Eur. Phys. J. C (2020) 80:978 https://doi.org/10.1140/epjc/s10052-020-08456-z Regular Article - Experimental Physics Long-baseline neutrino oscillation physics potential of the DUNE experiment DUNE Collaboration B. Abi141, R. Acciarri61, M. A. Acero8, G. Adamov65, D. Adams17, M. Adinolfi16, Z. Ahmad180, J. Ahmed183, T. Alion169, S. Alonso Monsalve21, C. Alt53, J. Anderson4, C. Andreopoulos158,118, M. P. Andrews61, F. Andrianala2, S. Andringa113,114, A. Ankowski159, M. Antonova77, S. Antusch10, A. Aranda-Fernandez39, A. Ariga11, L. O. Arnold42, M. A. Arroyave52, J. Asaadi173, A. Aurisano37, V. Aushev112, D. Autiero89, F. Azfar141, H. Back142, J. J. Back183, C. Backhouse178, P. Baesso16, L. Bagby61, R. Bajou144, S. Balasubramanian187, P. Baldi26, B. Bambah75, F. Barao91,113,114, G. Barenboim77, G. J. Barker183, W. Barkhouse135, C. Barnes125, G. Barr141, J. Barranco Monarca70, N. Barros55,113,114, J. L. Barrow61,171, A. Bashyal140, V. Basque123, F. Bay134, J. L. Bazo Alba151, J. F. Beacom139, E. Bechetoille89, B. Behera41, L. Bellantoni61, G. Bellettini149, V. Bellini33,79, O. Beltramello21, D. Belver22, N. Benekos21, F. Bento Neves113,114, J. Berger150, S. Berkman61, P. Bernardini81,161, R. M. Berner11, H. Berns25, S. Bertolucci14,78, M. Betancourt61, Y. Bezawada25, M. Bhattacharjee95, B. Bhuyan95, S. Biagi87, J. Bian26, M. Biassoni82, K. Biery61, B. Bilki12,99, M. Bishai17, A. Bitadze123, A. Blake116, B. Blanco Siffert60, F. D. M. Blaszczyk61, G. C. Blazey136, E. Blucher35, J. Boissevain119, S. Bolognesi20, T. Bolton109, M. Bonesini82,127, M. Bongrand115, F. Bonini17, A. Booth169, C. Booth163, S. Bordoni21, A. Borkum169, T. Boschi51, N. Bostan99, P. Bour44, S. B. Boyd183, D. Boyden136, J. Bracinik13, D. Braga61, D. Brailsford116, A. Brandt173, J. Bremer21, C. Brew158, E. Brianne123, S. J. Brice61, C. Brizzolari82,127, C. Bromberg126, G. Brooijmans42, J. Brooke16, A. Bross61, G. Brunetti85, N. Buchanan41, H. Budd155, D. Caiulo89, P. Calafiura117, J. Calcutt126, M. Calin18, S. Calvez41, E. Calvo22, L. Camilleri42, A. Caminata80, M. Campanelli178, D. Caratelli61, G. Carini17, B. Carlus89, P. Carniti82, I. Caro Terrazas41, H. Carranza173, A. Castillo162, C. Castromonte98, C. Cattadori82, F. Cavalier115, F. Cavanna61, S. Centro143, G. Cerati61, A. Cervelli78, A. Cervera Villanueva77, M. Chalifour21, C. Chang28, E. Chardonnet144, A. Chatterjee150, S. Chattopadhyay180, J. Chaves146, H. Chen17, M. Chen26, Y. Chen11, D. Cherdack74, C. Chi42, S. Childress61, A. Chiriacescu18, K. Cho107, S. Choubey71, A. Christensen41, D. Christian61, G. Christodoulou21, E. Church142, P. Clarke54, T. E. Coan167, A. G. Cocco84, J. A. B. Coelho115, E. Conley50, J. M. Conrad124, M. Convery159, L. Corwin164, P. Cotte20, L. Cremaldi131, L. Cremonesi178, J. I. Crespo-Anadón22, E. Cristaldo6, R. Cross116, C. Cuesta22, Y. Cui28, D. Cussans16, M. Dabrowski17, H. da Motta19, L. Da Silva Peres60, C. David61,189, Q. David89, G. S. Davies131, S. Davini80, J. Dawson144, K. De173, R. M. De Almeida63, P. Debbins99, I. De Bonis47, M. P. Decowski134,1, A. de Gouvêa137, P. C. De Holanda32, I. L. De Icaza Astiz169, A. Deisting156, P. De Jong134,1, A. Delbart20, D. Delepine70, M. Delgado3, A. Dell’Acqua21, P. De Lurgio4, J. R. T. de Mello Neto60, D. M. DeMuth179, S. Dennis31, C. Densham158, G. Deptuch61, A. De Roeck21, V. De Romeri77, J. J. De Vries31, R. Dharmapalan73, M. Dias177, F. Diaz151, J. S. Díaz97, S. Di Domizio64,80, L. Di Giulio21, P. Ding61, L. Di Noto64,80, C. Distefano87, R. Diurba130, M. Diwan17, Z. Djurcic4, N. Dokania168, M. J. Dolinski49, L. Domine159, D. Douglas126, F. Drielsma159, D. Duchesneau47, K. Duffy61, P. Dunne94, T. Durkin158, H. Duyang166, O. Dvornikov73, D. A. Dwyer117, A. S. Dyshkant136, M. Eads136, D. Edmunds126, J. Eisch100, S. Emery20, A. Ereditato11, C. O. Escobar61, L. Escudero Sanchez31, J. J. Evans123, E. Ewart97, A. C. Ezeribe163, K. Fahey61, A. Falcone82,127, C. Farnese143, Y. Farzan90, J. Felix70, E. Fernandez-Martinez122, P. Fernandez Menendez77, F. Ferraro64,80, L. Fields61, A. Filkins185, F. Filthaut134,154, R. S. Fitzpatrick125, W. Flanagan46, B. Fleming187, R. Flight155, J. Fowler50, W. Fox97, J. Franc44, K. Francis136, D. Franco187, J. Freeman61, J. Freestone123, J. Fried17, A. Friedland159, S. Fuess61, I. Furic62, A. P. Furmanski130, A. Gago151, H. Gallagher176, A. Gallego-Ros22, N. Gallice83,128, V. Galymov89, E. Gamberini21, T. Gamble163, R. Gandhi71, R. Gandrajula126, S. Gao17, D. Garcia-Gamez68, M. Á. García-Peris77, S. Gardiner61, D. Gastler15, G. Ge42, B. Gelli32, A. Gendotti53, S. Gent165, Z. Ghorbani-Moghaddam80, D. Gibin143, I. Gil-Botella22, C. Girerd89, A. K. Giri96, D. Gnani117, O. Gogota112, M. Gold132, S. Gollapinni119, K. Gollwitzer61, R. A. Gomes57, L. V. Gomez Bermeo162, L. S. Gomez Fajardo162, F. Gonnella13, J. A. Gonzalez-Cuevas6, M. C. Goodman4, O. Goodwin123, S. Goswami148, C. Gotti82, E. Goudzovski13, C. Grace117, M. Graham159, E. 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Zwaska61 1 University of Amsterdam, 1098 XG Amsterdam, The Netherlands 2 University of Antananarivo, Antananarivo 101, Antananarivo, Madagascar 3 Universidad Antonio Nariño, Bogotá, Colombia 4 Argonne National Laboratory, Argonne, IL 60439, USA 5 University of Arizona, Tucson, AZ 85721, USA 6 Universidad Nacional de Asunción, San Lorenzo, Paraguay 7 University of Athens, Zografou, GR 157 84, Greece 8 Universidad del Atlántico, Atlántico, Colombia 9 Banaras Hindu University, Varanasi 221 005, India 10 University of Basel, 4056 Basel, Switzerland 11 University of Bern, 3012 Bern, Switzerland 12 Beykent University, Istanbul, Turkey 13 University of Birmingham, Birmingham B15 2TT, UK 14 Università del Bologna, 40127 Bologna, Italy 15 Boston University, Boston, MA 02215, USA 16 University of Bristol, Bristol BS8 1TL, UK 17 Brookhaven National Laboratory, Upton, NY 11973, USA 18 University of Bucharest, Bucharest, Romania 19 Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ 22290-180, Brazil 123 978 Page 4 of 34 Eur. Phys. J. C (2020) 80 :978 20 CEA/Saclay IRFU Institut de Recherche sur les Lois Fondamentales de l’Univers, 91191 Gif-sur-Yvette CEDEX, France 21 CERN, The European Organization for Nuclear Research, 1211 Meyrin, Switzerland 22 CIEMAT, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, 28040 Madrid, Spain 23 Central University of South Bihar, Gaya 824236, India 24 University of California Berkeley, Berkeley, CA 94720, USA 25 University of California Davis, Davis, CA 95616, USA 26 University of California Irvine, Irvine, CA 92697, USA 27 University of California Los Angeles, Los Angeles, CA 90095, USA 28 University of California Riverside, Riverside, CA 92521, USA 29 University of California Santa Barbara, Santa Barbara, California 93106, USA 30 California Institute of Technology, Pasadena, CA 91125, USA 31 University of Cambridge, Cambridge CB3 0HE, UK 32 Universidade Estadual de Campinas, Campinas, SP 13083-970, Brazil 33 Università di Catania, 2 - 95131 Catania, Italy 34 Institute of Particle and Nuclear Physics of the Faculty of Mathematics and Physics of the Charles University, 180 00 Prague 8, Czech Republic 35 University of Chicago, Chicago, IL 60637, USA 36 Chung-Ang University, Seoul 06974, South Korea 37 University of Cincinnati, Cincinnati, OH 45221, USA 38 Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (Cinvestav), Mexico City, Mexico 39 Universidad de Colima, Colima, Mexico 40 University of Colorado Boulder, Boulder, CO 80309, USA 41 Colorado State University, Fort Collins, CO 80523, USA 42 Columbia University, New York, NY 10027, USA 43 Institute of Physics, Czech Academy of Sciences, 182 00 Prague 8, Czech Republic 44 Czech Technical University, 115 19 Prague 1, Czech Republic 45 Dakota State University, Madison, SD 57042, USA 46 University of Dallas, Irving, TX 75062-4736, USA 47 Laboratoire d’Annecy-le-Vieux de Physique des Particules, CNRS/IN2P3 and Université Savoie Mont Blanc, 74941 Annecy-le-Vieux, France 48 Daresbury Laboratory, Cheshire WA4 4AD, UK 49 Drexel University, Philadelphia, PA 19104, USA 50 Duke University, Durham, NC 27708, USA 51 Durham University, Durham DH1 3LE, UK 52 Universidad EIA, Antioquia, Colombia 53 ETH Zurich, Zurich, Switzerland 54 University of Edinburgh, Edinburgh EH8 9YL, UK 55 Faculdade de Ciências da Universidade de Lisboa - FCUL, 1749-016 Lisboa, Portugal 56 Universidade Federal de Alfenas, Poços de Caldas, MG 37715-400, Brazil 57 Universidade Federal de Goias, Goiania, GO 74690-900, Brazil 58 Universidade Federal de São Carlos, Araras, SP 13604-900, Brazil 59 Universidade Federal do ABC, Santo André, SP 09210-580, Brazil 60 Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-901, Brazil 61 Fermi National Accelerator Laboratory, Batavia, IL 60510, USA 62 University of Florida, Gainesville, FL 32611-8440, USA 63 Fluminense Federal University, 9 Icaraí, Niterói, RJ 24220-900, Brazil 64 Università degli Studi di Genova, Genova, Italy 65 Georgian Technical University, Tbilisi, Georgia 66 Gran Sasso Science Institute, L’Aquila, Italy 67 Laboratori Nazionali del Gran Sasso, L’Aquila, AQ, Italy 68 University of Granada & CAFPE, 18002 Granada, Spain 69 University Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France 70 Universidad de Guanajuato, Guanajuato C.P. 37000, Mexico 71 Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India 72 Harvard University, Cambridge, MA 02138, USA 73 University of Hawaii, Honolulu, HI 96822, USA 74 University of Houston, Houston, TX 77204, USA 75 University of Hyderabad, Gachibowli, Hyderabad 500 046, India 76 Institut de Fìsica d’Altes Energies, Barcelona, Spain 77 Instituto de Fisica Corpuscular, 46980, Paterna Valencia, Spain 78 Istituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna, BO, Italy 79 Istituto Nazionale di Fisica Nucleare Sezione di Catania, 95123 Catania, Italy 80 Istituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genova, GE, Italy 81 Istituto Nazionale di Fisica Nucleare Sezione di Lecce, 73100 Lecce, Italy 82 Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3-20126 Milan, Italy 83 Istituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milan, Italy 84 Istituto Nazionale di Fisica Nucleare Sezione di Napoli, 80126 Naples, Italy 123 Eur. Phys. J. C (2020) 80 :978 Page 5 of 34 978 85 Istituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padua, Italy 86 Istituto Nazionale di Fisica Nucleare Sezione di Pavia, 27100 Pavia, Italy 87 Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy 88 Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia 89 Institut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France 90 Institute for Research in Fundamental Sciences, Tehran, Iran 91 Instituto Superior Técnico-IST, Universidade de Lisboa, Lisboa, Portugal 92 Idaho State University, Pocatello ID 83209, USA 93 Illinois Institute of Technology, Chicago, IL 60616, USA 94 Imperial College of Science Technology and Medicine, London SW7 2BZ, UK 95 Indian Institute of Technology Guwahati, Guwahati 781 039, India 96 Indian Institute of Technology Hyderabad, Hyderabad 502285, India 97 Indiana University, Bloomington, IN 47405, USA 98 Universidad Nacional de Ingeniería, Lima 25, Peru 99 University of Iowa, Iowa City, IA 52242, USA 100 Iowa State University, Ames, IA 50011, USA 101 Iwate University, Morioka, Iwate 020-8551, Japan 102 University of Jammu, Jammu 180006, India 103 Jawaharlal Nehru University, New Delhi 110067, India 104 Jeonbuk National University, Jeonrabuk-do 54896, South Korea 105 University of Jyvaskyla, 40014 Jyvaskyla, Finland 106 High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan 107 Korea Institute of Science and Technology Information, Daejeon 34141, South Korea 108 K L University, Vaddeswaram, Andhra Pradesh 522502, India 109 Kansas State University, Manhattan, KS 66506, USA 110 Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan 111 National Institute of Technology, Kure College, Hiroshima 737-8506, Japan 112 Kyiv National University, 01601 Kyiv, Ukraine 113 Laboratório de Instrumentação e Física Experimental de Partículas, 1649-003 Lisboa, Portugal 114 Laboratório de Instrumentação e Física Experimental de Partículas, 3004-516 Coimbra, Portugal 115 Laboratoire de l’Accélérateur Linéaire, 91440 Orsay, France 116 Lancaster University, Lancaster LA1 4YB, UK 117 Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 118 University of Liverpool, L69 7ZE Liverpool, UK 119 Los Alamos National Laboratory, Los Alamos, NM 87545, USA 120 Louisiana State University, Baton Rouge, LA 70803, USA 121 University of Lucknow, Uttar Pradesh 226007, India 122 Madrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain 123 University of Manchester, Manchester M13 9PL, UK 124 Massachusetts Institute of Technology, Cambridge, MA 02139, USA 125 University of Michigan, Ann Arbor, MI 48109, USA 126 Michigan State University, East Lansing, MI 48824, USA 127 Università del Milano-Bicocca, 20126 Milan, Italy 128 Università degli Studi di Milano, 20133 Milan, Italy 129 University of Minnesota Duluth, Duluth, MN 55812, USA 130 University of Minnesota Twin Cities, Minneapolis, MN 55455, USA 131 University of Mississippi, University, MS 38677, USA 132 University of New Mexico, Albuquerque, NM 87131, USA 133 H. Niewodniczan´ski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 134 Nikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, Netherlands 135 University of North Dakota, Grand Forks, ND 58202-8357, USA 136 Northern Illinois University, DeKalb, Illinois 60115, USA 137 Northwestern University, Evanston, Il 60208, USA 138 University of Notre Dame, Notre Dame, IN 46556, USA 139 Ohio State University, Columbus, OH 43210, USA 140 Oregon State University, Corvallis, OR 97331, USA 141 University of Oxford, Oxford OX1 3RH, UK 142 Pacific Northwest National