Católica del Norte, Antofagasta, Chile 33 Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ 22290-180, Brazil 34 IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France 35 CERN, The European Organization for Nuclear Research, 1211 Meyrin, Switzerland 36 Institute of Particle and Nuclear Physics of the Faculty of Mathematics and Physics of the Charles University, 180 00 Prague 8, Czech Republic 37 University of Chicago, Chicago, IL 60637, USA 38 Chung-Ang University, Seoul 06974, South Korea 39 CIEMAT, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, 28040 Madrid, Spain 123 Eur. 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Savoie Mont Blanc, CNRS, LAPP-IN2P3, 74000 Annecy, France 53 Daresbury Laboratory, Cheshire WA4 4AD, UK 54 Drexel University, Philadelphia, PA 19104, USA 55 Duke University, Durham, NC 27708, USA 56 Durham University, Durham DH1 3LE, UK 57 University of Edinburgh, Edinburgh EH8 9YL, UK 58 Universidad EIA, Envigado, Antioquia, Colombia 59 ETH Zurich, Zurich, Switzerland 60 Eötvös Loránd University, Budapest 1053, Hungary 61 Faculdade de Ciências da Universidade de Lisboa-FCUL, 1749-016 Lisbon, Portugal 62 Universidade Federal de Alfenas, Poços de Caldas, MG 37715-400, Brazil 63 Universidade Federal de Goias, Goiania, GO 74690-900, Brazil 64 Universidade Federal de São Carlos, 13604-900 Araras, SP, Brazil 65 Universidade Federal do ABC, Santo André, SP 09210-580, Brazil 66 Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-901, Brazil 67 Fermi National Accelerator Laboratory, Batavia, IL 60510, USA 68 University of Ferrara, Ferrara, Italy 69 University of Florida, Gainesville, FL 32611-8440, USA 70 Fluminense Federal University, 9, Icaraí Niterói, RJ 24220-900, Brazil 71 Università degli Studi di Genova, Genoa, Italy 72 Georgian Technical University, Tbilisi, Georgia 73 University of Granada and CAFPE, 18002 Granada, Spain 74 Gran Sasso Science Institute, L’Aquila, Italy 75 Laboratori Nazionali del Gran Sasso, L’Aquila, AQ, Italy 76 University Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France 77 Universidad de Guanajuato, C.P. 37000 Guanajuato, Mexico 78 Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India 79 Harvard University, Cambridge, MA 02138, USA 80 University of Hawaii, Honolulu, HI 96822, USA 81 University of Houston, Houston, TX 77204, USA 82 University of Hyderabad, Gachibowli, Hyderabad 500 046, India 83 Idaho State University, Pocatello, ID 83209, USA 84 Institut de Física d’Altes Energies (IFAE)-Barcelona Institute of Science and Technology (BIST), Barcelona, Spain 85 Instituto de Física Corpuscular, CSIC and Universitat de València, 46980 Paterna, Valencia, Spain 86 Instituto Galego de Física de Altas Enerxías, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain 87 Illinois Institute of Technology, Chicago, IL 60616, USA 88 Imperial College of Science Technology and Medicine, London SW7 2BZ, UK 89 Indian Institute of Technology Guwahati, Guwahati 781 039, India 90 Indian Institute of Technology Hyderabad, Hyderabad 502285, India 91 Indiana University, Bloomington, IN 47405, USA 92 Istituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna, BO, Italy 93 Istituto Nazionale di Fisica Nucleare Sezione di Catania, 95123 Catania, Italy 94 Istituto Nazionale di Fisica Nucleare Sezione di Ferrara, 44122 Ferrara, Italy 95 Istituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genoa, GE, Italy 96 Istituto Nazionale di Fisica Nucleare Sezione di Lecce, Lecce 73100, Italy 97 Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3, 20126 Milan, Italy 98 Istituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milan, Italy 99 Istituto Nazionale di Fisica Nucleare Sezione di Napoli, 80126 Naples, Italy 100 Istituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padua, Italy 101 Istituto Nazionale di Fisica Nucleare Sezione di Pavia, 27100 Pavia, Italy 102 Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Pisa, Pisa, PI, Italy 103 Istituto Nazionale di Fisica Nucleare Sezione di Roma, 00185 Rome, RM, Italy 104 Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy 123 618 Page 6 of 25 Eur. 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C (2023) 83:618 105 Universidad Nacional de Ingeniería, Lima 25, Peru 106 Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia 107 University of Insubria, Via Ravasi, 2, 21100 Varese, VA, Italy 108 University of Iowa, Iowa City, IA 52242, USA 109 Iowa State University, Ames, IA 50011, USA 110 Institut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France 111 Institute for Research in Fundamental Sciences, Tehran, Iran 112 Instituto Superior Técnico-IST, Universidade de Lisboa, 1049-001 Lisbon, Portugal 113 Iwate University, Morioka, Iwate 020-8551, Japan 114 Jackson State University, Jackson, MS 39217, USA 115 University of Jammu, Jammu 180006, India 116 Jawaharlal Nehru University, New Delhi 110067, India 117 Jeonbuk National University, Jeonrabuk-do 54896, South Korea 118 Joint Institute for Nuclear Research, Dzhelepov Laboratory of Nuclear Problems, 6 Joliot-Curie, Dubna, Moscow Region 141980, Russia 119 University of , 40014 Jyvaskyla, Finland 120 Kansas State University, Manhattan, KS 66506, USA 121 Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan 122 High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan 123 Korea Institute of Science and Technology Information, Daejeon 34141, South Korea 124 K L University, Vaddeswaram, Andhra Pradesh 522502, India 125 National Institute of Technology, Kure College, Hiroshima 737-8506, Japan 126 Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine 127 Lancaster University, Lancaster LA1 4YB, UK 128 Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 129 Laboratório de Instrumentação e Física Experimental de Partículas, 1649-003 Lisboa and 3004-516, Coimbra, Portugal 130 University of Liverpool, Liverpool L69 7ZE, UK 131 Los Alamos National Laboratory, Los Alamos, NM 87545, USA 132 Louisiana State University, Baton Rouge, LA 70803, USA 133 University of Lucknow, Lucknow, Uttar Pradesh 226007, India 134 Madrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain 135 Johannes Gutenberg-Universität