Impact of cross-section uncertainties on supernova neutrino spectral parameter fitting in the Deep Underground Neutrino Experiment

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Impact of cross-section uncertainties on supernova neutrino spectral parameter fitting in the Deep Underground Neutrino Experiment © Published by the American Physical Society Published version DUNE Collaboration DUNE Collaboration. (2023). Impact of cross-section uncertainties on supernova neutrino spectral parameter fitting in the Deep Underground Neutrino Experiment. Physical Review D, 107, Article 112012. https://doi.org/10.1103/PhysRevD.107.112012 2023 Impact of cross-section uncertainties on supernova neutrino spectral parameter fitting in the Deep Underground Neutrino Experiment A. Abed Abud,34 B. Abi,160 R. Acciarri,66 M. A. Acero,11 M. R. Adames,199 G. Adamov,72 M. Adamowski,66 D. 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Gallagher,206 PHYSICAL REVIEW D 107, 112012 (2023) 2470-0010=2023=107(11)=112012(25) 112012-1 Published by the American Physical Society A. Gallas,164 N. Gallice,99,145 V. Galymov,111 E. Gamberini,34 T. Gamble,188 F. Ganacim,199 R. Gandhi,78 S. Ganguly,66 F. Gao,172 S. Gao,19 D. Garcia-Gamez,73 M. Á. García-Peris,84 S. Gardiner ,66 D. Gastler,17 A. Gauch,13 J. Gauvreau,157 P. Gauzzi,186,104 G. Ge,44 N. Geffroy,52 B. Gelli,29 S. Gent,192 L. Gerlach,19 Z. Ghorbani-Moghaddam,96 P. Giammaria,29 T. Giammaria,94,67 N. Giangiacomi,205 D. Gibin,162,101 I. Gil-Botella,38 S. Gilligan,159 A. Gioiosa,103 S. Giovannella,95 C. Girerd,111 A. K. Giri,90 C. Giugliano,94 D. Gnani,130 O. Gogota,128 S. Gollapinni,133 K. Gollwitzer,66 R. A. Gomes,63 L. V. Gomez Bermeo,187 L. S. Gomez Fajardo,187 F. Gonnella,15 D. Gonzalez-Diaz,85 M. Gonzalez-Lopez,136 M. C. Goodman,7O. Goodwin,138 S. Goswami,170 C. Gotti,98 J. Goudeau,134 E. Goudzovski,15 C. Grace,130 R. Gran,146 E. Granados,77 P. Granger,165 C. 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Tenti,92 K. Terao,189 F. Terranova,98,144 G. Testera,96 T. Thakore,39 A. Thea,182 A. Thompson,201 C. Thorn,19 S. C. Timm,66 V. Tishchenko,19 N. Todorović,156 L. Tomassetti,94,67 A. Tonazzo,165 D. Torbunov,19 M. Torti,98,144 M. Tortola,84 F. Tortorici,93,30 N. Tosi,92 D. Totani,26 M. Toups,66 C. Touramanis,132 R. Travaglini,92 J. Trevor,27 S. Trilov,18 W. H. Trzaska,121 Y. Tsai,23 Y.-T. Tsai,189 Z. Tsamalaidze,72 K. V. Tsang,189 N. Tsverava,72 S. Z. Tu,116 S. Tufanli,34 C. Tull,130 J. Turner,57 M. Tuzi,84 J. Tyler,122 E. Tyley,188 M. Tzanov,134 M. A. Uchida,28 J. Urheim,91 T. Usher,189 H. Utaegbulam,198 S. Uzunyan,153 M. R. Vagins,123,23 P. Vahle,217 S. Valder,197 G. D. A. Valdiviesso,62 E. Valencia,77 R. Valentim,207 Z. Vallari,27 E. Vallazza,98 J. W. F. Valle,84 S. Vallecorsa,34 R. Van Berg,168 R. G. Van de Water,133 D. Vanegas Forero,141 F. Varanini,101 D. Vargas Oliva,205 G. Varner,79 S. Vasina,120 N. Vaughan,159 K. Vaziri,66 J. Vega,45 S. Ventura,101 A. Verdugo,38 S. Vergani,28 M. A. Vermeulen,150 M. Verzocchi,66 M. Vicenzi,96,71 H. Vieira de Souza,165 C. Vignoli,75 C. Vilela,34 B. Viren,19 A. Vizcaya-Hernandez,43 T. Vrba,49 Q. Vuong,179 A. V. Waldron,176 M. Wallbank,39 J. Walsh,143 T. Walton,66 H. Wang,24 J. Wang,191 L. Wang,130 M. H. L. S. Wang,66 X. Wang,66 Y. Wang,24 K. Warburton,110 D. Warner,43 M. O. Wascko,88 D. Waters,209 A. Watson,15 IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-3 K. Wawrowska,182,197 P. Weatherly,55 A. Weber,137,66 M. Weber,13 H. Wei,134 A. Weinstein,110 D. Wenman,218 M. Wetstein,110 J. Whilhelmi,219 A. White,203 A. White,219 L. H. Whitehead,28 D. Whittington,198 M. J. Wilking,194 A. Wilkinson,209 C. Wilkinson,130 Z. Williams,203 F. Wilson,182 R. J. Wilson,43 W. Wisniewski,189 J. Wolcott,206 J. Wolfs,179 T. Wongjirad,206 A. Wood,80 K. Wood,130 E. Worcester,19 M. Worcester,19 M. Wospakrik,66 K. Wresilo,28 C. Wret,179 