Laboratory, Richland, WA 99352, USA 143 Universtà degli Studi di Padova, 35131 Padua, Italy 144 Université de Paris, CNRS, Astroparticule et Cosmologie, 75006 Paris, France 145 Università degli Studi di Pavia, 27100 Pavia, PV, Italy 146 University of Pennsylvania, Philadelphia, PA 19104, USA 147 Pennsylvania State University, University Park, PA 16802, USA 148 Physical Research Laboratory, Ahmedabad 380 009, India 149 Università di Pisa, 56127 Pisa, Italy 150 University of Pittsburgh, Pittsburgh, PA 15260, USA 123 978 Page 6 of 34 Eur. Phys. J. C (2020) 80 :978 151 Pontificia Universidad Católica del Perú, Lima, Peru 152 University of Puerto Rico, Mayaguez 00681, Puerto Rico, USA 153 Punjab Agricultural University, Ludhiana 141004, India 154 Radboud University, NL-6525, AJ Nijmegen, Netherlands 155 University of Rochester, Rochester, NY 14627, USA 156 Royal Holloway College, London TW20 0EX, UK 157 Rutgers University, Piscataway, NJ 08854, USA 158 STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK 159 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 160 Sanford Underground Research Facility, Lead, SD 57754, USA 161 Università del Salento, 73100 Lecce, Italy 162 Universidad Sergio Arboleda, 11022 Bogotá, Colombia 163 University of Sheffield, Sheffield S3 7RH, UK 164 South Dakota School of Mines and Technology, Rapid City, SD 57701, USA 165 South Dakota State University, Brookings, SD 57007, USA 166 University of South Carolina, Columbia, SC 29208, USA 167 Southern Methodist University, Dallas, TX 75275, USA 168 Stony Brook University, SUNY, Stony Brook, New York 11794, USA 169 University of Sussex, Brighton BN1 9RH, UK 170 Syracuse University, Syracuse, NY 13244, USA 171 University of Tennessee, Knoxville, TN 37996, USA 172 Texas A&M University - Corpus Christi, Corpus Christi, TX 78412, USA 173 University of Texas at Arlington, Arlington, TX 76019, USA 174 University of Texas at Austin, Austin, TX 78712, USA 175 University of Toronto, Toronto, Ontario M5S 1A1, Canada 176 Tufts University, Medford, MA 02155, USA 177 Universidade Federal de São Paulo, 09913-030 São Paulo, Brazil 178 University College London, London WC1E 6BT, UK 179 Valley City State University, Valley City, ND 58072, USA 180 Variable Energy Cyclotron Centre, 700 064 West Bengal, India 181 Virginia Tech, Blacksburg, VA 24060, USA 182 University of Warsaw, 00-927 Warsaw, Poland 183 University of Warwick, Coventry CV4 7AL, UK 184 Wichita State University, Wichita, KS 67260, USA 185 William and Mary, Williamsburg, VA 23187, USA 186 University of Wisconsin Madison, Madison, WI 53706, USA 187 Yale University, New Haven, CT 06520, USA 188 Yerevan Institute for Theoretical Physics and Modeling, Yerevan 0036, Armenia 189 York University, Toronto M3J 1P3, Canada Received: 2 June 2020 / Accepted: 10 September 2020 / Published online: 22 October 2020 © The Author(s) 2020 Abstract The sensitivity of the Deep Underground Neu- trino Experiment (DUNE) to neutrino oscillation is deter- mined, based on a full simulation, reconstruction, and event selection of the far detector and a full simulation and param- eterized analysis of the near detector. Detailed uncertain- ties due to the flux prediction, neutrino interaction model, and detector effects are included. DUNE will resolve the neutrino mass ordering to a precision of 5σ , for all δCP values, after 2 years of running with the nominal detec- tor design and beam configuration. It has the potential to observe charge-parity violation in the neutrino sector to a precision of 3σ (5σ ) after an exposure of 5 (10) years, a e-mail: marshall@lbl.gov b e-mail: callum.wilkinson@lhep.unibe.ch (corresponding author) c e-mail: etw@bnl.gov for 50% of all δCP values. It will also make precise mea- surements of other parameters governing long-baseline neu- trino oscillation, and after an exposure of 15 years will achieve a similar sensitivity to sin2 2θ13 to current reactor experiments. 1 Introduction The Deep Underground Neutrino Experiment (DUNE) is a next-generation, long-baseline neutrino oscillation exper- iment which will carry out a detailed study of neutrino mixing utilizing high-intensity νμ and ν¯μ beams measured over a long baseline. DUNE is designed to make signifi- cant contributions to the completion of the standard three- flavor picture by measuring all the parameters govern- 123 Eur. Phys. J. C (2020) 80 :978 Page 7 of 34 978 ing ν1–ν3 and ν2–ν3 mixing in a single experiment. Its main scientific goals are the definitive determination of the neutrino mass ordering, the definitive observation of charge-parity symmetry violation (CPV) for more than 50% of possible true values of the charge-parity violating phase, δCP, and precise measurement of oscillation parameters, par- ticularly δCP, sin2 2θ13, and the octant of θ23. These mea- surements will help guide theory in understanding if there are new symmetries in the neutrino sector and whether there is a relationship between the generational structure of quarks and leptons [1]. Observation of CPV in neutrinos would be an important step in understanding the origin of the baryon asymmetry of the universe [2,3]. The DUNE experiment will observe neutrinos from a high-power neutrino beam peaked at ∼2.5 GeV but with a broad range of neutrino energies, a near detector (ND) located at Fermi National Accelerator Laboratory, in Batavia, Illinois, USA, and a large liquid argon time-projection chamber (LArTPC) far detector (FD) located at the 4850 ft level of Sanford Underground Research Facility (SURF), in Lead, South Dakota, USA, 1285 km from the neu- trino production point. The neutrino beam provided by Long-Baseline Neutrino Facility (LBNF) [4] is produced using protons from Fermilab’s Main Injector, which are guided onto a graphite target, and a traditional horn-focusing system to select and focus particles produced in the target [5]. The polarity of the focusing magnets can be reversed to produce a beam dominated by either muon neutrinos or muon antineutrinos. A highly capable ND will constrain many systematic uncertainties for the oscillation analysis. The 40-kt (fiducial) FD is composed of four 10 kt (fidu- cial) LArTPC modules [6–8]. The deep underground loca- tion of the FD reduces cosmogenic and atmospheric sources of background, which also provides sensitivity to nucleon decay and low-energy neutrino detection, for example, the possible observation of neutrinos from a core-collapse supernova [5]. The entire complement of neutrino oscillation experi- ments to date has measured five of the neutrino mixing parameters [9–11]: the three mixing angles θ12, θ23, and θ13, and the two squared-mass differences Δm221 and |Δm231|, where Δm2i j = m2i −m2j is the difference between the squares of the neutrino mass states in eV2. The neutrino mass order- ing (i.e., the sign of Δm231) is unknown, though recent results show a weak preference for the normal ordering [12–14]. The value of δCP is not well known, though neutrino oscillation data are beginning to provide some information on its value [12,15]. The oscillation probability of νμ → νe through matter in the standard three-flavor model and a constant density approximation is, to first order [16]: P( ν(–)μ → ν(–)e)  sin2 θ23 sin2 2θ13 sin2(Δ31 − aL) (Δ31 − aL)2 Δ 2 31 + sin 2θ23 sin 2θ13 sin 2θ12 × sin(Δ31 − aL) (Δ31 − aL) Δ31 × sin(aL) (aL) Δ21 cos(Δ31 ± δCP) + cos2 θ23 sin2 2θ12 sin 2(aL) (aL)2 Δ221, (1) where a = ±GF Ne√ 2 ≈ ± 1 3500 km ( ρ 3.0 g/cm3 ) , GF is the Fermi constant, Ne is the number density of elec- trons in the Earth’s crust, Δi j = 1.267Δm2i j L/Eν , L is the baseline in km, and Eν is the neutrino energy in GeV. Both δCP and a terms are positive for νμ → νe and negative for ν¯μ → ν¯e oscillations; i.e., a neutrino-antineutrino asymme- try is introduced both by CPV (δCP) and the matter effect (a). The origin of the matter effect asymmetry is simply the presence of electrons and absence of positrons in the Earth [17,18]. The (anti-)electron neutrino appearance probability is shown in Fig. 1 at the DUNE baseline of 1285 km as a function of neutrino energy for several values of δCP. DUNE has a number of features that give it unique physics reach, complementary to other existing and planned experi- ments [19–21]. Its broad-band beam makes it sensitive to the shape of the oscillation spectrum for a range of neutrino ener- gies. DUNE’s relatively high energy neutrino beam enhances the size of the matter effect and will allow DUNE to mea- sure δCP and the mass ordering simultaneously. The unique LArTPC detector technology will enhance the resolution on DUNE’s measurement of the value of δCP, and along with the increased neutrino energy, gives DUNE a different set of sys- tematic uncertainties to other experiments, making DUNE complementary with them. This paper describes studies that quantify DUNE’s expected sensitivity to long-baseline neutrino oscillation, using the accelerator neutrino beam. Note that atmospheric neutrino samples would provide additional sensitivity to some of the same physics, but are not included in this work. The flux simulation and associated uncertainties are described in Sect. 2. Section 3 describes the neutrino inter- action model and systematic variations. The near and far detector simulation, reconstruction, and event selections are described in Sects. 4 and 5, respectively, with a nominal set of event rate predictions given in Sect. 6. Detector uncer- tainties are described in Sect. 7. The methods used to extract oscillation sensitivities are described in Sect. 8. The primary 123 978 Page 8 of 34 Eur. Phys. J. C (2020) 80 :978 Fig. 1 The appearance probability at a baseline of 1285 km, as a func- tion of neutrino energy, for δCP = −π/2 (blue), 0 (red), and π/2 (green), for neutrinos (top) and antineutrinos (bottom), for normal ordering sensitivity results are presented in Sect. 9. We present our conclusions in Sect. 10. 2 Neutrino beam flux and uncertainties The expected neutrino flux is generated using G4LBNF [5, 22], a Geant4-based [23] simulation of the LBNF neutrino beam. The simulation uses a detailed description of the LBNF optimized beam design [5], which includes a target and horns designed to maximize sensitivity to CPV given the physical constraints on the beamline design. Neutrino fluxes for neutrino-enhanced, forward horn cur- rent (FHC), and antineutrino-enhanced, reverse horn current (RHC), configurations of LBNF are shown in Fig. 2. Uncer- tainties on the neutrino fluxes arise primarily from uncertain- Neutrino energy (GeV) 0 2 4 6 8 10 P O T) 2 1 1 0 × /G eV (1 .1 2 's /m ν 710 810 910 1010 1110 DUNE Simulation μν μν eν eν Neutrino energy (GeV) 0 2 4 6 8 10 P O T) 2 1 1 0 × /G eV (1 .1 2 's /m ν 710 810 910 1010 1110 DUNE Simulation μν μν eν eν Fig. 2 Neutrino fluxes at the FD for neutrino-enhanced, FHC, beam running (top) and antineutrino, RHC, beam running (bottom) ties in hadrons produced off the target and uncertainties in the design parameters of the beamline, such as horn currents and horn and target positioning (commonly called “focusing uncertainties”) [5]. Given current measurements of hadron production and LBNF estimates of alignment tolerances, flux uncertainties are approximately 8% at the first oscillation maximum and 12% at the second. These uncertainties are highly correlated across energy bins and neutrino flavors. The unoscillated fluxes at the ND and FD are similar, but not identical. The relationship is well understood, and flux uncertainties mostly cancel for the ratio of fluxes between the two detectors. Uncertainties on the ratio are dominated by focusing uncertainties and are ∼ 1% or smaller except at the falling edge of the focusing peak (∼4 GeV), where they rise to 2%. The rise is due to the presence of many par- ticles which are not strongly focused by the horns in this energy region, which are particularly sensitive to focusing and alignment uncertainties. The near-to-far flux ratio and uncertainties on this ratio are shown in Fig. 3. Beam-focusing and hadron-production uncertainties on the flux prediction are evaluated by reproducing the full beamline simulation many times with variations of the input model according to those uncertainties. The resultant uncer- 123 Eur. Phys. J. C (2020) 80 :978 Page 9 of 34 978 Fig. 3 Ratio of ND and FD fluxes show for the muon neutrino compo- nent of the FHC flux and the muon antineutrino component of the RHC flux (top) and uncertainties on the FHC muon neutrino ratio (bottom) tainty on the neutrino flux prediction is described through a covariance matrix, where each bin corresponds to an energy range of a particular beam mode and neutrino species, sepa- rated by flux at the ND and FD. The output covariance matrix has 208×208 bins, despite having only ∼30 input uncertain- ties. To reduce the number of parameters used in the fit, the covariance matrix is diagonalized, and each principal com- ponent is treated as an uncorrelated nuisance parameter. The 208 principal components are ordered by the magnitude of their corresponding eigenvalues, which is the variance along the principal component (eigenvector) direction, and only the first ∼30 are large enough that they need to be included. This was validated by including more flux parameters and check- ing that there was no significant change to the sensitivity for a small number of test cases. By the 10th principal component, the eigenvalue is 1% of the largest eigenvalue. As may be expected, the largest uncertainties correspond to the largest principal components as shown in Fig. 4. The largest princi- pal component (component 0) matches the hadron production uncertainty on nucleon-nucleus interactions in a phase space region not covered by data. Components 3 and 7 correspond to the data-constrained uncertainty on proton interactions in the target