Mainz, 55122 Mainz, Germany 136 University of Manchester, Manchester M13 9PL, UK 137 Massachusetts Institute of Technology, Cambridge, MA 02139, USA 138 Max-Planck-Institut, 80805 Munich, Germany 139 University of Medellín, Medellín 050026, Colombia 140 University of Michigan, Ann Arbor, MI 48109, USA 141 Michigan State University, East Lansing, MI 48824, USA 142 Università del Milano-Bicocca, 20126 Milan, Italy 143 Università degli Studi di Milano, 20133 Milan, Italy 144 University of Minnesota Duluth, Duluth, MN 55812, USA 145 University of Minnesota Twin Cities, Minneapolis, MN 55455, USA 146 University of Mississippi, University, MS 38677, USA 147 Università degli Studi di Napoli Federico II , 80138 Naples, NA, Italy 148 University of New Mexico, Albuquerque, NM 87131, USA 149 H. Niewodnicza´nski Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland 150 Nikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, The Netherlands 151 University of North Dakota, Grand Forks, ND 58202-8357, USA 152 Northern Illinois University, DeKalb, IL 60115, USA 153 Northwestern University, Evanston, IL 60208, USA 154 University of Notre Dame, Notre Dame, IN 46556, USA 155 Occidental College, Los Angeles, CA 90041, USA 156 Ohio State University, Columbus, OH 43210, USA 157 Oregon State University, Corvallis, OR 97331, USA 158 University of Oxford, Oxford OX1 3RH, UK 159 Pacific Northwest National Laboratory, Richland, WA 99352, USA 160 Universtà degli Studi di Padova, 35131 Padua, Italy 161 Panjab University, Chandigarh, U.T. 160014, India 162 Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France 163 Université de Paris, CNRS, Astroparticule et Cosmologie, 75006 Paris, France 164 University of Parma, 43121 Parma, PR, Italy 165 Università degli Studi di Pavia, 27100 Pavia, PV, Italy 166 University of Pennsylvania, Philadelphia, PA 19104, USA 167 Pennsylvania State University, University Park, PA 16802, USA 168 Physical Research Laboratory, Ahmedabad 380 009, India 169 Università di Pisa, 56127 Pisa, Italy 170 University of Pittsburgh, Pittsburgh, PA 15260, USA 123 Eur. Phys. J. C (2023) 83:618 Page 7 of 25 618 171 Pontificia Universidad Católica del Perú, Lima, Peru 172 University of Puerto Rico, Mayaguez, PR 00681, USA 173 Punjab Agricultural University, Ludhiana 141004, India 174 Queen Mary University of London, London E1 4NS, UK 175 Radboud University, 6525 AJ Nijmegen, The Netherlands 176 University of Rochester, Rochester, NY 14627, USA 177 Royal Holloway College, London TW20 0EX, UK 178 Rutgers University, Piscataway, NJ 08854, USA 179 STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK 180 Università del Salento, 73100 Lecce, Italy 181 San Jose State University, San José, CA 95192-0106, USA 182 Sapienza University of Rome, 00185 Rome, RM, Italy 183 Universidad Sergio Arboleda, 11022 Bogotá, Colombia 184 University of Sheffield, Sheffield S3 7RH, UK 185 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 186 University of South Carolina, Columbia, SC 29208, USA 187 South Dakota School of Mines and Technology, Rapid City, SD 57701, USA 188 South Dakota State University, Brookings, SD 57007, USA 189 Southern Methodist University, Dallas, TX 75275, USA 190 Stony Brook University, SUNY, Stony Brook, NY 11794, USA 191 Sun Yat-Sen University, Guangzhou 510275, China 192 Sanford Underground Research Facility, Lead, SD 57754, USA 193 University of Sussex, Brighton BN1 9RH, UK 194 Syracuse University, Syracuse, NY 13244, USA 195 Universidade Tecnológica Federal do Paraná, Curitiba, Brazil 196 Texas A&M University, College Station, TX 77840, USA 197 Texas A&M University-Corpus Christi, Corpus Christi, TX 78412, USA 198 University of Texas at Arlington, Arlington, TX 76019, USA 199 University of Texas at Austin, Austin, TX 78712, USA 200 University of Toronto, Toronto, ON M5S 1A1, Canada 201 Tufts University, Medford, MA 02155, USA 202 Universidade Federal de São Paulo, São Paulo 09913-030, Brazil 203 Ulsan National Institute of Science and Technology, Ulsan 689-798, South Korea 204 University College London, London WC1E 6BT, UK 205 Valley City State University, Valley City, ND 58072, USA 206 Variable Energy Cyclotron Centre, Kolkata, West Bengal 700 064, India 207 Virginia Tech, Blacksburg, VA 24060, USA 208 University of Warsaw, 02-093 Warsaw, Poland 209 University of Warwick, Coventry CV4 7AL, UK 210 Wellesley College, Wellesley, MA 02481, USA 211 Wichita State University, Wichita, KS 67260, USA 212 College of William and Mary, Williamsburg, VA 23187, USA 213 University of Wisconsin Madison, Madison, WI 53706, USA 214 Yale University, New Haven, CT 06520, USA 215 Yerevan Institute for Theoretical Physics and Modeling, 0036 Yerevan, Armenia 216 York University, Toronto M3J 1P3, Canada Received: 30 June 2022 / Accepted: 20 June 2023 © The Author(s) 2023 Abstract The Pandora Software Development Kit and algorithm libraries provide pattern-recognition logic essential to the reconstruction of particle interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at ProtoDUNE-SP, a prototype for the Deep Underground Neutrino Experiment far detector. ProtoDUNE-SP, located at CERN, is exposed to ae-mail: leigh.ho[email protected] (corresponding author) a charged-particle test beam. This paper gives an overview of the Pandora reconstruction algorithms and how they have been tailored for use at ProtoDUNE-SP. In complex events with numerous cosmic-ray and beam background particles, the simulated reconstruction and identification efficiency for triggered test-beam particles is above 80% for the majority of particle type and beam momentum combinations. Specifically, simulated 1GeV/ccharged pions and protons are correctly reconstructed and identified with efficiencies of 86.1±0.6% and 84.1±0.6%, respectively. The efficiencies 123 618 Page 8 of 25 Eur. Phys. J. C (2023) 83:618 measured for test-beam data are shown to be within 5% of those predicted by the simulation. 