S. Wu,147 W. Wu,66 W. Wu,23 M. Wurm,137 J. Wyenberg,54 Y. Xiao,23 I. Xiotidis,88 B. Yaeggy,39 N. Yahlali,84 E. Yandel,26 G. Yang,194 K. Yang,160 T. Yang,66 A. Yankelevich,23 N. Yershov,107 K. Yonehara,66 Y. S. Yoon,37 T. Young,152 B. Yu,19 H. Yu,19 H. Yu,195 J. Yu,203 Y. Yu,87 W. Yuan,58 R. Zaki,221 J. Zalesak,48 L. Zambelli,52 B. Zamorano,73 A. Zani,99 L. Zazueta,217 G. P. Zeller,66 J. Zennamo,66 K. Zeug,218 C. Zhang,19 S. Zhang,91 Y. Zhang,172 M. Zhao,19 E. Zhivun,19 E. D. Zimmerman,42 S. Zucchelli,92,16 J. Zuklin,48 V. Zutshi,153 and R. Zwaska66 (The DUNE Collaboration) 1Abilene Christian University, Abilene, Texas 79601, USA 2University of Albany, SUNY, Albany, New York 12222, USA 3University of Amsterdam, NL-1098 XG Amsterdam, The Netherlands 4Antalya Bilim University, 07190 Döşemealtı/Antalya, Turkey 5University of Antananarivo, Antananarivo 101, Madagascar 6Universidad Antonio Nariño, Bogotá, Colombia 7Argonne National Laboratory, Argonne, Illinois 60439, USA 8University of Arizona, Tucson, Arizona 85721, USA 9Universidad Nacional de Asunción, San Lorenzo, Paraguay 10University of Athens, Zografou GR 157 84, Greece 11Universidad del Atlántico, Barranquilla, Atlántico, Colombia 12Augustana University, Sioux Falls, South Dakota 57197, USA 13University of Bern, CH-3012 Bern, Switzerland 14Beykent University, Istanbul, Turkey 15University of Birmingham, Birmingham B15 2TT, United Kingdom 16Universit`a del Bologna, 40127 Bologna, Italy 17Boston University, Boston, Massachusetts 02215, USA 18University of Bristol, Bristol BS8 1TL, United Kingdom 19Brookhaven National Laboratory, Upton, New York 11973, USA 20University of Bucharest, Bucharest, Romania 21University of California Berkeley, Berkeley, California 94720, USA 22University of California Davis, Davis, California 95616, USA 23University of California Irvine, Irvine, California 92697, USA 24University of California Los Angeles, Los Angeles, California 90095, USA 25University of California Riverside, Riverside California 92521, USA 26University of California Santa Barbara, Santa Barbara, California 93106 USA 27California Institute of Technology, Pasadena, California 91125, USA 28University of Cambridge, Cambridge CB3 0HE, United Kingdom 29Universidade Estadual de Campinas, Campinas, São Paoulo 13083-970, Brazil 30Universit`a di Catania, 2–95131 Catania, Italy 31Universidad Católica del Norte, Antofagasta, Chile 32Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro 22290-180, Brazil 33IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France 34CERN, The European Organization for Nuclear Research, 1211 Meyrin, Switzerland 35Institute of Particle and Nuclear Physics of the Faculty of Mathematics and Physics of the Charles University, 180 00 Prague 8, Czech Republic 36University of Chicago, Chicago, Illinois 60637, USA 37Chung-Ang University, Seoul 06974, South Korea 38CIEMAT, Centro de Investigaciones Energ´eticas, Medioambientales y Tecnológicas, E-28040 Madrid, Spain 39University of Cincinnati, Cincinnati, Ohio 45221, USA 40Centro de Investigación y de Estudios Avanzados del Instituto Polit´ecnico Nacional (Cinvestav), Mexico City, Mexico 41Universidad de Colima, Colima, Mexico 42University of Colorado Boulder, Boulder, Colorado 80309, USA 43Colorado State University, Fort Collins, Colorado 80523, USA 44Columbia University, New York, New York 10027, USA A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-4 45Comisión Nacional de Investigación y Desarrollo Aeroespacial, Lima, Peru 46Centro de Tecnologia da Informacao Renato Archer, Amarais Campinas, São Paulo, CEP 13069-901, Brazil 47Central University of South Bihar, Gaya 824236, India 48Institute of Physics, Czech Academy of Sciences, 182 00 Prague 8, Czech Republic 49Czech Technical University, 115 19 Prague 1, Czech Republic 50Dakota State University, Madison, South Dakota 57042, USA 