producing pions and kaons, respectively. Compo- Neutrino energy (GeV) 0 1 2 3 4 5 6 7 8 Fr ac tio na l s hi ft 0 0.02 0.04 0.06 0.08 0.1 0.12 Component 0 N+A unconstrained Component 3 π→pC Component 5 Target density Component 7 K→pC Component 11 Horn current DUNE Simulation Fig. 4 Select flux principal components are compared to specific underlying uncertainties from the hadron production and beam focusing models. Note that while these are shown as positive shifts, the absolute sign is arbitrary nents 5 and 11 correspond to two of the largest focusing uncertainties, the density of the target and the horn current, respectively. Other components not shown either do not fit a single uncertain parameter or may represent two or more degenerate systematics or ones that produce anti-correlations in neighboring energy bins. Future hadron production measurements are expected to improve the quality of, and the resulting constraints on, these flux uncertainty estimates. Approximately 40% of the inter- actions that produce neutrinos in the LBNF beam simula- tion have no direct data constraints. Large uncertainties are assumed for these interactions. The largest unconstrained sources of uncertainty are proton quasielastic interactions and pion and kaon rescattering in beamline materials. The proposed EMPHATIC experiment [24] at Fermilab will be able to constrain quasielastic and low-energy interactions that dominate the lowest neutrino energy bins. The NA61 experi- ment at CERN has taken data that will constrain many higher energy interactions, and also plans to measure hadrons pro- duced on a replica LBNF target, which would provide tight constraints on all interactions occurring in the target. A sim- ilar program at NA61 has reduced flux uncertainties for the T2K experiment from ∼10 to ∼5% [25]. Another proposed experiment, the LBNF spectrometer [26], would measure hadrons after both production and focusing in the horns to further constrain the hadron production uncertainties, and could also be used to experimentally assess the impact of shifted alignment parameters on the focused hadrons (rather than relying solely on simulation). 3 Neutrino interaction model and uncertainties A framework for considering the impact of neutrino inter- action model uncertainties on the oscillation analysis has 123 978 Page 10 of 34 Eur. Phys. J. C (2020) 80 :978 been developed. The default interaction model is imple- mented in v2.12.10 of the GENIE generator [27,28]. Varia- tions in the cross sections are implemented in various ways: using GENIE reweighting parameters (sometimes referred to as “GENIE knobs”); with ad hoc weights of events that are designed to parameterize uncertainties or cross-section corrections currently not implemented within GENIE; or through discrete alternative model comparisons. The lat- ter are achieved through alternative generators, alternative GENIE configurations, or custom weightings, which made extensive use of the NUISANCE package [29] in their devel- opment. The interaction model components and uncertainties can be divided into seven groups: (1) initial state, (2) hard scattering and nuclear modifications to the quasielastic, or one-particle one-hole (1p1h) process, (3) multinucleon, or two-particle two-hole (2p2h), hard scattering processes, (4) hard scattering in pion production processes, (5) higher invariant mass (W ) and neutral current (NC) processes, (6) final-state interactions (FSI), (7) neutrino flavor dependent differences. Uncertainties are intended to reflect current the- oretical freedom, deficiencies in implementation, and/or cur- rent experimental knowledge. The default nuclear model in GENIE describing the initial state of nucleons in the nucleus is the Bodek–Ritchie global Fermi gas model [30]. There are significant deficiencies that are known in global Fermi gas models: these include a lack of consistent incorporation of the high-momentum tails in the nucleon momentum distribution that result from correla- tions among nucleons; the lack of correlation between loca- tion within the nucleus and momentum of the nucleon; and an incorrect relationship between momentum and energy of the off-shell, bound nucleon within the nucleus. They have also been shown to agree poorly with neutrino-nucleus scat- tering data [31]. GENIE modifies the nucleon momentum distribution empirically to account for short-range correla- tion effects, which populates the high-momentum tail above the Fermi cutoff, but the other deficiencies persist. Alterna- tive initial state models, such as spectral functions [32,33], the mean field model of GiBUU [34], or continuum random phase approximation (CRPA) calculations [35] may provide better descriptions of the nuclear initial state [36], but are not considered further here. The primary uncertainties considered in 1p1h interactions (νl + n → l− + p, ν¯l + p → l+ + n) are the axial form factor of the nucleon and the nuclear screening—from the so- called random phase approximation (RPA) calculations—of low momentum transfer reactions. The Valencia group’s [37,38] description of RPA comes from summation of W± self-energy terms. In practice, this modifies the 1p1h (quasielastic) cross section in a non-trivial way, with associ- ated uncertainties presented in Ref. [39], which were evalu- ated as a function of Q2. Here we use T2K’s 2017/8 param- eterization of the Valencia RPA effect [12]. The shape of the correction and error is parameterized with a third-order Bernstein polynomial up to Q2 = 1.2 GeV2 where the form transitions to a decaying exponential. The BeRPA (Bernstein RPA) function has three parameters controlling the behavior at increasing Q2 (A, B and D), a fourth parameter (E) that controls the high-Q2 tail, and a fifth (U), which changes the position at which the behaviour changes from polynomial to exponential. The BeRPA parameterization modifies the cen- tral value of the model prediction, as decribed in Table 3. BeRPA parameters E and U are not varied in the analysis described here, the parameters A and B have a prefit uncer- tainty of 20%, and D has a prefit unertainty of 15%. The axial form factor parameterization we use, a dipole, is known to be inadequate [40]. However, the convolution of BeRPA uncertainties with the limited axial form factor uncertainties do provide more freedom as a function of Q2, and the two effects combined likely provide adequate freedom for the Q2 shape in quasielastic events. BBBA05 vector form factors are used [41]. The 2p2h contribution to the cross section comes from the Valencia model [37,38], the implementation in GENIE is described in Ref. [42]. However, MINERvA [43] and NOvA [44] have shown that this model underpredicts observed event rates on carbon. The extra strength from the “MINERvA tune” to 2p2h is applied as a two-dimensional Gaussian in (q0, q3) space, where q0 is the energy transfer from the lep- tonic system, and q3 is the magnitude of the three momentum transfer) to fit reconstructed MINERvA CC-inclusive data [43]. Reasonable predictions of MINERvA’s data are found by attributing the missing strength to any of 2p2h from np initial state pairs, 2p2h from nn initial state pairs, or 1p1h (quasielastic) processes. The default tune uses an enhance- ment of the np and nn initial strengths in the ratio predicted by the Valencia model, and alternative systematic variation tunes (“MnvTune” 1-3) attribute the missing strength to the individual interaction processes above. We add uncertainties for the energy dependence of this missing strength based on the MINERvA results [43], and assume a generic form for the energy dependence of the cross section using the “A” and “B” terms taken from Ref. [45]. These uncertainties are labeled E2p2h and are separated for neutrinos and antineu- trinos. We add uncertainties on scaling the 2p2h prediction from carbon to argon on electron-scattering measurements of short-range correlated (SRC) pairs taken on multiple targets [46], separately for neutrinos (ArC2p2h ν) and antineutrinos (ArC2p2h ν¯). GENIE uses a modified version of the Rein–Sehgal (R–S) model for pion production [47], including only the 16 res- onances recommended by the Particle Data group [48], and excluding interferences between resonances. The cross sec- tion is cut off at invariant masses, W ≥ 1.7 GeV (2 GeV in the original R-S model). No in-medium modifications to the 123 Eur. Phys. J. C (2020) 80 :978 Page 11 of 34 978 resonances are included, and by default they decay isotropi- cally in their rest frame, although there is a parameter denoted here as “θπ from Δ-decay”, for changing the angular distri- bution of pions produced through Δ resonance decays to match the experimentally observed distributions used in the original R-S paper [47]. Resonance decays to η and γ (plus a nucleon) are included from Ref. [48]. We use a tuning of the GENIE model to reanalyzed neutrino–deuterium bubble chamber data [49,50] as our base model, as noted in Table 3. We note that an improved Rein–Sehgal-like resonance model has been developed [51], and has been implemented in Monte Carlo generators, although is not used as the default model in the present work. The deep inelastic scattering (DIS) model implemented in GENIE uses the Bodek–Yang parametrization [52], using GRV98 parton distribution functions [53]. Hadronization is described by the AKGY model [54], which uses the KNO scaling model [55] for invariant masses W ≤ 2.3 GeV and PYTHIA6 [56] for invariant masses W ≥ 3 GeV, with a smooth transition between the two for intermediate invari- ant masses. A number of variable parameters affecting DIS processes are included in GENIE, as listed in Table 3, and described in Ref. [52]. In GENIE, the DIS model is extrap- olated to all values of invariant mass, and replaces the non- resonant background to pion production in the R-S model. The NOvA experiment [57] developed uncertainties beyond those provided by GENIE to describe their single pion to DIS transition region data. We follow their findings, and implement separate, uncorrelated uncertainties for all perturbations of 1, 2, and ≥ 3 pion final states, CC/NC, neu- trinos/antineutrinos, and interactions on protons/neutrons, with the exception of CC neutrino 1-pion production, where interactions on protons and neutrons are merged, following [50], which modifies the central value of the model predic- tion, as listed in Table 3. This leads to 23 distinct uncertainty channels with a label to denote the process it affects: NR [ν,ν¯] [CC,NC] [n,p] [1π ,2π ,3π ]. Each channel has an uncertainty of 50% for W ≤ 3 GeV, and an uncertainty which drops lin- early above W = 3 GeV until it reaches a flat value of 5% at W = 5 GeV, where external measurements better constrain this process. GENIE includes a large number of final state uncertain- ties on its final state cascade model [58–60], which are sum- marized in Table 2. A recent comparison of the underlying interaction probabilities used by GENIE is compared with other available simulation packages in Ref. [61]. The cross sections include terms proportional to the lep- ton mass, which are significant contributors at low ener- gies where quasielastic processes dominate. Some of the form factors in these terms have significant uncertainties in the nuclear environment. Ref. [62] ascribes the largest pos- sible effect to the presence of poorly constrained second- class current vector form factors in the nuclear environ- ment, and proposes a variation in the cross section ratio of σμ/σe of ±0.01/Max(0.2 GeV, Eν) for neutrinos and ∓0.018/Max(0.2 GeV, Eν) for antineutrinos. Note the anti- correlation of the effect in neutrinos and antineutrinos. This parameter is labeled νe/ν¯e norm. An additional normalization uncertainty (NC norm.) of 20% is applied to all NC events at the ND in this analy- sis to investigate whether the small contamination of NC events which passed the simple selection cuts had an effect on the analysis. Although a similar systematic could have been included (uncorrelated) at the FD, it was not in this analysis. Finally, some electron-neutrino interactions occur at four- momentum transfers where a corresponding muon-neutrino interaction is kinematically forbidden, therefore the nuclear response has not been constrained by muon-neutrino cross- section measurements. This region at lower neutrino energies has a significant overlap with the Bodek–Ritchie tail of the nucleon momentum distribution in the Fermi gas model [30]. There are significant uncertainties in this region, both from the form of the tail itself and from the lack of knowledge about the effect of RPA and 2p2h in this region. Here, a 100% uncertainty is applied in the phase space present for νe but absent for νμ (labeled νe phase space (PS)). The complete set of interaction model uncertainties includes GENIE implemented uncertainties (Tables 1 and 2), and new uncertainties developed for this effort (Table 4) which represent uncertainties beyond those implemented in the GENIE generator. Tunes which are applied to the default model, using the dials described, which represent known deficiencies in GENIE’s description of neutrino data, are listed in Table 3. The way model parameters are treated in the analysis is described by three categories: • Category 1: expected to be constrained with on-axis data; uncertainties are implemented in the same way for ND and FD. • Category 2: implemented in the same way for ND and FD, but on-axis ND data alone is not sufficient to constrain these parameters. They may be constrained by additional ND samples in future analyses, such as off-axis measure- ments. • Category 3: implemented only in the FD. Examples are parameters which only affect νe and νe rates which are small and difficult to precisely isolate from background at the ND. All GENIE uncertainties (original or modified), given in Tables 1 and 2, are all treated as Category 1. Table 4, which describes the uncertainties beyond those available within GENIE, includes a column identifying which of these cate- gories describes the treatment of each additional uncertainty. 