1 Introduction ProtoDUNE-SP [1] was a single-phase (SP) liquid argon time projection chamber (LArTPC) detector prototype for the Deep Underground Neutrino Experiment (DUNE) far detector [2]. Installation of the detector at the CERN Neutrino Platform was completed in August 2018, and chargedparticletest-beamdatawerecollectedfromAugust2018until the start of the CERN long shutdown period in December 2018. The primary engineering goal of the ProtoDUNE-SP detectorwasto prototype the production of large-scaleLArTPCs for use at the DUNE far detector (FD) [3]. Alongside the validation of production and installation procedures, ProtoDUNE-SP had goals related to testing the event reconstruction and performing detector calibration in a controlled environment. The primary physics goals were measurements of the interaction cross-sections for various charged particle species on a liquid argon target that will be very valuable for modelling neutrino interactions at DUNE. Pandora is a software package that has been developed for event reconstruction in high energy physics and is now in use at ProtoDUNE-SP [4]. It consists of a framework, the Pandora Software Development Kit (SDK) [5], and a number of experiment-specific content libraries containing patternrecognition logic. Originally developed for event reconstruction at future linear e+e−colliders [6,7], Pandora has since been successfully applied in LArTPC experiments, such as MicroBooNE [8]. Pandora brings a multi-algorithm philosophytoLArTPCeventreconstruction,applyingover100algorithms to develop the reconstruction from the input hits to a hierarchy of fully-reconstructed particles. Each algorithm is designed to address a specific aspect of event reconstruction, and they collectively provide robust and sophisticated pattern recognition. Pandora incorporates machine-learning techniques, such as boosted decision trees (BDTs) [9,10] and support vector machines [11], to drive decisions made at certain junctions of the event reconstruction. The Pandora event reconstruction can be run standalone and it has also been interfaced with LArSoft [12], a common software framework used by the majority of LArTPC experiments. The contents of this paper are as follows: Sect. 2describes the ProtoDUNE-SP experiment, Sect. 3describes the Pandora reconstruction, Sect. 4describes the simulated and experimental data samples, Sect. 5provides an assessment of the cosmic-ray reconstruction, Sect. 6examines the performance of the test-beam reconstruction, and Sect. 7provides concluding remarks. 2 Experimental details 2.1 Charged particle test beam A dedicated extension [13,14] to the CERN H4 beamline was constructed for ProtoDUNE-SP. The test beam contains a mixture of particle species: π+,e+,p,μ+, and K+.The polarity of the beam focusing magnets can be reversed to produce a beam containing negatively charged particles, but all test-beam data collected in 2018 was taken in the positive polarity mode. The beam momentum can be varied from 0.3to7GeV/cwith a resolution of Δp/p≤3% [15], providing particles with similar energies as those expected to be produced in the 0.5–5.0GeV neutrino interactions in the DUNE FD [16]. The test beam enters the detector through a beam plug in the upstream face and is approximately 10cm in diameter. The beam line has numerous instruments that are used to trigger the detector readout electronics, to measure the momentum and the trajectory of the test-beam particles prior to their entrance into the detector, and to identify their species. Full details of the test-beam design can be found in Refs. [4,13,14]. 2.2 ProtoDUNE-SP The ProtoDUNE-SP detector is extensively described in Refs.[1,4].Asimplifiedschematicofthedetectorisshownin Fig. 1. It has a cuboid geometry with active-volume dimensions: 7.2m (width), 6.1m (height) and 7.0m (length). It has a total liquid argon mass of 0.77kt making it the largest LArTPC constructed to date.1The nominal electric field in the active volume is 500V/cm, generated by the cathode plane (an array of Cathode Plane Assembly (CPA) modules), which is held at −180kV, and two sets of three Anode Plane Assemblies (APAs), one on either side of the central cathode, which are effectively grounded. The field cage ensures the uniformity of the electric field and shields it from the cryostat walls. The APAs are two-sided such that they can read out a drift volume on either side, as required for the DUNE FD. Each side of the APA has a plane of collection wires, referred to as the wplanes, that collect the ionisation charges from that side of the APA. In front of the collection plane there are two planes of induction wires, the inner one is denoted vand the outer u, that wrap around both sides of the APA. The w plane wires are vertical with a 4.790mm pitch between the wires. The uand vplane wires are aligned at ±35.7◦to the vertical, with a pitch of 4.669mm between the wires. A right-handed Cartesian coordinate system is used to describe the detector geometry: xdefines the drift axis and is either equal to or opposite to the drift direction, yis the 1The dual-phase LArTPC ProtoDUNE-DP, which was built shortly after ProtoDUNE-SP, was approximately the same size. 123 Eur. Phys. J. C (2023) 83:618 Page 15 of 25 618 Fig. 9 The reconstructed output using the PandoraCosmic algorithm chain in 3D, the x-y plane and the x-z plane for a simulated event in ProtoDUNE-SP. For illustrative purposes, only hits appearing in the beam-side central drift volumes in ProtoDUNE-SP have been reconstructed. Particles in red are deemed to be out of time, as they appear outside the physical boundary of the drift volumes because no offset in the drift position has been applied. Particles in black are those deemed to be in time. Out-of-time particles are tagged as cosmic-ray muons Fig. 10 The eleven “slices” created during the reconstruction of a simulated 3GeV/cπ+ProtoDUNE-SP interaction after the removal of the clear cosmic rays. Clockwise, from top left: 3D hits created by the ‘fast reconstruction’; and 2D hits in the u,vand wviews. Each unique colour represents a distinct slice, and the reconstructed beam particle slice is shown in red guished from the cosmic-ray muon background. The zoomed view shows that the parent π+beam particle has been identified (purple, moving from left to right) and correctly placed at the top of the reconstructed hierarchy, and two π0decay photons emanating from the primary interaction vertex have been reconstructed (black and red) and added to the reconstructed hierarchy as child particles. Alongside the 3D reconstructed output, this figure also shows the 2D hits that form the reconstructed particles in the u,vand wviews. 