51University of Dallas, Irving, Texas 75062-4736, USA 52Laboratoire d’Annecy de Physique des Particules, University Grenoble Alpes, University Savoie Mont Blanc, CNRS, LAPP-IN2P3, 74000 Annecy, France 53Daresbury Laboratory, Cheshire WA4 4AD, United Kingdom 54Dordt University, 700 7th Street NE, Sioux Center, Iowa 51250, USA 55Drexel University, Philadelphia, Pennsylvania 19104, USA 56Duke University, Durham, North Carolina 27708, USA 57Durham University, Durham DH1 3LE, United Kingdom 58University of Edinburgh, Edinburgh EH8 9YL, United Kingdom 59Universidad EIA, Envigado, Antioquia, Colombia 60Eötvös Loránd University, 1053 Budapest, Hungary 61Faculdade de Ciências da Universidade de Lisboa—FCUL, 1749-016 Lisboa, Portugal 62Universidade Federal de Alfenas, Poços de Caldas, Minas Gerais 37715-400, Brazil 63Universidade Federal de Goias, Goiania, Goiás 74690-900, Brazil 64Universidade Federal do ABC, Santo Andr´e, São Paulo 09210-580, Brazil 65Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-901, Brazil 66Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 67University of Ferrara, Ferrara, Italy 68University of Florida, Gainesville, Florida 32611-8440, USA 69Florida State University, Tallahassee, Florida, USA 70Fluminense Federal University, 9 Icaraí Niterói, Rio de Janeiro 24220-900, Brazil 71Universit`a degli Studi di Genova, Genova, Italy 72Georgian Technical University, Tbilisi, Georgia 73University of Granada and CAFPE, 18002 Granada, Spain 74Gran Sasso Science Institute, L’Aquila, Italy 75Laboratori Nazionali del Gran Sasso, L’Aquila, Italy 76University Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France 77Universidad de Guanajuato, Guanajuato 37000, Mexico 78Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India 79University of Hawaii, Honolulu, Hawaii 96822, USA 80University of Houston, Houston, Texas 77204, USA 81University of Hyderabad, Gachibowli, Hyderabad 500 046, India 82Idaho State University, Pocatello, Idaho 83209, USA 83Institut de Física d’Altes Energies (IFAE)—Barcelona Institute of Science and Technology (BIST), Barcelona, Spain 84Instituto de Física Corpuscular, CSIC and Universitat de Val`encia, 46980 Paterna, Valencia, Spain 85Instituto Galego de Física de Altas Enerxías, University of Santiago de Compostela, Santiago de Compostela 15782, Spain 86Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India 87Illinois Institute of Technology, Chicago, Illinois 60616, USA 88Imperial College of Science Technology and Medicine, London SW7 2BZ, United Kingdom 89Indian Institute of Technology Guwahati, Guwahati, 781 039, India 90Indian Institute of Technology Hyderabad, Hyderabad, 502285, India 91Indiana University, Bloomington, Indiana 47405, USA 92Istituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna, Italy 93Istituto Nazionale di Fisica Nucleare Sezione di Catania, I-95123 Catania, Italy 94Istituto Nazionale di Fisica Nucleare Sezione di Ferrara, I-44122 Ferrara, Italy 95Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Frascati, Frascati, Roma, Italy 96Istituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genova GE, Italy 97Istituto Nazionale di Fisica Nucleare Sezione di Lecce, 73100 Lecce, Italy 98Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3—I-20126 Milano, Italy 99Istituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milano, Italy 100Istituto Nazionale di Fisica Nucleare Sezione di Napoli, I-80126 Napoli, Italy IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-5 101Istituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padova, Italy 102Istituto Nazionale di Fisica Nucleare Sezione di Pavia, I-27100 Pavia, Italy 103Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Pisa, Pisa, Italy 104Istituto Nazionale di Fisica Nucleare Sezione di Roma, 00185 Roma, Italy 105Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy 106Universidad Nacional de Ingeniería, Lima 25, Peru 107Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia 108University of Insubria, Via Ravasi, 2, 21100 Varese, Italy 109University of Iowa, Iowa City, Iowa 52242, USA 110Iowa State University, Ames, Iowa 50011, USA 111Institut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France 112Institute for Research in Fundamental Sciences, Tehran, Iran 113Instituto Superior T´ecnico—IST, Universidade de Lisboa, Lisboa, Portugal 114Instituto Tecnológico de Aeronáutica, São Jos´e dos Campos, Brazil 115Iwate University, Morioka, Iwate 020-8551, Japan 116Jackson State University, Jackson, Missouri 39217, USA 117University of Jammu, Jammu 180006, India 118Jawaharlal Nehru University, New Delhi 110067, India 119Jeonbuk National University, Jeonrabuk-do 54896, South Korea 120Joint Institute for Nuclear Research, Dzhelepov Laboratory of Nuclear Problems 6 Joliot-Curie, Dubna, Moscow Region 141980, Russia 121University of Jyväskylä, FI-40014 Jyväskylä, Finland 122Kansas State University, Manhattan, Kansas 66506, USA 123Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan 124High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan 125Korea Institute of Science and Technology Information, Daejeon 34141, South Korea 126K L University, Vaddeswaram, Andhra Pradesh 522502, India 127National Institute of Technology, Kure College, Hiroshima 737-8506, Japan 128Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine 129Lancaster University, Lancaster LA1 4YB, United Kingdom 130Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 131Laboratório de Instrumentação e Física Experimental de Partículas, 1649-003 Lisboa and 3004-516 Coimbra, Portugal 132University of Liverpool, Liverpool L69 7ZE, United Kingdom 133Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 134Louisiana State University, Baton Rouge, Louisiana 70803, USA 135University of Lucknow, Uttar Pradesh 226007, India 136Madrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain 137Johannes Gutenberg-Universität Mainz, 55122 Mainz, Germany 138University of Manchester, Manchester M13 9PL, United Kingdom 139Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 140Max-Planck-Institut, Munich 80805, Germany 141University of Medellín, Medellín 050026, Colombia 142University of Michigan, Ann Arbor, Michigan 48109, USA 143Michigan State University, East Lansing, Michigan 48824, USA 144Universit`a del Milano-Bicocca, 20126 Milano, Italy 145Universit`a degli Studi di Milano, I-20133 Milano, Italy 146University of Minnesota Duluth, Duluth, Minnesota 55812, USA 147University of Minnesota Twin Cities, Minneapolis, Minnesota 55455, USA 148University of Mississippi, University, Mississippi 38677, USA 149Universit`a degli Studi di Napoli Federico II, 80138 Napoli, Italy 150Nikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, Netherlands 151National Institute of Science Education and Research (NISER), Odisha 752050, India 152University of North Dakota, Grand Forks, North Dakota 58202-8357, USA 153Northern Illinois University, DeKalb, Illinois 60115, USA 154Northwestern University, Evanston, Illinois 60208, USA 155University of Notre Dame, Notre Dame, Indiana 46556, USA 156University of Novi Sad, 21102 Novi Sad, Serbia 157Occidental College, Los Angeles, California 90041, USA 158Ohio State University, Columbus, Ohio 43210, USA A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-6 159Oregon State University, Corvallis, Oregon 97331, USA 160University of Oxford, Oxford OX1 3RH, United Kingdom 161Pacific Northwest National Laboratory, Richland, Washington 99352, USA 162Universt`a degli Studi di Padova, I-35131 Padova, Italy 163Panjab University, Chandigarh 160014, India 164Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France 165Universit´e Paris Cit´e, CNRS, Astroparticule et Cosmologie, Paris, France 