123 978 Page 12 of 34 Eur. Phys. J. C (2020) 80 :978 Table 1 Neutrino interaction cross-section systematic parameters con- sidered in GENIE. GENIE default central values and uncertainties are used for all parameters except the CC resonance axial mass. The cen- tral values are the GENIE nominals, and the 1σ uncertainty is as given. Missing GENIE parameters were omitted where uncertainties devel- oped for this analysis significantly overlap with the supplied GENIE freedom, the response calculation was too slow, or the variations were deemed unphysical Description 1σ Quasielastic MQEA , Axial mass for CCQE +0.25−0.15 GeV QE FF, CCQE vector form factor shape N/A pF Fermi surface momentum for Pauli blocking ±30% Low W MRESA , Axial mass for CC resonance ±0.05 GeV MRESV Vector mass for CC resonance ±10% Δ-decay ang., θπ from Δ decay (isotropic → R-S) N/A High W (BY model) AHT, higher-twist in scaling variable ξw ±25% BHT, higher-twist in scaling variable ξw ±25% CV1u, valence GRV98 PDF correction ±30% CV2u, valence GRV98 PDF correction ±40% Other neutral current MNCRESA , Axial mass for NC resonance ±10% MNCRESV , Vector mass for NC resonance ±5% Table 2 The intra-nuclear hadron transport systematic parameters implemented in GENIE with associated uncertainties considered in this work. Note that the ‘mean free path’ parameters are omitted for both N–N and π–N interactions as they produced unphysical variations in observable analysis variables. Table adapted from Ref [28] Description 1σ (%) N. CEX, nucleon charge exchange probability ± 50 N. EL, nucleon elastic reaction probability ± 30 N. INEL, nucleon inelastic reaction probability ± 40 N. ABS, nucleon absorption probability ±20 N. PROD, nucleon π -production probability ± 20 π CEX, π charge exchange probability ± 50 π EL, π elastic reaction probability ± 10 π INEL, π inelastic reaction probability ± 40 π ABS, π absorption probability ± 20 π PROD, π π -production probability ± 20 4 The near detector simulation and reconstruction The ND hall will be located at Fermi National Accelerator Laboratory (Fermilab), 574 m from where the protons hit the beam target, and 60 m underground. The baseline design for the DUNE ND system consists of a LArTPC with a downstream magnetized multi-purpose detector (MPD), and Table 3 Neutrino interaction cross-section systematic parameters that receive a central-value tune and modify the nominal event rate predic- tions Description Value Quasielastic BeRPA A controls low Q2 A : 0.59 B controls low-mid Q2 B : 1.05 D controls mid Q2 D : 1.13 E controls high Q2 fall-off E : 0.88 U controls transition from polynomial to exponential U : 1.20 2p2h q0 , q3 dependent correction to 2p2h events Low W single pion production Axial mass for CC resonance in GENIE 0.94 Normalization of CC1π non-resonant interaction 0.43 Table 4 List of extra interaction model uncertainties in addition to those provided by GENIE, and the category to which they belong in the analysis. Note that in this analysis, the NC norm. systematic is not applied at the FD, as described in the text Uncertainty Mode Category BeRPA [A,B,D] 1p1h/QE 1 ArC2p2h [ν,ν¯] 2p2h 1 E2p2h [A,B] [ν,ν¯] 2p2h 2 NR [ν,ν¯] [CC,NC] [n,p] [1π ,2π ,3π ] Non-res. pion 1 νe PS νe,νe inclusive 3 νe/νe norm νe,νe inclusive 3 NC norm. NC 2* an on-axis beam monitor. Additionally, it is planned for the LArTPC and MPD to be movable perpendicular to the beam axis, to take measurements at a number of off-axis angles. The use of off-axis angles is complementary to the on-axis analysis described in this work through the DUNE-PRISM concept, originally developed in the context of the J-PARC neutrino beamline in Ref. [63]. We note that there are many possible ND samples which are not included in the current analysis, but which may either help improve the sensitivity in future, or will help control uncertainties to the level assumed here. These include: neutrino–electron scattering studies, which can independently constrain the flux normalization to ∼2% [64]; additional flux constraints from the low-ν method, which exploits the fact that the low energy transfer (low-ν) cross section is roughly constant with neutrino energy [65– 70]; and using interactions on the gaseous argon (GAr) in the MPD. There is also the potential to include events where the muon does not pass through the MPD, e.g. using multiple Coulomb scattering to estimate the muon momentum [71]. 123 Eur. Phys. J. C (2020) 80 :978 Page 13 of 34 978 The LArTPC is a modular detector based on the ArgonCube design [72], with fully-3D pixelated read- out [73] and optical segmentation [74]. These features greatly reduce reconstruction ambiguities that hamper mono- lithic, projective-readout time projection chambers (TPCs), and enable the ND to function in the high-intensity environ- ment of the DUNE ND site. Each module is itself a LArTPC with two anode planes and a shared central cathode. The active dimensions of each module are 1×3×1 m (x × y×z), where the z direction is along the neutrino beam axis, and the y direction points upward. Charge drifts in the ±x direc- tion, with a maximum drift distance of 50 cm for ionization electrons. The full liquid argon (LAr) detector consists of an array of modules in a single cryostat. The minimum active size required for full containment of hadronic showers in the LBNF beam is 3 × 4 × 5 m. High-angle muons can also be contained by extending the width to 7 m. For this analysis, 35 modules are arranged in an array 5 modules deep in the z direction and 7 modules across in x so that the total active dimensions are 7 × 3 × 5 m. The total active LAr volume is 105 m3, corresponding to a mass of 147 tons. The MPD used in the analysis consists of a high- pressure gaseous argon time-projection chamber (GArTPC) in a cylindrical pressure vessel at 10 bar, surrounded by a granular, high-performance electromagnetic calorimeter, which sits immediately downstream of the LAr cryostat. The pressure vessel is 5 m in diameter and 5 m long. The TPC is divided into two drift regions by a central cathode, and filled with a 90%:10% Ar:CH4 gas mixture, such that 97% of neutrino interactions will occur on the Ar target. The GArTPC is described in detail in Ref. [5]. The electromagnetic calorimeter (ECAL) is composed of a series of absorber layers followed by arrays of scintillator and is described in Ref. [75]. The entire MPD sits inside a magnetic field, which allows the MPD to precisely measure the momentum and discriminate the sign of particles passing through it. Neutrino interactions are simulated in the active volume of the LArTPC. The propagation of neutrino interaction prod- ucts through the LArTPC and MPD detector volumes is sim- ulated using a Geant4-based model [23]. Pattern recognition and reconstruction software has not yet been developed for the ND. Instead, we perform a parameterized reconstruction based on true energy deposits in active detector volumes as simulated by Geant4. The analysis described here uses events originating in the LAr component, within a a fiducial volume (FV) that excludes 50 cm from the sides and upstream edge, and 150 cm from the downstream edge of the active region, for a total of 6 × 2 × 3 m2. Muons with kinetic energy greater than ∼1 GeV typically exit the LAr. An energetic forward-going muon will pass through the ECAL and into the gaseous TPC, where its momentum and charge are reconstructed by curva- ture. For these events, it is possible to differentiate between μ+ and μ− event by event. Muons that stop in the LAr or ECAL are reconstructed by range. Events with wide-angle muons that exit the LAr and do not match to the GArTPC are rejected, as the muon momentum is not reconstructed. The asymmetric transverse dimensions of the LAr volume make it possible to reconstruct wide-angle muons with some efficiency. The charge of muons stopping in the LAr volume cannot be determined event by event. However, the wrong-sign flux is predominantly concentrated in the high-energy tail, where leptons are more likely to be forward and energetic. In FHC beam running, the wrong-sign background in the focusing peak is negligibly small, and μ− is assumed for all stopping muon tracks. In RHC beam running, the wrong-sign back- ground is larger in the peak region. Furthermore, high-angle leptons are generally at higher inelasticity, which enhances the wrong-sign contamination in the contained muon sub- sample. To mitigate this, a Michel electron is required at the end of the track. The wrong-sign μ− captures on Ar with 75% probability, effectively suppressing the relative μ− compo- nent by a factor of four. True muons and charged pions are evaluated as potential muon candidates. The track length is determined by follow- ing the true particle trajectory until it undergoes a hard scat- ter or ranges out. The particle is classified as a muon if its track length is at least 1 m, and the mean energy deposit per centimeter of track length is less than 3 MeV. The mean energy cut rejects tracks with detectable hadronic interac- tions. The minimum length requirement imposes an effec- tive threshold on true muons of about 200 MeV kinetic energy, but greatly suppresses potential NC backgrounds with low-energy, non-interacting charged pions. Charged- current events are required to have exactly one muon, and if the charge is reconstructed, it must be of the appropriate charge. As in the FD reconstruction described in Sect. 5, hadronic energy in the ND is reconstructed by summing all charge deposits in the LAr active volume that are not associated with the muon. To reject events where the hadronic energy is poorly reconstructed due to particles exiting the detector, a veto region is defined as the outer 30 cm of the active volume on all sides. Events with more than 30 MeV total energy deposit in the veto region are excluded from the anal- ysis. This leads to an acceptance that decreases as a function of hadronic energy, as shown in the bottom panel of Fig. 5. Neutron energy is typically not observed, resulting in poor reconstruction of events with energetic neutrons, as well as in events where neutrons are produced in secondary interac- tions inside the detector. The reconstructed neutrino energy is the sum of the reconstructed hadronic energy and the recon- structed muon energy. 123 978 Page 14 of 34 Eur. Phys. J. C (2020) 80 :978 0 2 4 6 8 10 Muon longitudinal momentum (GeV/c) 0 0.5 1 1.5 2 2.5 3 M uo n tr an sv er se m om en tu m (G eV /c ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1DUNE Simulation 0 1 2 3 4 5 Hadronic energy (GeV) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceptance (Full F.V.) )3Acceptance (Central 1m Fraction per 0.5 GeV DUNE Simulation Fig. 5 Top: LAr+MPD acceptance for νμ CC events as a function of muon transverse and longitudinal momentum. Bottom: Acceptance as a function of hadronic energy; the black line is for the full Fiducial Volume (FV) while the red line is for a 1×1×1 m3 volume in the center, where the acceptance is higher due to the better hadron containment. The blue curve shows the expected distribution of true hadronic energy in the DUNE ND flux normalized to unity; 56% of events have hadronic energy below 1 GeV where the acceptance is high The oscillation analysis presented here includes samples of νμ and ν¯μ charged-current interactions originating in the LAr portion of the ND, as shown in Fig. 6. These samples are binned in two dimensions as a function of reconstructed neutrino energy and inelasticity, yrec = 1− E recμ /E recν , where E recμ and E recν are the reconstructed muon and neutrino ener- gies, respectively. Backgrounds to ν(–)μ CC arise from NC π± production where the pion leaves a long track and does not shower. Muons below about 400 MeV kinetic energy have a significant background from charged pions, so these CC events are excluded from the selected sample. Wrong-sign contamination in the beam is an additional background, par- ticularly at low reconstructed neutrino energies in RHC. 5 The far detector simulation and reconstruction The 40-kt DUNE FD consists of four separate LArTPC detector modules, each with a FV of at least 10 kt, installed ∼1.5 km underground at the Sanford Underground Research Facility (SURF) [76]. DUNE is committed to deploying both single-phase [77] and dual-phase [78] LArTPC technologies, and is investigating advanced detector designs for the fourth detector module. As such, the exact order of construction and number of modules of each design is unknown. In this work, the FD reconstruction performance is assessed assuming a single-phase design for all four modules, which does not fully exploit the benefits of different technologies with indepen- dent systematics in the sensitivity studies. A full simulation chain has been developed, from the generation of neutrino events in a Geant4 model of the FD geometry, to efficiencies and reconstructed neutrino energy estimators of all samples used in the sensitivity analysis. The total active LAr volume of each single-phase DUNE FD detector module is 13.9 m long, 12.0 m high and 13.3 m wide, with the 13.3 m width in the drift direction subdivided into four independent drift regions, with two shared cathodes. Full details of the single-phase detector module design can be found in Ref. [79]. The total active volume of each module is ∼13 kt, the FV of at least 10 kt is defined by studies of neu- trino energy resolution, using the neutrino energy estimators described below. At the anode, there are two wrapped-wire readout induction planes, which are offset by ±35.7◦ to the vertical, and a vertical collection plane. Neutrino interactions of all flavors are simulated such that weights can be applied to produce samples for any set of oscillation parameters. The interaction model described in Sect. 3 was used to model the neutrino-argon interactions in the volume of the cryostat, and the final-state particles are propagated in the detector through Geant4. The electronics response to the ionization electrons and scintillation light is simulated to produce digitized signals in the wire planes and photon detectors (PDs) respectively. Raw detector signals are processed using algorithms to remove the impact of the LArTPC electric field and elec- tronics response from the measured signal, to identify hits, and to cluster hits that may be grouped together due to prox- imity in time and space. Clusters from different wire planes are matched to form high-level objects such as tracks and showers. These high level objects are used as inputs to the neutrino energy reconstruction algorithm. The energy of the incoming neutrino in CC events is esti- mated by adding the lepton and hadronic energies recon- structed using the Pandora toolkit [80,81]. If the event is selected as νμ CC, the neutrino energy is estimated as the sum of the energy of the longest reconstructed track and the hadronic energy. The energy of the longest reconstructed track is estimated from its range if the track is contained in the detector. If the longest track exits the detector, its energy is estimated from multiple Coulomb scattering. The hadronic energy is estimated from the charge of reconstructed hits that are not in the longest track, and corrections are applied to each hit charge for recombination and the electron lifetime. 