4 Simulated and experimental data Each event in simulation and data corresponds to one 3ms readout window of the detector, where the readout was initiatedby thetriggered test-beamparticle.In addition,a number ofbackgroundparticlesofbothcosmic-rayandtest-beamorigin also traverse the detector, as shown in Fig. 2. Unless otherwise specified, the simulated events include a data-driven simulation of the space charge effect. 123 618 Page 16 of 25 Eur. Phys. J. C (2023) 83:618 Fig. 11 The reconstruction output for a candidate 1GeV/cπ+charge exchange event from ProtoDUNE-SP data run 5387. The left image shows the 3D reconstruction output, highlighting the reconstructed particle hierarchy identified as the test-beam particle interaction: the reconstructed beam π+in purple comes from the left before interacting to produce two visible reconstructed π0decay photons in red and black. The figures on the right show, from top to bottom, the u,vand wview hits respectively for the fully reconstructed event with the beam particle interaction highlighted by the dashed black box Thetest-beamparticlegenerationusesaGEANT4simulation of the beamline [13,14]. The triggered test-beam particle is placed into the event with t0=ttrigger =0 and other beam interactionsareoverlaidatrandomtimes,assumingauniform distribution, to give background beam interactions spanning the entire 3ms detector readout window. Cosmic rays are simulated using CORSIKA v7.4 [24] and are generated over a 6ms time range (centred on the trigger time) in order to completely cover the entire 3ms detector readout window. The simulation of particle propagation and interaction in the ProtoDUNE-SP detector is also performed by GEANT4, and the detector response simulation was performed using LArSoft v08_27_01 [12]. The Pandora pattern recognition was performed using LArPandoraContent version v03_15_02, which in turn depends on version v03_03_02 of the Pandora SDK. The experimental test-beam data samples considered in this article were collected from August 2018 to December 2018. Due to time constraints, test-beam data were collected only in the positive polarity mode at five different particle momentum settings: 1, 2, 3, 6 and 7GeV/c. For this reason, only simulated interactions at these same five momentum settings are shown in this article. Both data and simulation events go through signal processing and hit finding stages, as described in Ref. [4]. The events are input into Pandora after the reconstruction of hits 123 Eur. Phys. J. C (2023) 83:618 Page 17 of 25 618 from the signals identified on the detector readout wires. The average time taken to reconstruct a full ProtoDUNE-SP event with Pandora using the LArSoft framework is approximately 40s on an Intel Core Processor (Broadwell) 2.3GHz CPU while using an average of 2.8GB of memory. 5 Cosmic ray reconstruction performance The performance of the event reconstruction is first evaluated using the simulation and then compared to the experimental data. The method presented here to evaluate the performance of ProtoDUNE-SP event reconstruction for simulated interactions involves matching Monte-Carlo (MC) particles with reconstructed particles based on the number of shared hits, which are those hits common to the reconstructed and true particles. Selection criteria are applied to ensure that the MC particles are “reconstructable” and can be included in the performance metrics. The MC particles must produce at least 15 hits in the detector, with at least five hits in at least two of the three readout views. Furthermore, MC particle hits produced by non-primary neutrons, and photons produced by track-like primaries, that deposit energy a long way from the primary particle are not considered. Matches are made by finding the match involving the largest number of shared hits between the reconstructed and MC particle. Once matched, the reconstructed and MC particles are declared unavailable for further matches. This process is then repeated for all remaining particles in the event. At this stage all reconstructed and MC particles have at most one match. Any remaining reconstructed particles that have no match are associated to the MC particle (that by definition must already have a single match) with which they share the most hits, irrespective of the number of matches the MC particle already has. Once the reconstructed particles have been matched to the MC particles, the following metrics can be defined for each matched pair: –Efficiency: The fraction of MC particles that are matched to at least one reconstructed particle. The Clopper– Pearson method [25] is used to calculate the confidence intervalonefficiencymeasurementspresentedinthisarticle. –Purity: The fraction of hits in the reconstructed particle that are shared with the MC particle. –Completeness: The fraction of hits in the MC particle that are shared with the reconstructed particle. Whenreportingthereconstructionefficiency,onlymatches with at least 50% purity and 10% completeness are consideredtoensurethatthereconstructedparticleispredominantly associated with a single MC particle, and that the match is not ofverylowquality.Thesecuts are notappliedwhen reporting the completeness and purity of matches. 