166University of Parma, 43121 Parma, Italy 167Universit`a degli Studi di Pavia, 27100 Pavia, Italy 168University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 169Pennsylvania State University, University Park, Pennsylvania 16802, USA 170Physical Research Laboratory, Ahmedabad 380 009, India 171Universit`a di Pisa, I-56127 Pisa, Italy 172University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA 173Pontificia Universidad Católica del Perú, Lima, Perú 174University of Puerto Rico, Mayaguez 00681, Puerto Rico, USA 175Punjab Agricultural University, Ludhiana 141004, India 176Queen Mary University of London, London E1 4NS, United Kingdom 177Radboud University, NL-6525 AJ Nijmegen, Netherlands 178Rice University, Houston, Texas 77005, USA 179University of Rochester, Rochester, New York 14627, USA 180Royal Holloway College London, London TW20 0EX, United Kingdom 181Rutgers University, Piscataway, New Jersey 08854, USA 182STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom 183Universit`a del Salento, 73100 Lecce, Italy 184San Jose State University, San Jose, California 95192-0106, USA 185Universidade Estadual de Santa Cruz, CEP 45662-000, Ilheús, Bahia, Brazil 186Sapienza University of Rome, 00185 Rome, Italy 187Universidad Sergio Arboleda, 11022 Bogotá, Colombia 188University of Sheffield, Sheffield S3 7RH, United Kingdom 189SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA 190University of South Carolina, Columbia, South Carolina 29208, USA 191South Dakota School of Mines and Technology, Rapid City, South Dakota 57701, USA 192South Dakota State University, Brookings, South Dakota 57007, USA 193Southern Methodist University, Dallas, Texas 75275, USA 194Stony Brook University, SUNY, Stony Brook, New York 11794, USA 195Sun Yat-Sen University, Guangzhou 510275, China 196Sanford Underground Research Facility, Lead, South Dakota 57754, USA 197University of Sussex, Brighton BN1 9RH, United Kingdom 198Syracuse University, Syracuse, New York 13244, USA 199Universidade Tecnológica Federal do Paraná, Curitiba, Brazil 200Tel Aviv University, Tel Aviv-Yafo, Israel 201Texas A&M University, College Station, Texas 77840, USA 202Texas A&M University—Corpus Christi, Corpus Christi, Texas 78412, USA 203University of Texas at Arlington, Arlington, Texas 76019, USA 204University of Texas at Austin, Austin, Texas 78712, USA 205University of Toronto, Toronto, Ontario M5S 1A1, Canada 206Tufts University, Medford, Massachusetts 02155, USA 207Universidade Federal de São Paulo, 09913-030 São Paulo, Brazil 208Ulsan National Institute of Science and Technology, Ulsan 689-798, South Korea 209University College London, London WC1E 6BT, United Kingdom 210Valley City State University, Valley City, North Dakota 58072, USA 211Variable Energy Cyclotron Centre, 700 064 West Bengal, India 212Virginia Tech, Blacksburg, Virginia 24060, USA 213University of Warsaw, 02-093 Warsaw, Poland 214University of Warwick, Coventry CV4 7AL, United Kingdom 215Wellesley College, Wellesley, Massachusetts 02481, USA 216Wichita State University, Wichita, Kansas 67260, USA 217William and Mary, Williamsburg, Virginia 23187, USA 218University of Wisconsin Madison, Madison, Wisconsin 53706, USA IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-7 219Yale University, New Haven, Connecticut 06520, USA 220Yerevan Institute for Theoretical Physics and Modeling, Yerevan 0036, Armenia 221York University, Toronto, Ontario M3J 1P3, Canada (Received 3 April 2023; accepted 12 May 2023; published 29 June 2023) A primary goal of the upcoming Deep Underground Neutrino Experiment (DUNE) is to measure the Oð10ÞMeV neutrinos produced by a Galactic core-collapse supernova if one should occur during the lifetime of the experiment. The liquid-argon-based detectors planned for DUNE are expected to be uniquely sensitive to the νecomponent of the supernova