123 Eur. Phys. J. C (2020) 80 :978 Page 15 of 34 978 Fig. 6 ND samples in both FHC (blue) and RHC (red), shown in the reconstructed neutrino energy and reconstructed inelasticity binning used in the analysis, shown for a 7 year staged exposure, with an equal split between FHC and RHC. Backgrounds are also shown (dashed lines), which are dominated by NC events, although there is some con- tribution from wrong-sign νμ background events in RHC An additional correction is made to the hadronic energy to account for missing energy due to neutral particles and final- state interactions. If the event is selected as νe CC, the energy of the neutrino is estimated as the sum of the energy of the reconstructed electromagnetic (EM) shower with the highest energy and the hadronic energy. The former is estimated from the charges of the reconstructed hits in the shower, and the latter from the hits not in the shower; the recombination and electron lifetime corrections are applied to the charge of each hit. The same hadronic shower energy calibration is used for both ν and ν¯ based on a sample of ν and ν¯ events. In the energy range of 0.5–4 GeV that is relevant for oscil- lation measurements, the observed neutrino energy resolu- tion is ∼15–20%, depending on lepton flavor and reconstruc- tion method. The muon energy resolution is 4% for contained tracks and 18% for exiting tracks. The electron energy resolu- tion is approximately 4%⊕9%/√E , with some shower leak- age that gives rise to a non-Gaussian tail that is anticorrelated with the hadronic energy measurement. The hadronic energy resolution is 34%, which could be further improved by iden- tifying individual hadrons, adding masses of charged pions, and applying particle-specific recombination corrections. It may also be possible to identify final-state neutrons by look- ing for neutron-nucleus scatters, and use event kinematics to further inform the energy estimate. These improvements are under investigation and are not included in this analysis. Event classification is carried out through image recogni- tion techniques using a convolutional neural network, named convolutional visual network (CVN). Detailed descriptions of the CVN architecture can be found in Ref. [82]. The pri- mary goal of the CVN is to efficiently and accurately produce event selections of the following interactions: νμ CC and νe CC in FHC, and ν¯μ CC and ν¯e CC in RHC. In order to build the training input to the DUNE CVN three images of the neutrino interactions are produced, one for each of the three readout views of the LArTPC, using the recon- structed hits on individual wire planes. Each pixel contains information about the integrated charge in that region. An example of a simulated 2.2 GeV νe CC interaction is shown in a single view in Fig. 7 demonstrating the fine-grained detail available from the LArTPC technology. The CVN is trained using approximately three million simulated neutrino interactions. A statistically independent sample is used to generate the physics measurement sensi- tivities. The training sample is chosen to ensure similar num- bers of training examples from the different neutrino flavors. Validation is performed to ensure that similar classification performance is obtained for the training and test samples to ensure that the CVN is not overtrained. 123 978 Page 16 of 34 Eur. Phys. J. C (2020) 80 :978 Fig. 7 A simulated 2.2 GeV νe CC interaction shown in the collection view of the DUNE LArTPCs. The horizontal axis shows the wire num- ber of the readout plane and the vertical axis shows time. The colorscale shows the charge of the energy deposits on the wires. The interaction looks similar in the other two views. Reproduced from Ref. [82] For the analysis presented here, we use the CVN score for each interaction to belong to one of the following classes: νμ CC, νe CC, ντ CC and NC. The νe CC score distribu- tion, P(νeCC), and the νμ CC score distribution, P(νμCC), are shown in Fig. 8. Excellent separation between the signal and background interactions is seen in both cases. The event selection requirement for an interaction to be included in the νe CC (νμ CC) is P(νeCC) > 0.85 (P(νμCC) > 0.5), opti- mized to produce the best sensitivity to charge parity (CP) violation. Since all of the flavor classification scores must sum to unity, the interactions selected in the two event selec- tions are completely independent. The same selection criteria are used for both FHC and RHC beam running. Figure 9 shows the efficiency as a function of recon- structed energy (under the electron neutrino hypothesis) for the νe event selection, and the corresponding selection effi- ciency for the νμ event selection. The νe and νμ efficiencies in both FHC and RHC beam modes all exceed 90% in the neutrino flux peak. The ability of the CVN to identify neutrino flavor is depen- dent on its ability to resolve and identify the charged lepton. Backgrounds originate from the mis-identification of charged pions for νμ disappearance, and photons for νe appearance. The probability for these backgrounds to be introduced varies with the momentum and isolation of the energy depositions from the pions and photons. The efficiency was also observed to drop as a function of track/shower angle (with respect to the incoming neutrino beam direction) when energy deposi- tions aligned with wire planes. The shapes of the efficiency functions in lepton momentum, lepton angle, and hadronic energy fraction (inelasticity) are all observed to be consistent 0 0.2 0.4 0.6 0.8 1 ScoreeνCVN 1−10 1 10 210 310 Ev en ts DUNE Simulation signal)eν + eνCC ( background)μν + μνCC ( background)τν + τνCC ( background)ν + νNC ( beam background)eν + eνCC ( 0 0.2 0.4 0.6 0.8 1 ScoreμνCVN 1−10 1 10 210 310E ve nt s DUNE Simulation signal)μν + μνCC ( background)τν + τνCC ( background)ν + νNC ( Fig. 8 The distribution of CVN νe CC (top) and νμ CC scores (bottom) for FHC shown with a log scale. Reproduced from Ref. [82] with results from previous studies, including hand scans of LArTPC simulations. The CVN is susceptible to bias if there are features in the data that are not present in the simulation, so before its use on data, it will be important to comprehen- sively demonstrate that the selection is not sensitive to the choice of reference models. A discussion of the bias studies performed so far, and those planned in future, can be found in Ref. [82]. 6 Expected far detector event rate and oscillation parameters In this work, FD event rates are calculated assuming the fol- lowing nominal deployment plan, which is based on a tech- nically limited schedule: 123 Eur. Phys. J. C (2020) 80 :978 Page 17 of 34 978 Fig. 9 Top: the νe CC selection efficiency for FHC (left) and RHC (right) simulation with the criterion P(νeCC) > 0.85. Bottom: the νμ CC selection efficiency for FHC (left) and RHC (right) simulation with the criterion P(νμCC) > 0.5. The results from DUNE’s Conceptual Design Report (CDR) are shown for comparison [7]. The solid (dashed) lines show results from the CVN (CDR) for signal νe CC and ν¯e CC events in black and NC background interaction in red. The blue region shows the oscillated flux (A.U.) to illustrate the most important regions of the energy distribution. Reproduced from Ref. [82] • Start of beam run: two FD module volumes for total fidu- cial mass of 20 kt, 1.2 MW beam • After one year: add one FD module volume for total fidu- cial mass of 30 kt • After three years: add one FD module volume for total fiducial mass of 40 kt • After 6 years: upgrade to 2.4 MW beam 123 978 Page 18 of 34 Eur. Phys. J. C (2020) 80 :978 Table 5 Conversion between number of years in the nominal staging plan, and kt-MW-years, the two quantities used to indicate exposure in this analysis Years kt-MW-years 7 336 10 624 15 1104 Table 5 shows the conversion between number of years under the nominal staging plan, and kt-MW-years, which are used to indicate the exposure in this analysis. For all studies shown in this work, a 50%/50% ratio of FHC to RHC data was assumed, based on studies which showed a roughly equal mix of running produced a nearly optimal δCP and mass ordering sensitivity. The exact details of the run plan are not included in the staging plan. Event rates are calculated with the assumption of 1.1 ×1021 protons on target (POT) per year, which assumes a combined uptime and efficiency of the Fermilab accelerator accelerator complex and the LBNF beamline of 57% [5]. Figures 10 and 11 show the expected rate of selected events for νe appearance and νμ disappearance, respectively, includ- ing expected flux, cross section, and oscillation probabilities, as a function of reconstructed neutrino energy at a baseline of 1285 km. The spectra are shown for a 3.5 year (staged) exposure each for FHC and RHC beam modes, for a total run time of seven years. The rates shown are scaled to obtain different exposures. Tables 6 and 7 give the integrated rate for the νe appearance and νμ disappearance spectra, respec- tively. Note that the total rates are integrated over the range of reconstructed neutrino energies used in the analysis, 0.5– 10 GeV. The nominal neutrino oscillation parameters used in Figs. 10 and 11 and the uncertainty on those parameters (used later in the analysis) are taken from the NuFIT [9,83] global fit to neutrino data, and their values are given in Table 8. See also Refs. [10] and [11] for other recent global fits. As can be seen in Fig. 10, the background to νe appearance is composed of: (1) CC interactions of νe and ν¯e intrinsic to the beam; (2) misidentified NC interactions; (3) misidentified νμ and ν¯μ CC interactions; and (4) ντ and ν¯τ CC interactions in which the τ ’s decay leptonically into electrons/positrons. NC and ντ backgrounds emanate from interactions of higher- energy neutrinos that feed down to lower reconstructed neu- trino energies due to missing energy in unreconstructed final- state neutrinos. The selected NC and CC νμ generally include an asymmetric decay of a relatively high energy π0 cou- pled with a prompt photon conversion. As can be seen in Fig. 11, the backgrounds to the νμ disappearance are due to wrong-sign νμ interactions, which cannot easily be distin- guished in the unmagnetized DUNE FD, and NC interactions, where a pion has been misidentified as the primary muon. As expected, the νμ background in RHC is much larger than the ν¯μ background in FHC. Reconstructed Energy (GeV) 1 2 3 4 5 6 7 8 Ev en ts p er 0 .2 5 G eV 0 20 40 60 80 100 120 140 160 AppearanceeνDUNE Normal Ordering = 0.08813θ2 2sin = 0.58023θ 2sin 3.5 years (staged) ) CCeν + eνSignal ( ) CCeν + eνBeam ( NC ) CCμν + μν( ) CCτν + τν( /2π = -CPδ = 0CPδ /2π = +CPδ Reconstructed Energy (GeV) 1 2 3 4 5 6 7 8 Ev en ts p er 0 .2 5 G eV 0 5 10 15 20 25 30 35 40 45 50 AppearanceeνDUNE Normal Ordering = 0.08813θ2 2sin = 0.58023θ 2sin 3.5 years (staged) ) CCeν + eνSignal ( ) CCeν + eνBeam ( NC ) CCμν + μν( ) CCτν + τν( /2π = -CPδ = 0CPδ /2π = +CPδ Fig. 10 νe and ν¯e appearance spectra: reconstructed energy distribu- tion of selected νe CC-like events assuming 3.5 years (staged) running in the neutrino-beam mode (top) and antineutrino-beam mode (bottom), for a total of seven years (staged) exposure. Statistical uncertainties are shown on the datapoints. The plots assume normal mass ordering and include curves for δCP = −π/2, 0, and π/2 7 Detector uncertainties Detector effects impact the event selection efficiency as well as the reconstruction of quantities used in the oscillation fit, such as neutrino energy. The main sources of detector system- atic uncertainties are limitations of the expected calibration and modeling of particles in the detector. The ND LArTPC uses similar technology to the FD, but important differences lead to uncertainties that do not fully correlate between the two detectors. First, the readout tech- nology is different, as the ND LArTPC uses pixels as well as a different, modular photon detector. Therefore, the charge 123 Eur. Phys. J. C (2020) 80 :978 Page 19 of 34 978 