5.1 Reconstruction performance for simulated interactions The left panel of Fig.12 shows the reconstruction efficiency forcosmic-ray muons asa function ofthetotal number oftrue hits produced by the particle in the detector (including hits from delta-ray showers and Michel electrons). The overall integrated reconstruction efficiency for cosmic-ray muons is 95.73 ±0.03%. The reconstruction efficiency increases as a function of the number of hits, rising from 50% for 15 hits up to 99% for particles producing more than 400 hits. The reconstruction inefficiency for particles producing fewer hits is due to cosmic-ray muons being absorbed into larger neighbouring particles. This is more common for cosmicray muons producing a small number of hits, but it is also possible for long cosmic-ray muon track if the surrounding topology is sufficiently complex. The completeness and purity of the reconstructed cosmicray muons are shown in right panel of Fig. 12, both of which have very clear peaks at one. These figures show that 97.6% of reconstructed cosmic-ray muons have a purity greater than 80% and 81.9% of reconstructed cosmic-ray muons have a completeness greater than 80%. The tail on the low side of the completeness distribution is caused by the reconstruction splitting up a cosmic-ray muon track into two distinct particles. Approximately 8% of the cosmic-ray muons are matched to two reconstructed particles, meaning that the reconstruction failed to reconstruct the particle as a single object. This can happen for a number of reasons, including failing to stitch the tracks at the drift volume boundaries, crossing cosmic-ray topologies and large delta-ray showers overlappingwithwiththemuontracks.Thepurityistypically close to 100%, which indicates merging distinct cosmic-ray muons together is unlikely. It is possible to identify the time, t0, that a cosmic-ray muon enters the LArTPC if the reconstructed particle was stitched between drift volumes by the process discussed in Sect. 3.1. The distribution of the t0residual, the difference between the reconstructed and true value of t0, for stitched cosmic-ray muons is shown in Fig. 13. The dashed black histogram shows the case where no space charge distortion was applied to the simulation and the distribution is centred on zero, as expected. Once space charge is included (the solid black distribution), a number of features become apparent when considering the cathode- (blue) and APA-stitched (red) components separately. The APA-stitched distribution remains centred on zero because the charge deposited close to the APA travels only a short distance and is unaffected by space charge distortions. Conversely, charges drifting from thecathodeare maximallyaffectedsincetheytraveltheentire 123 618 Page 18 of 25 Eur. Phys. J. C (2023) 83:618 2 10 3 10 4 10 Number of Hits 0.0 0.5 1.0 Cosmic Ray Reconstruction Efficiency SimulationDUNE:ProtoDUNE-SP 0.0 0.2 0.4 0.6 0.8 1.0 Completeness or Purity 5 − 10 4 − 10 3 − 10 2− 10 1 − 10 1 Fraction of Entries Completeness Purity SimulationDUNE:ProtoDUNE-SP Fig. 12 Left: the reconstruction efficiency for simulated cosmic-ray muons as a function of the true number of hits (summed over the three readout views) produced by the cosmic-ray muon. Right: the completeness and purity of the reconstructed cosmic-ray muons shown on a log scale Fig. 13 The difference between the reconstructed and true t0for simulated cosmic-ray muons that have been stitched at either the CPA or APA with (solid black) or without (dashed black) space charge distortions. The black distribution is shown divided into the CPA- (blue) and APA-stitched (red) components. A time difference of 20µs corresponds to shift of about 3cm in the drift direction drift distance, resulting in a distribution that is shifted by a few microseconds. Figure5shows the effect of space charge on a reconstructed cathode-stitched cosmic-ray muon compared to the true trajectory. The bowing effect results in an overestimationoftheshiftinthedrift direction, and hence the reconstructed t0. Measurements of the SCE presented in Ref. [4]helptoexplaintwofurtherfeaturesofthedistribution.The magnitude of the SCE varies across the LArTPC resulting in a broadening of the t0residual distribution. Finally, the asymmetric nature of the space charge distortions at the cathode causes a double-peak structure for cathode-stitched tracks, depending on whether the particle crossed the cathode from positive to negative xor vice versa. In order to give context to the topologies that the reconstruction is faced with at ProtoDUNE-SP, an estimate of the number of cosmic-ray muons passing through the detector per event in simulation has been made. The number of reconstructed cosmic-ray muons matched to distinct cosmic-ray muon MC particles, i.e. that deposit more than 100 hits in the detector, is shown as a function of the total number of distinct cosmic-ray muons on a per-event basis in Fig. 14. The distribution shows a strong linear correlation, but the gradient is approximately 1.08, corresponding to the aforementioned 8% of cosmic rays that were reconstructed as two particles. However, it demonstrates that on average the cosmic-ray muons are well reconstructed. The mean number of distinct cosmic-ray muons per event is 52, while the mean number of matched reconstructed particles is 56, with negligible uncertainties. 5.2 Reconstruction performance for cosmic-ray data Reconstruction metrics for cosmic-ray muon data have also been evaluated. Figure15 shows the number of reconstructed particles tagged as distinct cosmic-ray muons per event in ProtoDUNE-SP. For a cosmic-ray muon to be tagged as distinct it must deposit at least 100 hits in the detector. This cut is applied in order to define a substantial, distinct signal in the detector. Furthermore, applying this cut yields a minimum reconstruction efficiency of 90%, based on the simulated efficiencies in Fig. 12, which ensures this metric gives an accurate reflection of the true number of distinct cosmic-ray muons entering ProtoDUNE-SP. Approximately 5% fewer cosmic-ray muons are reconstructed per event in data than simulation, with the data distribution peaking at 51.8±0.1 and the simulated distribution peaking at 54.9±0.1. This could be due to an overestimation of the cosmic ray flux in the simulation. Preliminary studies show that additional geometric selection criteria significantly improve the agreement 123 Eur. Phys. J. C (2023) 83:618 Page 19 of 25 618 Fig. 14 The number of reconstructed cosmic-ray muons as a function of the number of true cosmic-ray muons on a per-event basis. The cosmic-ray muons were required to produce at least 100 hits in the detector Fig. 15 The number of reconstructed distinct cosmic-ray muon particles per event for data (black) and simulation (red). The cosmic-ray muons were required to produce at least 100 hits in the detector in the mean number of reconstructed particles between data and simulation. The distribution of the reconstructed t0values for cathode crossing and anode crossing cosmic-ray muons is shown in Fig. 16. The range of this distribution can be predicted by considering the readout time window (−250µs to 2750µs) and the time for charge to drift from the cathode to the APAs (2250µs). The cathode-crossing cosmic-ray muons have t0 values in the range −2500µs to 500µs: the lower value is the start of the readout window minus the drift time, and the upper value is the end of the readout window minus the drift time. For APA-crossing cosmic rays, the t0values fall only within the readout window. Thus, the total distribution spans the range −2500 µs<t0<2750 µs. Good agreement is Fig. 16 The reconstructed t0distribution in ProtoDUNE-SP for cathode crossing and anode crossing cosmic-ray muons obtained from the Pandora stitching process in data and simulation. The distributions have been area normalised for comparison seen between data and simulation and the distributions fall within the expected time window predicted above. 6 Test-beam reconstruction performance The reconstruction and identification of the triggered testbeam particle is a key part of the hadron cross-section analyses at ProtoDUNE-SP. This section evaluates the performance on simulation and experimental data. 6.1 Reconstruction performance for simulated interactions The reconstruction of the triggered test-beam particle end point is of particular interest for cross-section analyses because it is critical to know where the particle either interacted or stopped [26,27]. The differences between the reconstructed and true values for the end position coordinates of these particles are shown in Fig. 17 for 1GeV protons and positively charged pions. The end point was corrected for SCE distortions using the procedure described in Ref. [4] andtheresultingdistributions arenarrow andcentredonzero, indicating good resolution and low bias. The right distribution shows the difference between the reconstructed and true positions in 3D, where 68% of the beam particle end points are reconstructed within 2cm of the true value. Theefficiencytofully reconstruct triggeredtest-beam particles and to correctly identify them as of beam origin has been studied. In addition to the full simulation (including the triggered test-beam particle, beam-halo particles and cosmic rays), two additional simulated samples were used to understand the potential loss of efficiency due to background particles. The cosmics removed sample has the cosmic rays removed from the event and hence consists only of the trig123 618 Page 20 of 25 Eur. Phys. J. C (2023) 83:618 Fig. 17 Left: the difference between the reconstructed and true end position of 1GeV/cprimary proton and charged pion test-beam particles shown for the x(black), y(blue) and z(red) coordinates. Right: the three dimensional distance between the reconstructed and true end points gered test-beam particle and any beam-halo particles, and the cosmics and halo removed sample further removes the beam-halo particles from the event, meaning only the triggered test-beam particle remains. Figure 18 shows six distributions that visualise the reconstruction performance for the standard simulation (black), the cosmics removed sample (red), and the cosmics and halo removed sample (cyan). Each column shows, from top to bottom: the triggered test-beam particle reconstruction and identification efficiency, meaning that the particle was well reconstructed and correctly identified as being the triggered test-beam particle; and the completeness and purity of the triggered test-beam particle and subsequent hierarchy. The left column is for 1GeV/cπ+interactions and the right column shows 1GeV/ce +events. The top figures show the reconstruction and identification efficiencyforthetriggeredtest-beamparticlesasafunctionof the number of 2D hits they produce in the detector (including hits produced by their interaction and decay products). The efficiencies for the full simulation both increase as a function of the number of hits and eventually plateau at ∼90% for charged pions and ∼95% for positrons. Removing cosmicray muons from the simulation significantly increases the efficiency over the whole range of the number of hits. At 1GeV/cthere are few beam halo particles, so only a small efficiency increase is seen after the sequential removal of the beam halo. As expected, the efficiency is approximately 100% after the removal of all background particles, demonstrating that the performance on the full simulation is limited by the physics of the interactions and complex overlapping topologies. Similar behaviour is seen for the other beam particle types and the different momentum setting values. The average reconstruction and identification efficiency of the full simulation sample, for all particle types and beam momentum settings, is given in Table 1and shown graphically in Fig. 19. There are more beam halo particles in the 6 and 7GeV/cbeam samples, which reduce the efficiency for charged pions and protons because they can be hidden within a beam halo positron shower. The efficiency remains high for high-energy positrons since they produce very large electromagnetic showers. The middle and bottom rows of Fig. 18 show the completeness and purity of the reconstructed test-beam particle hierarchy, respectively. The four distributions are peaked at, or close to, one, indicating that the triggered test-beam particle is being reconstructed as a single, complete particle. Removing the cosmic-raymuons significantly improves both completeness and purity of the test-beam particle reconstruction. This improvement is expected as there are fewer hits to contaminate the reconstructed beam slice, or to incorrectly split the reconstructed beam particle in the slicing algorithm. Removing both cosmic-ray muons and beam halo particles enforces a purity of 100% as all possible sources of contamination have been removed, and there is a small increase in the completeness. The effect of removing the cosmic rays is larger, which is to be expected as there are significantly more cosmic rays than beam halo particles, such that the slicing algorithm, a source of incomplete triggered test-beam particles, is less active for events where cosmic-ray muons have been removed irrespective of the presence of the secondorder beam halo effect. 