Long-baseline neutrino oscillation physics potential of the DUNE experiment

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.Alt 53, J. Anderson4, C. Andreopoulos158,118, M. P. Andrews61, F. Andrianala2, S. Andringa113,114,A.Ankowski 159, M. Antonova77, S. Antusch10, A. Aranda-Fernandez39, A. Ariga11, L. O. Arnold42, M. A. Arroyave52, J. Asaadi173, A. Aurisano37, V. Aushev112,D.Autiero 89, 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.Barrow 61,171, A. Bashyal140, V. Basque123,F.Bay 134, J. L. Bazo Alba151, J. F. Beacom139, E. Bechetoille89, B. Behera41, L. Bellantoni61, G. Bellettini149, V. Bellini33,79, O. Beltramello21,D.Belver 22, 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.Bian 26, M. Biassoni82, K. Biery61, B. Bilki12,99, M. Bishai17, A. Bitadze123,A.Blake 116, 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.Bostan 99, P. Bour44,S.B.Boyd 183, D. Boyden136, J. Bracinik13, D. Braga61, D. Brailsford116, A. Brandt173,J.Bremer 21,C.Brew 158, E. Brianne123, S. J. Brice61, C. Brizzolari82,127, C. Bromberg126, G. Brooijmans42, J. Brooke16,A.Bross 61, G. Brunetti85, N. Buchanan41, H. Budd155, D. Caiulo89, P. Calafiura117, J. Calcutt126, M. Calin18,S.Calvez 41,E.Calvo 22, 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.Chaves 146, H. Chen17, M. Chen26, Y. Chen11, D. Cherdack74,C.Chi 42, S. Childress61, A. Chiriacescu18,K.Cho 107, 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.Cotte 20,L.Cremaldi 131, L. Cremonesi178, J. I. Crespo-Anadón22, E. Cristaldo6,R.Cross 116, C. Cuesta22,Y.Cui 28, D. Cussans16, M. Dabrowski17,H.daMotta 19, L. Da Silva Peres60,C.David 61,189,Q.David 89,G.S.Davies 131,S.Davini 80, J. Dawson144,K.De 173, 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.Deisting 156, P. De Jong134,1, A. Delbart20, D. Delepine70, M. Delgado3, A. Dell’Acqua21, P. De Lurgio4,J.R.T.deMelloNeto 60,D.M.DeMuth 179, S. Dennis31, C. Densham158, G. Deptuch61, A. De Roeck21, V. De Romeri77,J.J.DeVries 31, R. Dharmapalan73,M.Dias 177,F.Diaz 151, J. S. Díaz97, S. Di Domizio64,80, L. Di Giulio21,P.Ding 61,L.DiNoto 64,80, C. Distefano87, R. Diurba130,M.Diwan 17, Z. Djurcic4, N. Dokania168, M. J. Dolinski49,L.Domine 159, 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.Eisch 100, 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. 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Zutshi136,R.Zwaska 61 1University of Amsterdam, 1098 XG Amsterdam, The Netherlands 2University of Antananarivo, Antananarivo 101, Antananarivo, Madagascar 3Universidad Antonio Nariño, Bogotá, Colombia 4Argonne National Laboratory, Argonne, IL 60439, USA 5University of Arizona, Tucson, AZ 85721, USA 6Universidad Nacional de Asunción, San Lorenzo, Paraguay 7University of Athens, Zografou, GR 157 84, Greece 8Universidad del Atlántico, Atlántico, Colombia 9Banaras 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. Niewodnicza´nski 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 Neutrino Experiment (DUNE) to neutrino oscillation is determined, based on a full simulation, reconstruction, and event selection of the far detector and a full simulation and parameterized analysis of the near detector. Detailed uncertainties 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 detector 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, ae-mail: [email protected] be-mail: [email protected] (corresponding author) ce-mail: [email protected] for 50% of all δCP values. It will also make precise measurements of other parameters governing long-baseline neutrino oscillation, and after an exposure of 15 years will achieve a similar sensitivity to sin22θ13 to current reactor experiments. 1 Introduction The Deep Underground Neutrino Experiment (DUNE) is a next-generation, long-baseline neutrino oscillation experiment which will carry out a detailed study of neutrino mixing utilizing high-intensity νμand ¯νμbeams measured over a long baseline. DUNE is designed to make significant contributions to the completion of the standard threeflavor picture by measuring all the parameters govern123 Eur. Phys. J. C (2020) 80 :978 Page 7 of 34 978 ing ν1–ν3and ν2–ν3mixing 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, particularly δCP,sin 22θ13, and the octant of θ23. These measurements 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) locatedatFermiNationalAcceleratorLaboratory,inBatavia, 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 neutrino 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 (fiducial) LArTPC modules [6–8]. The deep underground location 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 experiments 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 Δm2 21 and |Δm2 31|, whereΔm2 ij =m2 i−m2 jisthedifferencebetweenthesquares of the neutrino mass states in eV2. The neutrino mass ordering (i.e., the