Reconstructed Energy (GeV) 1 2 3 4 5 6 7 8 Ev en ts p er 0 .2 5 G eV 0 100 200 300 400 500 600 700 800 DisappearanceμνDUNE = 0.58023θ 2sin 2 eV-3 10× = 2.451 322mΔ 3.5 years (staged) CCμνSignal CCμν NC ) CCeν + eν( ) CCτν + τν( Reconstructed Energy (GeV) 1 2 3 4 5 6 7 8 Ev en ts p er 0 .2 5 G eV 0 50 100 150 200 250 300 350 DisappearanceμνDUNE = 0.58023θ 2sin 2 eV-3 10× = 2.451 322mΔ 3.5 years (staged) CCμνSignal CCμν NC ) CCeν + eν( ) CCτν + τν( Fig. 11 νμ and ν¯μ disappearance spectra: reconstructed energy dis- tribution of selected νμ CC-like events assuming 3.5 years (staged) running in the neutrino-beam mode (top) and antineutrino-beam mode (bottom), for a total of seven years (staged) exposure. Statistical uncer- tainties are shown on the datapoints. The plots assume normal mass ordering response will be different between near and far detectors due to differences in electronics readout, noise, and local effects like alignment. Second, the high-intensity environment of the ND complicates associating detached energy deposits to events, a problem which is not present in the FD. Third, the calibration strategies will be different. For example, the ND has a high-statistics calibration sample of through-going, momentum-analyzed muons from neutrino interactions in the upstream rock, which is not available with high statistics for the FD. Finally, the reconstruction efficiency will be inher- ently different due to the relatively small size of the ND. Con- tainment of charged hadrons will be significantly worse at the Table 6 νe and ν¯e appearance rates: integrated rate of selected νe CC- like events between 0.5 and 10.0 GeV assuming a 3.5-year (staged) exposure in the neutrino-beam mode and antineutrino-beam mode. The rates are shown for both NO and IO, and signal events are shown for both δCP = 0 and δCP = −π/2 Sample Expected Events δCP = 0 δCP = − π2 NO IO NO IO ν mode Oscillated νe 1155 526 1395 707 Oscillated ν¯e 19 33 14 28 Total oscillated 1174 559 1409 735 Beam νe + ν¯e CC background 228 235 228 235 NC background 84 84 84 84 ντ + ν¯τ CC background 36 36 35 36 νμ + ν¯μ CC background 15 15 15 15 Total background 363 370 362 370 ν¯ mode Oscillated νe 81 39 95 53 Oscillated ν¯e 236 492 164 396 Total oscillated 317 531 259 449 Beam νe + ν¯e CC background 145 144 145 144 NC background 40 40 40 40 ντ + ν¯τ CC background 22 22 22 22 νμ + ν¯μ CC background 6 6 6 6 Total background 216 215 216 215 ND, especially for events with energetic hadronic showers or with vertices near the edges of the FV. An uncertainty on the overall energy scale is included in the analysis presented here, as well as particle response uncertainties that are separate and uncorrelated between four species: muons, charged hadrons, neutrons, and electromag- netic showers. In the ND, muons reconstructed by range in LAr and by curvature in the MPD are treated separately. The energy scale and particle response uncertainties are allowed to vary with energy; each term is described by three free parameters: E ′rec = Erec × ( p0 + p1 √ Erec + p2√Erec ) (2) where Erec is the nominal reconstructed energy, E ′rec is the shifted energy, and p0, p1, and p2 are free fit parameters that are allowed to vary within a priori constraints. Note that the parameters produce a shift to the kinematic variables in an event, as opposed to simply assigning a weight to each sim- ulated event. The energy scale and resolution parameters are conservatively treated as uncorrelated between the ND and FD. With a better understanding of the relationship between ND and FD calibration and reconstruction techniques, it may be possible to correlate some portion of the energy response. 123 978 Page 20 of 34 Eur. Phys. J. C (2020) 80 :978 Table 7 νμ and ν¯μ disappearance rates: integrated rate of selected νμ CC-like events between 0.5 and 10.0 GeV assuming a 3.5-year (staged) exposure in the neutrino-beam mode and antineutrino-beam mode. The rates are shown for both NO and IO, with δCP = 0 Sample Expected Events NO IO ν mode νμ signal 7235 7368 ν¯μ CC background 542 542 NC background 213 213 ντ + ν¯τ CC background 53 54 νe + ν¯e CC background 9 5 ν¯ mode ν¯μ signal 2656 2633 νμ CC background 1590 1600 NC background 109 109 ντ + ν¯τ CC background 31 31 νe + ν¯e CC background 2 2 Table 8 Central value and relative uncertainty of neutrino oscillation parameters from a global fit [9,83] to neutrino oscillation data. The matter density is taken from Ref. [84]. Because the probability distri- butions are somewhat non-Gaussian (particularly for θ23), the relative uncertainty is computed using 1/6 of the 3σ allowed range from the fit, rather than 1/2 of the 1σ range. For θ23, θ13, and Δm231, the best-fit values and uncertainties depend on whether normal mass ordering (NO) or inverted mass ordering (IO) is assumed Parameter Central value Relative uncertainty (%) θ12 0.5903 2.3 θ23 (NO) 0.866 4.1 θ23 (IO) 0.869 4.0 θ13 (NO) 0.150 1.5 θ13 (IO) 0.151 1.5 Δm221 7.39×10−5 eV2 2.8 Δm232 (NO) 2.451×10−3 eV2 1.3 Δm232 (IO) − 2.512×10−3 eV2 1.3 ρ 2.848 g cm−3 2 The full list of assumed energy scale uncertainties is given as Table 9. In addition to the uncertainties on the energy scale, uncertainties on energy resolutions are also included. These are treated as fully uncorrelated between the near and far detectors and are taken to be 2% for muons, charged hadrons, and EM showers and 40% for neutrons. The scale of these assumed uncertainties is motivated by what has been achieved in recent experiments, includ- ing calorimetric based approaches (NOvA, MINERvA) and LArTPCs (LArIAT, MicroBooNE, ArgoNeuT). The DUNE performance is expected to significantly exceed the perfor- mance of these current surface-based experiments. NOvA [44] has achieved < 1% (5%) uncertainties on the energy Table 9 Uncertainties applied to the energy response of various parti- cles. p0, p1, and p2 correspond to the constant, square root, and inverse square root terms in the energy response parameterization given in Eq. (2). All are treated as uncorrelated between the ND and FD Particle type Allowed variation p0 (%) p1 (%) p2 (%) All (except muons) 2 1 2 μ (range) 2 2 2 μ (curvature) 1 1 1 p, π± 5 5 5 e, γ , π0 2.5 2.5 2.5 n 20 30 30 scale of muons (protons). Uncertainties associated to the pion and proton re-interactions in the detector medium are expected to be controlled from ProtoDUNE and LArIAT data, as well as the combined analysis of low density (gaseous) and high density (LAr) NDs. Uncertainties in the E field also contribute to the energy scale uncertainty [85], and calibration is needed (with cosmics at ND, laser system at FD) to constrain the overall energy scale. The recombi- nation model will continue to be validated by the suite of LAr experiments and is not expected to be an issue for nom- inal field provided minimal E field distortions. Uncertainties in the electronics response are controlled with a dedicated charge injection system and validated with intrinsic sources, Michel electrons and 39Ar. The response of the detector to neutrons is a source of active study and will couple strongly to detector technology. The validation of neutron interactions in LAr will continue to be characterized by dedicated measurements (e.g., CAP- TAIN [86,87]) and the LAr program (e.g., ArgoNeuT [88]). However, the association of the identification of a neutron scatter or capture to the neutron’s true energy has not been demonstrated, and significant reconstruction issues exist, so a large uncertainty (20%) is assigned comparable to the obser- vations made by MINERvA [89] assuming they are attributed entirely to the detector model. Selection of photon candi- dates from π0 is also a significant reconstruction challenge, but a recent measurement from MicroBooNE indicates this is possible and the reconstructed π0 invariant mass has an uncertainty of 5%, although with some bias [90]. The p1 and p2 terms in Eq. (2) allow the energy response to vary as a function of energy. The energy dependence is conservatively assumed to be of the same order as the abso- lute scale uncertainties given by the p0 terms. In addition to impacting energy reconstruction, the E field model also affects the definition of the FD fiducial volume, which is sensitive to electron drift. An additional 1% uncer- tainty is assumed on the total fiducial mass, which is con- servatively treated as uncorrelated between the νμ and νe 123 Eur. Phys. J. C (2020) 80 :978 Page 21 of 34 978 samples due to the potential distortion caused by large elec- tromagnetic showers in the electron sample. These uncer- tainties affect only the overall normalization, and are called FV numu FD and FV nue FD in Fig. 12. The ND and FD have different acceptance to CC events due to the very different detector sizes. The FD is sufficiently large that acceptance is not expected to vary significantly as a function of event kinematics. However, the ND selection requires that hadronic showers be well contained in LAr to ensure a good energy resolution, resulting in a loss of accep- tance for events with energetic hadronic showers. The ND also has regions of muon phase space with lower acceptance due to tracks exiting the side of the TPC but failing to match to the MPD, which are currently not used in the sensitivity analysis. Uncertainties are evaluated on the muon and hadron acceptance of the ND. The detector acceptance for muons and hadrons is shown in Fig. 5. Inefficiency at very low lep- ton energy is due to events being misreconstructed as neutral current. For high energy, forward muons, the inefficiency is only due to events near the edge of the FV where the muon happens to miss the MPD. At high transverse momentum, muons begin to exit the side of the LAr active volume, except when they happen to go along the 7 m axis. The acceptance is sensitive to the modeling of muons in the detector. An uncer- tainty is estimated based on the change in the acceptance as a function of muon kinematics. Inefficiency at high hadronic energy is due to the veto on more than 30 MeV deposited in the outer 30 cm of the LAr active volume. Rejected events are typically poorly reconstructed due to low containment, and the acceptance is expected to decrease at high hadronic energy. Similar to the muon reconstruction, this acceptance is sensitive to detector modeling, and an uncertainty is evaluated based on the change in the acceptance as a function of true hadronic energy. 8 Sensitivity methods Previous DUNE sensitivity predictions have used the GLoBES framework [7,91,92]. In this work, fits are performed using the CAFAna [93] analysis framework, developed originally for the NOvA experiment. Systematics are implemented using one-dimensional response functions for each analysis bin, and oscillation weights are calculated exactly, in fine (50 MeV) bins of true neutrino energy. For a given set of inputs, flux, oscillation parameters, cross sections, detector energy response matrices, and detector efficiency, an expected event rate can be produced. Minimization is performed using the minuit [94] package. Oscillation sensitivities are obtained by simultaneously fitting the νμ → νμ, ν¯μ → ν¯μ (Fig. 11), νμ → νe, and Fig. 12 The ratio of post-fit to pre-fit uncertainties for various sys- tematic parameters for a 15-year staged exposure. The red band shows the constraint from the FD only in 15 years, while the green shows the ND+FD constraints. Flux parameters are named “Flux #i” represent- ing the i th principal flux component, cross-section parameter names are given in Sect. 3, and detector systematics are described in Sect. 7, where the p0, p1 and p2 parameters are described in Table 9 ν¯μ → ν¯e (Fig. 10) FD spectra along with the νμ FHC and ν¯μ RHC samples from the ND (Fig. 6). In the studies, all oscillation parameters shown in Table 8 are allowed to vary. Gaussian penalty terms (taken from Table 8) are applied to θ12 and Δm212 and the matter density, ρ, of the Earth along the DUNE baseline [84]. Unless otherwise stated, studies presented here include a Gaussian penalty term on θ13 (also taken from Table 8), which is precisely measured by exper- iments sensitive to reactor antineutrino disappearance [95– 97]. The remaining parameters, sin2 θ23, Δm232, and δCP are allowed to vary freely, with no penalty term. Note that the penalty terms are treated as uncorrelated with each other, or other parameters, which is a simplification. In particular, the reactor experiments that drive the constraint on θ13 in the NuFIT analysis are also sensitive to Δm232, so the constraint on θ13 should be correlated with Δm232. We do not expect this to have a significant impact on the fits, and this effect only matters for those results with the θ13 Gaussian penalty term included. 123 978 Page 22 of 34 Eur. Phys. J. C (2020) 80 :978 Flux, cross section, and FD detector parameters are allowed to vary in the fit, but are constrained by a penalty term proportional to the pre-fit uncertainty. ND detector param- eters are not allowed to vary in the fit, but their effect is included via a covariance matrix based on the shape differ- ence between ND prediction and the “data” (which comes from the simulation in this sensitivity study). The covari- ance matrix is constructed with a throwing technique. For each “throw”, all ND energy scale, resolution, and accep- tance parameters are simultaneously thrown according to their respective uncertainties, and the modified prediction is produced by varying the relevant quantities away from the nominal prediction according to the thrown parameter values. The bin-to-bin covariance is determined by compar- ing the resulting spectra with the nominal prediction, in the same binning as is used in the oscillation sensitivity analy- sis. This choice protects against overconstraining that could occur given the limitations of the parameterized ND recon- struction described in Sect. 4 taken together with the high statistical power at the ND, but is also a simplification. The compatibility of a particular oscillation hypothesis with both ND and FD data is evaluated using a negative log- likelihood ratio, which converges to a χ2 at high-statistics [48]: χ2(ϑ, x) = −2 log L(ϑ, x) = 2 Nbins∑ i [ Mi (ϑ, x) − Di + Di ln ( Di Mi (ϑ, x) )] + Nsysts∑ j [ Δx j σ j ]2 + N NDbins∑ k N NDbins∑ l (Mk(x) − Dk) V −1kl (Ml(x) − Dl) , (3) where ϑ and x are the vector of oscillation parameter and nuisance parameter values respectively; Mi (ϑ, x) and Di are the Monte Carlo (MC) expectation and fake data in the i th reconstructed bin (summed over all selected samples), with the oscillation parameters neglected for the ND; Δx j and σ j are the difference between the nominal and current value, and the prior uncertainty on the j th nuisance parameter with uncertainties evaluated and described in Sects. 