6.2 Reconstruction performance for test-beam data In order to compare the triggered test-beam particle reconstruction and identification efficiency between data and MC, a less strict definition of efficiently reconstructed test-beam particles is used in comparison to the one described in 123 Eur. Phys. J. C (2023) 83:618 Page 21 of 25 618 Fig. 18 Primary beam particle reconstruction and identification efficiency (top row) and the reconstructed particle completeness (middle row) and purity (bottom row) for 1GeV/cπ+(left column) and 1GeV/c e+(right column) beam. The black distributions show the performance for the full ProtoDUNE-SP simulation, and the red and cyan curves show events with no cosmic rays, and no cosmic rays and no beam halo, respectively. In a number of places the red distribution is exactly covered by the cyan points 123 618 Page 22 of 25 Eur. Phys. J. C (2023) 83:618 Table 1 The reconstruction and identification efficiency for the triggered test-beam particle in ProtoDUNE-SP simulation for positrons, charged pions, protons and charged kaons for different beam momenta. Charged kaons are negligible in number from 1 to 3GeV/c. The simulatedevents include the triggered test-beam particle, beam haloparticles and numerous cosmic rays Momentum Reconstruction efficiency (%) (GeV/c) Positrons e+Pions π+Protons (p)Kaons K+Muons μ+ 1 88.0+0.2 −0.286.1+0.6 −0.684.1+0.6 −0.6– 88.6+2.1 −2.5 2 89.9+1.2 −1.387.3+1.3 −1.586.8+1.9 −2.1– 100.0+0.0 −9.2 3 90.5+1.1 −1.287.5+0.5 −0.586.1+1.1 −1.2– 94.0+2.2 −3.1 6 90.9+0.9 −1.078.8+0.6 −0.678.9+1.8 −1.980.7+2.5 −2.795.4+2.2 −3.5 7 92.1+1.0 −1.175.3+0.9 −1.073.8+2.6 −2.878.3+3.4 −3.885.7+5.5 −7.6 Sect.6.1. The following selection is used to obtain the sample of events that are highly likely to contain a beam particle, and hence form the denominator for the efficiency calculation. Data: 1. The beam trigger is active. 2. A single track is reconstructed in the beam monitors immediately upstream of ProtoDUNE-SP. 3. The high-voltage applied to the cathode is stable at − 180kV. 4. The readout electronics on the beam-side of the detector are active. 5. There are at least 10 3D hits in the region where the beam particle enters the detector. These 3D hits are produced as part of the disambiguation procedure described in Sect. 3, not within the Pandora software. Simulation: 1. There is a triggered test-beam particle in the MC particle hierarchy 2. There are at least 10 3D hits in the region where the beam particle enters the detector. The efficiency is then defined as the fraction of the selected events with a reconstructed beam particle hierarchy. Therearesomelimitationsintheabilityofthebeaminstrumentation alone to give the unambiguous particle identification required to calculate the denominator of the reconstructionandidentificationefficiency.Pionsandantimuonsarenot distinguished, and since triggered test-beam charged pions can decay in the beamline to antimuons, they are included as a joint sample. For the 6 and 7GeV/csamples, positrons, charged pions and antimuons can not be distinguished, and are hence not included in the comparisons.5A summary of the momentum settings used for data and MC comparisons is as follows: π+/μ+from1to3GeV/c,e+from 1 to 3GeV/c, pfrom 1 to 7GeV/c, and K+for 6 and 7GeV/c. 5Physics analysis is possible as positrons are reconstructed as showers and can be easily selected. However, calculation of the absolute efficiency in data is not possible. Fig. 19 The beam particle identification efficiency for the test-beam particle in ProtoDUNE-SP simulation for different beam momenta. No data were collected at 4GeV/cor 5GeV/c, so no entries are shown for these momenta Two additional simulation samples were produced to investigate the effect of potential systematic uncertainties. 1. The SCE-off sample does not have a simulation of the space charge effect. It gives an estimate of potential efficiency mismodelling due to differences in the SCE between data and MC. Since a sample with increased SCE was not available, the efficiency difference from using the SCE-off sample was used to produce a symmetric band around the standard simulation efficiency values. 2. A sample with the beam halo component reduced by 15%. This sample was motivated by Ref. [14] that shows that the MC overestimates the beam trigger rate, and hence the event pileup. The difference between the efficiency measured from the standard simulation and this sample was taken as a symmetric systematic uncertainty centred on the standard simulation efficiency. 123 Eur. Phys. J. C (2023) 83:618 Page 23 of 25 618 Fig. 20 The triggered test-beam particle reconstruction efficiency for ProtoDUNE-SP as a function of the beam momentum in data and simulation, for charged pions and antimuons (top left), positrons (top right), protons (bottom left) and charged kaons (bottom right). The pale red simulation band shows the total uncertainty and the statistical-only uncertainty is shown in dark red Furthermore, to account for potential differences in the 3D hit finding between data and MC, the selection criterion requiring 10 3D hits in the region where the beam enters the detector was varied for the simulation to 8 and 12 and the change in efficiency was taken as a systematic uncertainty, giving the higher and lower limits on the systematic uncertainty band, respectively. This variation only has a significant effect for the 1GeV/csample because the low energy particles produce fewer hits than those at higher energies. The total systematic uncertainty is calculated as the quadrature sum of the aforementioned individual systematic uncertainties under the assumption of Gaussian uncertainties. Figure 20 shows the reconstruction and identification efficiency for triggered test-beam charged pions, positrons, protons and kaons as