sign of Δm2 31) is unknown, though recent results showa weak preference forthenormal 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→νethrough matter in the standard three-flavor model and a constant density approximation is, to first order [16]: P(ν (–) μ→ν (–) e)≃sin2θ23 sin22θ13 sin2(Δ31 −aL) (Δ31 −aL)2Δ2 31 +sin 2θ23 sin 2θ13 sin 2θ12 ×sin(Δ31 −aL) (Δ31 −aL)Δ31 ×sin(aL) (aL)Δ21 cos(Δ31 ±δCP) +cos2θ23 sin22θ12 sin2(aL) (aL)2Δ2 21, (1) where a=±GFNe √2≈± 1 3500 km ρ 3.0g/cm3, GFis the Fermi constant, Neis the number density of electrons in the Earth’s crust, Δij =1.267Δm2 ijL/Eν,Lis the baseline in km, and Eνis the neutrino energy in GeV. Both δCP and aterms are positive for νμ→νeand negative for ¯νμ→¯νeoscillations; i.e., a neutrino-antineutrino asymmetry 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. 1at 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 experiments [19–21]. Its broad-band beam makes it sensitive to the shape of the oscillation spectrum for a range of neutrino energies. DUNE’s relatively high energy neutrino beam enhances the size of the matter effect and will allow DUNE to measure 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 systematic 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 3describes the neutrino interaction model and systematic variations. The near and far detector simulation, reconstruction, and event selections are described in Sects. 4and 5, respectively, with a nominal set of event rate predictions given in Sect. 6. Detector uncertainties 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 function 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.ThesimulationusesadetaileddescriptionoftheLBNF 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 current (FHC), and antineutrino-enhanced, reverse horn current (RHC), configurations of LBNF are shown in Fig. 2. Uncertainties on the neutrino fluxes arise primarily from uncertainNeutrino energy (GeV) 0246810 POT) 21 10×/GeV (1.1 2 's/mν 7 10 8 10 9 10 10 10 11 10 DUNE Simulation μ νμ ν e νe ν Neutrino energy (GeV) 0246810 POT) 21 10×/GeV (1.1 2 's/mν 7 10 8 10 9 10 10 10 11 10 DUNE Simulation μ νμ ν e νe ν 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 ofalignment 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 particles 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 uncer123 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 component 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, separated by flux at the ND and FD. The output covariance matrix has 208×208 bins, despite having only ∼30 input uncertainties. To reduce the number of parameters used in the fit, the covariance matrix is diagonalized, and each principal component 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 checking 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 principalcomponent(component0)matchesthehadronproduction 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. CompoNeutrino energy (GeV) 012345678 Fractional shift 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 interactions that produce neutrinos in the LBNF beam simulation 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 abletoconstrainquasielasticandlow-energyinteractionsthat dominate the lowest neutrino energy bins. The NA61 experiment at CERN has taken data that will constrain many higher energy interactions, and also plans to measure hadrons produced on a replica LBNF target, which would provide tight constraints on all interactions occurring in the target. A similar 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 interaction model uncertainties on the oscillation analysis has 123 978 Page 16 of 34 Eur. Phys. J. C (2020) 80 :978 Fig. 7 A simulated 2.2GeVνeCC interaction shown in the collection view of the DUNE LArTPCs. The horizontal axis shows the wire number 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: νμCC, νeCC, ντCC and NC. The νeCC score distribution, P(νeCC), and the νμCC 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 νeCC (νμCC) is P(νeCC)>0.85 (P(νμCC)>0.5), optimized 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 selections are completely independent. The same selection criteria are used for both FHC and RHC beam running. Figure 9shows the efficiency as a function of reconstructed energy (under the electron neutrino hypothesis) for the νeevent selection, and the corresponding selection efficiency for the νμevent selection. The νeand νμefficiencies in both FHC and RHC beam modes all exceed 90% in the neutrino flux peak. TheabilityoftheCVNto identify neutrino flavoris dependent on its ability to resolve and identify the charged lepton. Backgroundsoriginatefromthemis-identificationofcharged pions for νμdisappearance, and photons for νeappearance. Theprobabilityforthesebackgroundstobeintroduced 