2, 3 and 7; and Vkl is the covariance matrix between ND bins described previously. In order to avoid falling into a false minimum, all fits are repeated for four different δCP values (-π , -π /2, 0, π /2), both mass orderings, and in both octants, and the lowest χ2 value is taken as the minimum. Two approaches are used for the sensitivity studies pre- sented in this work. First, Asimov studies [98] are carried out in which the fake (Asimov) dataset is the same as the nominal MC. In these, the true value of all systematic uncer- Table 10 Treatment of the oscillation parameters for the simulated data set studies. Note that for some studies θ13 has a Gaussian penalty term applied based on the NuFIT value, and for others it is thrown uniformly within a range determined from the NuFIT 3σ allowed range Parameter Prior Range sin2 θ23 Uniform [0.4; 0.6] |Δm232| (×10−3 eV2) Uniform |[2.3; 2.7]| δCP (π ) Uniform [−1;1] θ13 Gaussian NuFIT Uniform [0.13; 0.2] tainties and oscillation parameters except those of interest (which are fixed at a test point) remain unchanged, and can vary in the fit, but are constrained by their pre-fit uncertainty. Second, studies are performed where many statistical and systematic throws are made according to their pre-fit Gaus- sian uncertainties, and fits of all parameters are carried out for each throw. A distribution of post-fit values is built up for the parameter of interest. In these, the expected resolution for oscillation parameters is determined from the spread in best-fit values obtained from an ensemble of throws that vary according to both the statistical and systematic uncertainties. For each throw, the true value of each nuisance parameter is chosen randomly from a distribution determined by the a priori uncertainty on the parameter. For some studies, oscil- lation parameters are also randomly chosen as described in Table 10. Poisson fluctuations are then applied to all analysis bins, based on the mean event count for each bin after the systematic adjustments have been applied. For each throw in the ensemble, the test statistic is minimized, and the best- fit value of all parameters is determined. The median throw and central 68% of throws derived from these ensembles are shown. Sensitivity calculations for CPV, neutrino mass ordering, and octant are performed, in addition to studies of oscillation parameter resolution in one and two dimensions. In these cases, the experimental sensitivity is quantified using a like- lihood ratio as the test statistic: Δχ2 = χ2B − χ2A, (4) where χ2B and χ2A are both obtained from Eq. (3), using a coherent systematic and statistical throw. The size of Δχ2 is a measure of how well the data can exclude model B in favor of model A, given the uncertainty in the model. For example, the sensitivity for excluding the IO in favor of the NO would be given as χ2IO − χ2NO. Note that the Δχ2 for the mass ordering may be negative, depending on how the test is set up. The sensitivity for discovering CPV is the preference for the CP violating hypothesis over the CP conserving hypothesis, χ20,π − χ2CPV. 123 Eur. Phys. J. C (2020) 80 :978 Page 23 of 34 978 Post-fit uncertainties on systematic parameters are shown for Asimov fits at the NuFIT best-fit point to both the ND+FD samples, and the FD-only samples in Fig. 12, as a fraction of the pre-fit systematic uncertainties described in Sects. 2, 3, and 7. The FD alone can only weakly constrain the flux and cross-section parameters, which are much more strongly constrained when the ND is included. The ND is, however, unable to strongly constrain the FD detector systematics as they are treated as uncorrelated, and due to the treatment of ND detector systematics in a covariance matrix in Eq. (3). Adding the ND does slightly increase the constraint on detec- tor parameters as it breaks degeneracies with other param- eters. Several important cross-section uncertainties are also not constrained by the ND. In particular, an uncertainty on the ratio of νμ to νe cross sections is totally unconstrained, which is not surprising given the lack of ND νe samples in the current analysis. The most significant flux terms are con- strained at the level of 20% of their a priori values. Less significant principal components have little impact on the observed distributions at either detector, and receive weaker constraints. Figure 13 shows the pre- and post-fit systematic uncer- tainties on the FD FHC samples for Asimov fits at the NuFIT best-fit point including both ND and FD samples with a 15 year exposure. It shows how the parameter constraints seen in Fig. 12 translate to a constraint on the event rate. Similar results are seen for the RHC samples. The large reduction in the systematic uncertainties is largely due to the ND con- straint on the systematic uncertainties apparent from Fig. 12. 9 Sensitivities In this section, various sensitivity results are presented. For the sake of simplicity, unless otherwise stated, only true nor- mal ordering is shown. Possible variations of sensitivity are presented in two ways. Results produced using Asimovs are shown as lines, and differences between two Asimov scenar- ios are shown with a colored band. Note that the band in the Asimov case is purely to guide the eye, and does not denote a confidence interval. For results produced using many throws of oscillation parameters, systematic and statistical uncer- tainties, ∼300,000 throws were used to calculate the sen- sitivity for each scenario. The median sensitivity is shown with a solid line, and a transparent filled area indicates the region containing the central 68% of throws, which can be interpreted as the 1σ uncertainty on the sensitivity. Figure 14 shows the significance with which CPV (δCP = [0,±π ]) can be observed in both NO and IO as a function of the true value of δCP for exposures corresponding to seven and ten years of data, using the staging scenario described in Sect. 6, and using the toy throwing method described in Sect. 8 to investigate their effect on the sensitivity. This sensi- Fig. 13 νμ (top) and νe (bottom) FD FHC spectra for a 15 year staged exposure with oscillation parameters set to the NuFIT best-fit point, shown as a function of reconstructed neutrino energy. The statistical uncertainty on the total rate is shown on the data points, and the pre- and post-fit systematic uncertainties are shown as shaded bands. The post-fit uncertainty includes the effect of the ND samples in the fit, and corresponds to the parameter constraints shown in Fig. 12 tivity has a characteristic double peak structure because the significance of a CPV measurement necessarily decreases around CP-conserving values of δCP. The median CPV sensi- tivity reaches 5σ for a small range of values after an exposure of seven years in NO, and a broad range of values after a ten year exposure. In IO, DUNE has slightly stronger sensitivity to CPV, and reaches 5σ for a broad range of values after a seven year exposure. Note that with statistical and systematic throws, the median sensitivity never reaches exactly zero. Figure 15 shows the DUNE Asimov sensitivity to CPV in NO when the true values of θ23, θ13, andΔm232 vary within the 3σ range allowed by NuFIT. The largest effect is the variation in sensitivity with the true value of θ23, where degeneracy with δCP and matter effects are significant. Values of θ23 in the lower octant lead to the best sensitivity to CPV. The true values of θ13 and Δm232 are highly constrained by global data and, within these constraints, do not have a dramatic impact on the sensitivity. Note that in the Asimov cases shown in 123 978 Page 24 of 34 Eur. Phys. J. C (2020) 80 :978 Fig. 14 Significance of the DUNE determination of CP-violation (δCP = [0,±π ]) as a function of the true value of δCP, for seven (blue) and ten (orange) years of exposure, in both normal (top) and inverted (bottom) ordering. The width of the transparent bands cover 68% of fits in which random throws are used to simulate statistical varia- tions and select true values of the oscillation and systematic uncertainty parameters, constrained by pre-fit uncertainties. The solid lines show the median sensitivity Fig. 15, the median sensitivity reaches 0 at CP-conserving values of δCP (unlike the case with the throws as in Fig. 14), but in regions far from CP-conserving values, the Asimov sensitivity and the median sensitivity from the throws agree well. Figure 16 shows the result of Asimov studies investigating the significance with which CPV can be determined in NO for 75% and 50% of δCP values, and when δCP = −π/2, as a function of exposure in kt-MW-years, which can be con- verted to years using the staging scenario described in Sect. 6. The width of the bands show the impact of applying an exter- Fig. 15 Asimov sensitivity to CP violation, as a function of the true value of δCP, for ten years of exposure. Curves are shown for variations in the true values of θ23 (top), θ13 (middle) and Δm232 (bottom), which correspond to their 3σ NuFIT range of values, as well as the NuFIT central value, and maximal mixing 123 Eur. Phys. J. C (2020) 80 :978 Page 25 of 34 978 Fig. 16 Significance of the DUNE determination of CP-violation (δCP = [0, π ]) for the case when δCP =−π/2, and for 50% and 75% of possible true δCP values, as a function of exposure in kt-MW-years. Top: The width of the band shows the impact of applying an external constraint on θ13. Bottom: The width of the band shows the impact of varying the true value of sin2 θ23 within the NuFIT 90% C.L. region nal constraint on θ13. CP violation can be observed with 5σ significance after about seven years (336 kt-MW-years) if δCP = −π/2 and after about ten years (624 kt-MW-years) for 50% of δCP values. CP violation can be observed with 3σ significance for 75% of δCP values after about 13 years of running. In the bottom plot of Fig. 16, the width of the bands shows the impact of applying an external constraint on θ13, while in the bottom plot, the width of the bands is the result of varying the true value of sin2 θ23 within the NuFIT 90% C.L. allowed region. Figure 17 shows the significance with which the neutrino mass ordering can be determined in both NO and IO as a function of the true value of δCP, for both seven and ten Fig. 17 Significance of the DUNE determination of the neutrino mass ordering, as a function of the true value of δCP, for seven (blue) and ten (orange) years of exposure. The width of the transparent bands cover 68% of fits in which random throws are used to simulate statistical varia- tions and select true values of the oscillation and systematic uncertainty parameters, constrained by pre-fit uncertainties. The solid lines show the median sensitivity year exposures, including the effect of all other oscillation and systematic parameters using the toy throwing method described in Sect. 8. The characteristic shape results from near degeneracy between matter and CPV effects that occurs near δCP = π/2 (−δCP = π/2) for true normal (inverted) ordering. Studies have indicated that special attention must be paid to the statistical interpretation of neutrino mass order- ing sensitivities [99–101] because the Δχ2 metric does not follow the expected chi-square function for one degree of freedom, so the interpretation of the √ Δχ2 as the sensitivity is complicated. However, it is clear from Fig. 17 that DUNE is able to distinguish the mass ordering for both true NO and 123 978 Page 26 of 34 Eur. Phys. J. C (2020) 80 :978 Fig. 18 Asimov sensitivity to the neutrino mass ordering, as a function of the true value of δCP, for ten years of exposure. Curves are shown for variations in the true values of θ23 (top), θ13 (middle) and Δm232 (bottom), which correspond to their 3σ NuFIT range of values, as well as the NuFIT central value. and maximal mixing IO, and using the corrections from, for example, Ref. [99], DUNE would still achieve 5σ significance for the central 68% of all throws shown in Fig. 17. We note that for both seven and ten years (it was not checked for lower exposures), there were no parameter throws used in generating the plots (∼300,000 each) for which the incorrect mass ordering was preferred. Figure 18 shows the DUNE Asimov sensitivity to the neu- trino mass ordering when the true values of θ23, θ13, and Δm232 vary within the 3σ range allowed by NuFIT. As for CPV (in Fig. 15), the largest variation in sensitivity is with the true value of θ23, but in this case, the upper octant leads to the best sensitivity. Again, the true values of θ13 and Δm232 do not have a dramatic impact on the sensitivity. The median Fig. 19 Significance of the DUNE determination of the neutrino mass ordering for the case when δCP =−π/2, and for 100% of possible true δCP values, as a function of exposure in kt-MW-years. Top: The width of the band