flux, enabling a wide variety of physics and astrophysics measurements. A key requirement for a correct interpretation of these measurements is a good understanding of the energy-dependent total cross section σðEνÞfor charged-current νeabsorption on argon. In the context of a simulated extraction of supernova νespectral parameters from a toy analysis, we investigate the impact of σðEνÞmodeling uncertainties on DUNE’s supernova neutrino physics sensitivity for the first time. We find that the currently large theoretical uncertainties on σðEνÞmust be substantially reduced before the νeflux parameters can be extracted reliably; in the absence of external constraints, a measurement of the integrated neutrino luminosity with less than 10% bias with DUNE requires σðEνÞto be known to about 5%. The neutrino spectral shape parameters can be known to better than 10% for a 20% uncertainty on the cross-section scale, although they will be sensitive to uncertainties on the shape of σðEνÞ. A direct measurement of low-energy νe-argon scattering would be invaluable for improving the theoretical precision to the needed level. DOI: 10.1103/PhysRevD.107.112012 I. INTRODUCTION A massive star (M>8M⊙) employs nuclear fusion to sustain itself by first consuming lighter elements such as hydrogen and helium and later consuming heavier elements. In the canonical narrative, at the end of the star’s lifetime, the innermost nickel-iron core can no longer undergo nuclear fusion. Gravity causes the core to collapse into a protoneutron star. Neutron degeneracy stalls the collapse; the core rebounds and produces shock waves which propagate outward from the core. Once the shock waves breach the surface of the star, they expel stellar material and leave behind a compact remnant. This process is referred to as a core-collapse supernova. A core collapse releases 99% of the star’s gravitational potential energy via neutrinos in a prompt burst lasting several seconds [1]. While the protoneutron star traps photons and other particles with electromagnetic and strong interactions, neutrinos easily escape because they interact weakly. The neutrino flux is expected to contain interesting signatures related to different phenomena occurring during a core-collapse supernova [2–6], including insight into the explosion mechanism. While the neutrinos detected from SN1987A [7–10] did help to confirm the basic outline of the core-collapse supernova process, they did not provide tight constraints on astrophysical models. Additional neutrino signals from core-collapse supernovae observed in detectors worldwide [11] will provide data to study the mechanism behind the core collapse, as well as information on the properties of neutrinos themselves. Obtaining a high-statistics measurement of core-collapse supernova neutrinos is among the primary physics goals for the Deep Underground Neutrino Experiment (DUNE). To detect these low-energy neutrinos, DUNE will utilize its far detector (relative to the beam at Fermilab) located 1.5 km underground at the Sanford Underground Research Facility in South Dakota. The DUNE far detector is currently planned to consist of four liquid argon time-projection chambers (LArTPCs) each with a total volume of around seventeen kilotons [12]. These LArTPC detectors will be sensitive to interactions of neutrinos in the few tens of MeV range [13]. Among large neutrino experiments, DUNE will be uniquely sensitive to the νecomponent of the supernova signal via the charged-current reaction νeþ40Ar →e−þ40K:ð1Þ Theνecomponentofthe supernovaneutrinofluxisexpected to contain unique features which make its future detection with DUNE a valuable scientific opportunity [12]. The neutrinos generated by a core-collapse supernova have much lower energies (few to tens of MeV) than the GeV-scale neutrino beams of interest for DUNE’s