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 depositions 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 Score e νCVN 1 − 10 1 10 2 10 3 10 Events DUNE Simulation signal) e ν + e νCC ( background) μ ν + μ νCC ( background) τ ν + τ νCC ( background)ν + νNC ( beam background) e ν + e νCC ( 0 0.2 0.4 0.6 0.8 1 Score μ νCVN 1− 10 1 10 2 10 3 10 Events DUNE Simulation signal) μ ν + μ νCC ( background) τ ν + τ νCC ( background)ν + νNC ( Fig. 8 The distribution of CVN νeCC (top) and νμCC 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 comprehensively 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 following nominal deployment plan, which is based on a technically limited schedule: 123 Eur. Phys. J. C (2020) 80 :978 Page 17 of 34 978 Fig. 9 Top: the νeCC 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 νeCC and ¯νeCC 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 fiducial mass of 20 kt, 1.2 MW beam •After one year: add one FD module volume for total fiducial mass of 30 kt •After three years: add one FD module volume for total fiducial mass of 40kt •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 5shows 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,basedonstudies which showedaroughlyequalmix 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]. Figures10and11showtheexpectedrateofselectedevents forνeappearance and νμdisappearance,respectively, including 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 6and 7give the integrated rate for the νeappearance and νμdisappearance spectra, respectively. 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. 10and 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 νeappearance is composed of: (1) CC interactions of νeand ¯νeintrinsic to thebeam;(2) misidentified NC interactions;(3)misidentified νμand ¯νμCC interactions; and (4) ντand ¯ντCC interactions in which the τ’s decay leptonically into electrons/positrons. NC and ντbackgrounds emanate from interactions of higherenergy neutrinos that feed down to lower reconstructed neutrino energies due to missing energy in unreconstructed finalstate neutrinos. The selectedNC and CC νμgenerallyinclude an asymmetric decay of a relatively high energy π0coupled with a prompt photon conversion. As can be seen in Fig. 11, the backgrounds to the νμdisappearance are due to wrong-sign νμinteractions, which cannot easily be distinguishedintheunmagnetizedDUNEFD,andNCinteractions, where a pion has been misidentified as the primary muon. As expected, the νμbackground in RHC is much larger than the ¯νμbackground in FHC. Reconstructed Energy (GeV) 12345678 Events per 0.25 GeV 0 20 40 60 80 100 120 140 160 Appearance e νDUNE Normal Ordering = 0.088 13 θ2 2 sin = 0.580 23 θ 2 sin 3.5 years (staged) ) CC e ν + e νSignal ( ) CC e ν + e νBeam ( NC ) CC μ ν + μ ν( ) CC τ ν + τ ν( /2π = - CP δ = 0 CP δ /2π = + CP δ Reconstructed Energy (GeV) 12345678 Events per 0.25 GeV 0 5 10 15 20 25 30 35 40 45 50 Appearance e νDUNE Normal Ordering = 0.088 13 θ2 2 sin = 0.580 23 θ 2 sin 3.5 years (staged) ) CC e ν + e νSignal ( ) CC e ν + e νBeam ( NC ) CC μ ν + μ ν( ) CC τ ν + τ ν( /2π = - CP δ = 0 CP δ /2π = + CP δ Fig. 10 νeand ¯νeappearance spectra: reconstructed energy distribution of selected νeCC-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, suchasneutrinoenergy.Themainsourcesofdetectorsystematic 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 technology 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) 12345678 Events per 0.25 GeV 0 100 200 300 400 500 600 700 800 Disappearance μ νDUNE = 0.580 23 θ 2 sin 2 eV -3 10× = 2.451 32 2 mΔ 3.5 years (staged) CC μ νSignal CC μ ν NC ) CC e ν + e ν( ) CC τ ν + τ ν( Reconstructed Energy (GeV) 12345678 Events per 0.25 GeV 0 50 100 150 200 250 300 350 Disappearance μ νDUNE = 0.580 23 θ 2 sin 2 eV -3 10× = 2.451 32 2 mΔ 3.5 years (staged) CC μ νSignal CC μ ν NC ) CC e ν + e ν( ) CC τ ν + τ ν( Fig. 11 νμand ¯νμdisappearance spectra: reconstructed energy distribution of selected νμCC-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 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-analyzedmuonsfromneutrinointeractionsinthe upstream rock, which is not available with high statistics for the FD. Finally, the reconstruction efficiency will be inherently different due to the relatively small size of the ND. Containment of charged hadrons will be significantly worse at the Table 6 νeand ¯νeappearance rates: integrated rate of selected νeCClike 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 =0andδCP =−π/2 Sample Expected Events δCP =0δCP =−π 2 NO IO NO IO νmode Oscillated νe1155 526 1395 707 Oscillated ¯νe19 33 14 28 Total oscillated 1174 559 1409 735 Beam νe+¯νeCC background 228 235 228 235 NC background 84 84 84 84 ντ+¯ντCC background 36 36 35 36 νμ+¯νμCC