shows the impact of applying an external constraint on θ13. Bottom: The width of the band shows the impact of varying the true value of sin2 θ23 within the NuFIT 90% C.L. region 123 Eur. Phys. J. C (2020) 80 :978 Page 27 of 34 978 Fig. 20 Sensitivity to determination of the θ23 octant as a function of the true value of sin2 θ23, for ten (orange) and fifteen (green) years of exposure, for both normal (top) and inverted (bottom) ordering. The width of the transparent bands cover 68% of fits in which random throws are used to simulate statistical variations and select true values of the oscillation and systematic uncertainty parameters, constrained by pre-fit uncertainties. The solid lines show the median sensitivity Asimov sensitivity tracks the median throws shown in Fig. 17 well for the reasonably high exposures tested — this was not checked for exposures below seven years (336 kt-MW-years). Figure 19 shows the result of Asimov studies assessing the significance with which the neutrino mass ordering can be determined for 100% of δCP values, and when δCP = −π/2, as a function of exposure in kt-MW-years, for true NO. The width of the bands show the impact of applying an external constraint on θ13. The bottom plot shows the impact of varying the true value of sin2 θ23 within the NuFIT 90% C.L. region. As DUNE will be able to establish the neutrino mass ordering at the 5σ level for 100% of δCP values after Fig. 21 Resolution in degrees for the DUNE measurement of δCP, as a function of the true value of δCP, for seven (blue), ten (orange), and fifteen (green) years of exposure. The width of the band shows the impact of applying an external constraint on θ13 a relatively short period, these plots only extend to 500 kt- MW-years. The measurement of νμ → νμ oscillations depends on sin2 2θ23, whereas the measurement of νμ → νe oscillations depends on sin2 θ23. A combination of both νe appearance and νμ disappearance measurements can probe both maximal mixing and the θ23 octant. Figure 20 shows the sensitivity to determining the octant as a function of the true value of sin2 θ23, in both NO and IO. We note that the octant sensitivity strongly depends on the use of the external θ13 constraint. In addition to the discovery potential for neutrino the mass ordering and CPV, and sensitivity to the θ23 octant, DUNE will improve the precision on key parameters that govern neutrino oscillations, including δCP, sin2 2θ13, Δm231, and sin2 θ23. Figure 21 shows the resolution, in degrees, of DUNE’s measurement of δCP, as a function of the true value of δCP, for true NO. The resolution on a parameter is produced from the central 68% of post-fit parameter values using many throws of the systematic and remaining oscillation parameters, and statistical throws. The resolution of this measurement is sig- nificantly better near CP-conserving values of δCP, compared to maximally CP-violating values. For fifteen years of expo- sure, resolutions between 5◦–15◦ are possible, depending on the true value of δCP. A smoothing algorithm has been applied to interpolate between values of δCP at which the full analysis has been performed. Figures 22 and 23 show the resolution of DUNE’s mea- surements of δCP and sin2 2θ13 and of sin2 2θ23 and Δm232, respectively, as a function of exposure in kt-MW-years. The 123 978 Page 28 of 34 Eur. Phys. J. C (2020) 80 :978 Fig. 22 Resolution of DUNE measurements of δCP (top) and sin2 2θ13 (bottom), as a function of exposure in kt-MW-years. As seen in Fig. 21, the δCP resolution has a significant dependence on the true value of δCP, so curves for δCP = −π/2 (red) and δCP = 0 (green) are shown. For δCP, the width of the band shows the impact of applying an external constraint on θ13. No constraint is applied when calculating the sin2 2θ13 resolution resolution on a parameter is produced from the central 68% of post-fit parameter values using many throws of the sys- tematic other oscillation parameters, and statistical throws. As seen in Fig. 21, the δCP resolution varies significantly with the true value of δCP, but for favorable values, resolutions near 5◦ are possible for large exposure. The DUNE measurement of sin2 2θ13 approaches the precision of reactor experiments for high exposure, allowing a comparison between the two results, which is of interest as a test of the unitarity of the PMNS matrix. Fig. 23 Resolution of DUNE measurements of sin2 2θ23 (top) and Δm232 (bottom), as a function of exposure in kt-MW-years. The width of the band for the sin2 2θ23 resolution shows the impact of applying an external constraint on θ13. For the Δm232 resolution, an external con- straint does not have a significant impact, so only the unconstrained curve is shown One of the primary physics goals for DUNE is the simul- taneous measurement of all oscillation parameters governing long-baseline neutrino oscillation, without a need for external constraints. Figure 24 shows the 90% constant Δχ2 allowed regions in the sin2 2θ13–δCP and sin2 θ23–Δm232 planes for seven, ten, and fifteen years of running, when no external constraints are applied, compared to the current measure- ments from world data. An additional degenerate lobe visible at higher values of sin2 2θ13 and in the wrong sin2 θ23 octant is present in the seven and ten year exposures, but is resolved 123 Eur. Phys. J. C (2020) 80 :978 Page 29 of 34 978 Fig. 24 Two-dimensional 90% constant Δχ2 confidence regions in the sin2 2θ13–δCP (top) and sin2 θ23–Δm232 (botton) planes, for seven, ten, and fifteen years of exposure, with equal running in neutrino and antineutrino mode. The 90% C.L. region for the NuFIT global fit is shown in yellow for comparison. The true values of the oscillation parameters are assumed to be the central values of the NuFIT global fit and the oscillation parameters governing long-baseline oscillation are unconstrained after long exposures. The time to resolve the degeneracy with DUNE data alone depends on the true oscillation parame- ter values. For shorter exposures, the degeneracy observed in Fig. 24 can be resolved by introducing an external con- straint on the value of θ13. Figure 25 shows two-dimensional 90% constant Δχ2 allowed regions in the sin2 θ23–δCP plane with an external constraint on θ13 applied. In this case, the degenerate octant solution has disappeared for all exposures shown. Fig. 25 Two-dimensional 90% constant Δχ2 confidence regions in sin2 θ23–δCP plane, for seven, ten, and fifteen years of exposure, with equal running in neutrino and antineutrino mode. The 90% C.L. region for the NuFIT global fit is shown in yellow for comparison. The true values of the oscillation parameters are assumed to be the central values of the NuFIT global fit and θ13 is constrained by NuFIT Figure 26 explores the resolution sensitivity that is expected in the sin2 θ23–δCP and sin2 θ23–Δm232 planes for various true oscillation parameter values, with an external constraint on θ13. The true oscillation parameter values used are denoted by stars, and the NuFIT best fit values are used as the true value of all those not explicitly shown. Values of sin2 θ23 = 0.42, 0.5, 0.58 were used in both planes, and additionally, values of δCP = -π/2, 0, π/2 were used in the sin2 θ23–δCP plane. It can be observed that the resolu- tion in the value of sin2 θ23 is worse at sin2 θ23 = 0.5, and improves for values away from maximal in either octant. As was seen in Fig. 21, the resolution of δCP is smaller near the CP-conserving value of δCP = 0, and increases towards the maximally CP-violating values δCP = ±π/2. The exposures required to reach selected sensitivity mile- stones for the nominal analysis are summarized in Table 11. Note that the sensitivity to CPV and for determining the neutrino mass ordering was shown to be dependent on the value of θ23 in Figs. 15 and 18, so these milestones should be treated as approximate. δCP = −π/2 is taken as a ref- erence value of maximal CPV close to the current global best fit. Similarly, a resolution of 0.004 on sin2 2θ13 is used as a reference as the current resolution obtained by reactor experiments. 123 978 Page 30 of 34 Eur. Phys. J. C (2020) 80 :978 Fig. 26 Two-dimensional 90% constant Δχ2 confidence regions in the sin2 θ23–δCP (left) and sin2 θ23–Δm232 (right) planes for different oscil- lation parameter values and seven, ten, and fifteen years of exposure, with equal running in neutrino and antineutrino mode. The 90% C.L. region for the NuFIT global fit is included in yellow for comparison. In all cases, an external constraint on the value of θ13 is applied. The true oscillation parameter values used are denoted by stars, and the NuFIT best fit values are used as the true value of all those not explicitly shown. Test values of sin2 θ23 = 0.42, 0.5, 0.58 were used for both top and bot- tom plots. In the top plot, test values of δCP = -π/2, 0, π/2 were used Table 11 Exposure in years, assuming true normal ordering and equal running in neutrino and antineutrino mode, required to reach selected physics milestones in the nominal analysis, using the NuFIT best-fit values for the oscillation parameters. The staging scenario described in Sect. 6 is assumed. Exposures are rounded to the nearest year Physics milestone Exposure (sin2 θ23 = 0.580) Staged years kt-MW-years 5σ mass ordering 1 16 δCP = -π/2 5σ mass ordering 2 66 100% of δCP values 3σ CP violation 3 100 δCP = -π/2 3σ CP violation 5 197 50% of δCP values 5σ CP violation 7 334 δCP = -π/2 5σ CP violation 10 646 50% of δCP values 3σ CP violation 13 936 75% of δCP values δCP resolution of 10◦ 8 400 δCP = 0 δCP resolution of 20◦ 12 806 δCP = -π/2 sin2 2θ13 resolution of 0.004 15 1079 10 Conclusion The analyses presented here are based on full, end-to-end simulation, reconstruction, and event selection of FD Monte Carlo and parameterized analysis of ND Monte Carlo of the DUNE experiment. Detailed uncertainties from flux, the neutrino interaction model, and detector effects have been included in the analysis. Sensitivity results are obtained using a sophisticated, custom fitting framework. These stud- ies demonstrate that DUNE will be able to measure δCP to high precision, unequivocally determine the neutrino mass ordering, and make precise measurements of the parameters governing long-baseline neutrino oscillation. We note that further improvements are expected once the full potential of the DUNE ND is included in the analysis. In addition to the samples used explicitly in this analysis, the LArTPC is expected to measure numerous exclusive final- state CC channels, as well as νe and NC events. Addition- ally, neutrino-electron elastic scattering [64] and the low-ν technique [65–70] may be used to constrain the flux. Addi- tional samples of events from other detectors in the DUNE ND complex are not explicitly included here, but there is an assumption that we will be able to control the uncertainties to the level used in the analysis, and it should be understood that that implicitly relies on having a highly capable ND. 123 Eur. Phys. J. C (2020) 80 :978 Page 31 of 34 978 DUNE will be able to establish the neutrino mass ordering at the 5σ level for 100% of δCP values between two and three years. CP violation can be observed with 5σ significance after ∼7 years if δCP = −π/2 and after ∼10 years for 50% of δCP values. CP violation can be observed with 3σ significance for 75% of δCP values after ∼13 years of running. For 15 years of exposure, δCP resolution between 5◦ and 15◦ are possible, depending on the true value of δCP. The DUNE measurement of sin2 2θ13 approaches the precision of reactor experiments for high exposure, allowing measurements that do not rely on an external sin2 2θ13 constraint and facilitating a comparison between the DUNE and reactor sin2 2θ13 results, which is of interest as a potential signature for physics beyond the standard model. DUNE will have significant sensitivity to the θ23 octant for values of sin2 θ23 less than about 0.47 and greater than about 0.55. We note that the results found are broadly consistent with those found in Ref. [7], using a much simpler analysis. The measurements made by DUNE will make significant contributions to completion of the standard three-flavor mix- ing picture, and provide invaluable inputs to theory work understanding whether there are new symmetries in the neu- trino sector and the relationship between the generational structure of quarks and leptons. The observation of CPV in neutrinos would be an important step in understanding the origin of the baryon asymmetry of the universe. The pre- cise measurements of the three-flavor mixing parameters that DUNE will provide may also yield inconsistencies that point us to physics beyond the standard three-flavor model. Acknowledgements This document was prepared by the DUNE col- laboration using the resources of the Fermi National Accelerator Lab- oratory (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, Fun- dación “La Caixa” and MICINN, Spain; SERI and SNSF, Switzerland; TÜB˙ITAK, Turkey; The Royal Society and UKRI/STFC, UK; 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-AC02-05CH11231. Data Availability Statement This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This manuscript describes a sensitivity study for the DUNE experiment using simulation only, and as such there are no experimental data to report.] Open Access This article is licensed under a Creative Commons Attri- bution 4.0 International License, which permits use, 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, pro- vide 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 indi- cated 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 permit- ted use, you will need to obtain permission directly from the copy- right holder. 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