a function of the beam momentum setting. The simulation is shown with statistical uncertainties (darker red) and the quadrature sum of statistical and systematic uncertainties (pale red). Agreement is seen between the data and simulation and any discrepancies are within 5%. As expected, the lowest efficiency is seen at 1GeV/cwhere the particles deposit the least energy in the detector. In particular, 1GeV/cprotons are the most difficult to reconstruct since they travel the shortest distance within the detector. Figure 20 also shows that the fraction of events with a reconstructedbeam slice for the pion/muon sample is slightly overestimated in MC compared to data. A number of factors could cause this behaviour. The SCE is underestimated in the simulation [4], which means that the reconstructed beam slices are slightly easier to identify in the simulation. Furthermore, the ratio of muons to pions can differ between data and MC but it is not possible to distinguish these two types of particles due to their similar masses, and a difference in the reconstruction efficiency between pions and muons will induce a data vs MC discrepancy. Finally, in the experimental data, there is a higher probability that beam pion and muon tracks will be broken at the boundary between the first two APAs due to the presence a malfunctioning electron diverter [4] that distorts the electric field, which could cause a small reduction in efficiency. Newer versions of the simulation will account for these three effects. However, small differences in the integrated efficiency between data and MC do not have a big impact for the cross-section analyses because the overall normalisation cancels in the cross-section calculation. 123 618 Page 24 of 25 Eur. Phys. J. C (2023) 83:618 7 Conclusions A summary of Pandora, a pattern-recognition software package, has been presented alongside relevant modifications allowing it to be applied to simulated and experimental data interactions in the ProtoDUNE-SP LArTPC detector. Pandora is the primary event reconstruction used in all ProtoDUNE-SP physics analyses and enables the measurement of hadronic cross sections on liquid argon, the primary physics goal of the experiment. The performance of Pandora has been extensively evaluated for simulated charged test-beam and cosmic-ray interactions in the ProtoDUNESP detector. Several pattern-recognition metrics have been evaluated enabling a comparison of data and simulation. It is not trivial to extrapolate the performance measured in ProtoDUNE-SP due to the much higher detector occupancy compared to the FD, but it will provide a lower bound on the expected performance and the results presented here demonstrate the potential of Pandora to provide accurate and efficient event reconstruction. The efficiency to reconstruct the triggered test-beam particle and correctly identify it as of beam origin exceeds 80% for the majority of particle types (e+,π+,p,K+,μ+) and momentum setting combinations (1, 2, 3, 6 and 7GeV/c). It was also shown that the main cause of these inefficienciesarises from background contamination from bothcosmic and beam-halo sources. In background-removed simulation samples the triggered test-beam particle reconstruction and identification efficiency above a few hundred hits is almost 100% in all cases. A comparison of data and MC shows agreement within 5% for the reconstruction and identification efficiency for different triggered beam-particle species across the beam momentum values, and possible sources for the small observed efficiency differences were discussed. Over the coming years, developments to the patternrecognition are expected from the introduction of new algorithms and the incorporation of deep-learning techniques to drive some key decisions within the Pandora multi-algorithm approach. Examples include improved vertex finding, event slicing and hit classification. Whilst many of these new algorithms are being developed for the DUNE FD, they will be tested on the ProtoDUNE-SP simulation and data. ProtoDUNE-SP has been dismantled but a very similar upgraded detector called ProtoDUNE-HD is under construction in the same cryostat, which is due to commence data taking in 2023. Acknowledgements The ProtoDUNE-SP detector was constructed and operated on the CERN Neutrino Platform. We gratefully acknowledge the support of the CERN management, and the CERN EP, BE, TE, EN and IT Departments for NP04/ProtoDUNE-SP. This document was prepared by the DUNE collaboration using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. 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. This work was supported by CNPq, FAPERJ, FAPEG and FAPESP, Brazil; CFI, IPP and NSERC, Canada; CERN; MŠMT, Czech Republic; ERDF, H2020-EU and MSCA, European Union; CNRS/IN2P3 and CEA, France; INFN, Italy; FCT, Portugal; NRF, South Korea; CAM, Fundación “La Caixa”, Junta de Andalucía-FEDER, MICINN, and Xunta de Galicia, Spain; SERI and SNSF, Switzerland; TÜB˙ ITAK, Turkey; The Royal Society and UKRI/STFC, United Kingdom; DOE and NSF, United States of America. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC0205CH11231. Data Availability Statement This manuscript has no associated data orthedata will notbedeposited. [Authors’ comment:ThePandoraevent reconstruction described in this paper operates on low-level data and does not directly produce physics results, hence there is no associated data release.] Open Access This article is licensed under a Creative Commons Attribution 4.0InternationalLicense,whichpermitsuse, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecomm ons.org/licenses/by/4.0/. Funded by SCOAP3.SCOAP 3supports the goals of the International Year of Basic Sciences for Sustainable Development. References 1. A. Abed Abud et al. Design, construction and operation of the ProtoDUNE-SP LiquidArgonTPC. JINST 17(01), P01005 (2022). https://doi.org/10.1088/1748-0221/17/01/p01005 2. B. Abi et al. Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report, Volume I Introduction to DUNE. JINST 15(08), T08008 (2020). https://doi.org/10.1088/ 1748-0221/15/08/T08008 3. 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