background 15 15 15 15 Total background 363 370 362 370 ¯νmode Oscillated νe81 39 95 53 Oscillated ¯νe236 492 164 396 Total oscillated 317 531 259 449 Beam νe+¯νeCC background 145 144 145 144 NC background 40 40 40 40 ντ+¯ντCC background 22 22 22 22 νμ+¯νμCC 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 electromagnetic 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 p2are 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 simulated 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 νμand ¯νμdisappearance 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 νmode νμsignal 7235 7368 ¯νμCC background 542 542 NC background 213 213 ντ+¯ντCC background 53 54 νe+¯νeCC background 9 5 ¯νmode ¯νμsignal 2656 2633 νμCC background 1590 1600 NC background 109 109 ντ+¯ντCC background 31 31 νe+¯νeCC 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 distributions are somewhat non-Gaussian (particularly for θ23), the relative uncertainty is computed using 1/6 of the 3σallowed range from the fit, rather than 1/2 of the 1σrange. For θ23,θ13,andΔm2 31, 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 Δm2 21 7.39×10−5eV22.8 Δm2 32 (NO) 2.451×10−3eV21.3 Δm2 32 (IO) −2.512×10−3eV21.3 ρ2.848 g cm−32 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, including calorimetric based approaches (NOvA, MINERvA) and LArTPCs (LArIAT, MicroBooNE, ArgoNeuT). The DUNE performance is expected to significantly exceed the performance 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 particles. p0,p1,andp2correspond 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±555 e, γ,π02.5 2.5 2.5 n203030 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 recombination model will continue to be validated by the suite of LAr experiments and is not expected to be an issue for nominal 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., CAPTAIN [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,andsignificant reconstruction issues exist,so a large uncertainty (20%) is assigned comparable to the observationsmadeby MINERvA [89]assumingtheyare attributed entirely to the detector model. Selection of photon candidates from π0is also a significant reconstruction challenge, but a recent measurement from MicroBooNE indicates this is possible and the reconstructed π0invariant mass has an uncertainty of 5%, although with some bias [90]. The p1and p2terms 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 absolute scale uncertainties given by the p0terms. 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% uncertainty is assumed on the total fiducial mass, which is conservatively treated as uncorrelated between the νμand νe 123 Eur. Phys. J. C (2020) 80 :978 Page 21 of 34 978 samples due to the potential distortion caused by large electromagnetic showers in the electron sample. These uncertainties 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 acceptance 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 lepton 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 the7 m axis. The acceptance is sensitive to the modeling of muons in the detector. An uncertainty 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 PreviousDUNEsensitivitypredictionshaveusedtheGLoBES 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,¯νμ→¯νμ(Fig. 11), νμ→νe, and Fig. 12 The ratio of post-fit to pre-fit uncertainties for various systematic 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” representing the ith principal flux component, cross-section parameter names are given in Sect. 3, and detector systematics are described in Sect. 7, where the p0,p1and p2parameters are described in Table 9 ¯νμ→¯νe(Fig. 10) FD spectra along with the νμFHC and ¯νμRHC samples from the ND (Fig. 6). In the studies, all oscillation parameters shown in Table 8areallowedtovary. Gaussian penalty terms (taken from Table 8) are applied to θ12 and Δm2 12 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 experiments sensitive to reactor antineutrino disappearance [95– 97]. The remaining parameters, sin2θ23,Δm2 32, 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 Δm2 32, so the constraint on θ13 should be correlated with Δm2 32. 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 allowedto varyinthefit, butareconstrainedbya penaltyterm proportional to the pre-fit uncertainty. ND detector parameters are not allowed to vary in the fit, but their effect is included via a covariance matrix based on the shape difference between ND prediction and the “data” (which comes from the simulation in this sensitivity study). The covariance matrix is constructed with a throwing technique. For each “throw”, all ND energy scale, resolution, and acceptance 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 comparing the resulting spectra with the nominal prediction, in the same binning as is used in the oscillation sensitivity analysis. This choice protects against overconstraining that could occur given the limitations of the parameterized ND reconstruction described in Sect. 4taken 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 loglikelihood ratio, which converges to a χ2at high-statistics [48]: χ2(ϑ,x)=−2logL(ϑ,x) =2 Nbins  iMi(ϑ,x)−Di+Diln Di Mi(ϑ,x) + Nsysts  jΔxj σj2 + NND bins  k NND bins  l (Mk(x)−Dk)V−1 kl (Ml(x)−Dl), (3) where ϑand xare the vector of oscillation parameter and nuisance parameter values respectively; Mi(ϑ,x)and Diare the Monte Carlo (MC) expectation and fake data in the ith reconstructed bin (summed over all selected samples), with the oscillation parameters neglected for the ND; Δxjand σj are the difference between the nominal and current value, and the prior uncertainty on the jth nuisance parameter with uncertainties evaluated and described in Sects. 2,3and 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 χ2value is taken as the minimum. Two approaches are used for the sensitivity studies presented 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 uncerTable 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 3σallowed range Parameter Prior Range sin2θ23 Uniform [0.4; 0.6] |Δm2 32|(×10−3eV2) 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 Gaussian 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, oscillation 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 bestfit 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 likelihood ratio as the test statistic: Δχ2=χ2 B−χ2 A,(4) where χ2 Band χ2 Aare both obtained from Eq. (3), using a coherent systematic and statistical throw. The size of Δχ2is 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 χ2 IO −χ2 NO. Note that the Δχ2for the mass orderingmaybe negative,dependingonhow the test issetup. The sensitivity for discovering CPV is the preference for the CP violating hypothesis over the CP conserving hypothesis, χ2 0,π −χ2 CPV. 123 Eur. Phys. J. C (2020) 80 :978 Page 23 of 34 978 Post-fit uncertainties on systematic parameters are shown forAsimovfitsat the NuFITbest-fitpoint to boththeND+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 detector parameters as it breaks degeneracies with other parameters. Several important cross-section uncertainties are also not constrained by the ND. In particular, an uncertainty on the ratio of νμto νecross sections is totally unconstrained, which is not surprising given the lack of ND νesamples in the current analysis. The most significant flux terms are constrained 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 preand post-fit systematic uncertainties 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 constraint 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 normal 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 scenarios 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 uncertainties, ∼300,000 throws were used to calculate the sensitivity 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 1σuncertainty 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. 8to investigate their effect on the sensitivity. This sensiFig. 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 preand 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 sensitivity reaches 5σfor 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 5σfor 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 NOwhenthetruevaluesofθ23,θ13,andΔm2 32 varywithinthe 3σrangeallowedbyNuFIT.Thelargesteffectisthevariation 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 Δm2 32 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 throwsareusedtosimulate 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 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 convertedto years using the staging scenario describedin Sect.6. The width of the bands show the impact of applying an exterFig. 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 Δm2 32 (bottom), which correspond to their 3σNuFIT 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 sin2θ23 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 sin2θ23 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 throwsareusedtosimulate 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 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 bepaid to thestatistical interpretation ofneutrinomass ordering sensitivities [99–101] because the Δχ2metric does not follow the expected chi-square function for one degree of freedom, so the interpretation of the Δχ2as 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 32 of 34 Eur. Phys. J. C (2020) 80 :978 15. T2K Collaboration, K. Abe et al., Constraint on the matterantimatter symmetry-violating phase in neutrino oscillations. 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