accelerator-based oscillation physics program. Below 100 MeV, no measurements of charged-current neutrino-argon cross Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-8 β-amplitude and the level density of the Fermi gas model corrected to take into account shell effects. The GTBD calculation considers only the contributions of allowed transitions, σðEν;0þÞand σðEν;1þÞ, with a realistic description of the energy of the GT resonance peak [45,46]. Third, some calculations use an effective (or quenched) value of the nucleon axial-vector coupling constant for which its bare value gA¼1.2756 from the experimental data [33] is multiplied by a factor of around 0.8. There is still a lack of consensus in the nuclear physics community about whether this quenching is needed. For the family of models considered in this paper, the RPA calculations do not use a renormalization of gA[39], while the RQRPA model used gA¼1. The PQRPA calculations also adopted gA¼1to be consistent with comparisons of 2s1d and 2p1f shellmodel predictions with measured allowed β-decay rates [50] and with recent double-beta decay calculations. The QRPA calculations reported in Ref. [43] use a universal quenching factor fq¼geff A=gA¼0.74 to reproduce measured GT strength distributions. The NSM þRPA calculations within the VMU potential used a similar quenching factor fq¼0.775 with gA¼1.263. This choice enabled the NSM þRPA model to describe the experimental cumulative sum of the GT strength rather well. On the other hand, recent studies on variations of gAin the GTBD have shown that best results for a set of 94 nuclei of interest are obtained with gA¼1[51]. The GT distribution used for the NSM þRPA calculation is shifted toward higher energy values with significantly smaller strengths for <10 MeV neutrino energies, resulting in a characteristic cutoff at energies below about 8 MeV. Despite the differences explored above, the main features of measured weak-interaction observables, such as β-decay strengths and inclusive muon capture rates, are reasonably well described for multiple nuclei by the majority of the nuclear structure models considered herein. By incorporating these cross-section models into our SNO w GL o BES calculations, we studied the impact of variations in the shape of σðEνÞon the simulated measurements of supernova neutrino flux parameters. Many of the cross section models required reformatting with extra data points for usage in SNO w GL o BES ; Appendix Aprovides more details on the interpolation procedure that was used. Figures 6and 7show that the cross-section models differ considerably and lead to a wide range of predictions for the supernova νesignal in DUNE. Appendix Bprovides a table of the corresponding event rates as output by SNO w GL o BES (see Table IV). Figure 8shows representative expected event rates in DUNE for the CC νe−40Ar absorption process and a supernova at a distance of 10 kpc from Earth. The large differences in the cross-section model predictions at low neutrino energy translate to large variations in the plotted observed energy distributions. Apart from effects of cross-section mismodeling (which are considered in the next section), the expected statistical uncertainty on the event rate has a strong effect on the precision with which the supernova flux parameter values may be measured. The sensitivity regions shown in Fig. 9are obtained by considering the statistical uncertainty and using the same cross-section model to generate the fake data and extract the results. The GTBD cross section model, which predicts 7770 νeCC events, results in the tightest constraints on the flux parameters. The QRPA-C model predicts 1383 events and thus provides the loosest constraints. B. Cross-section normalization uncertainty As a first examination of the impact of cross-section uncertainties on the extraction of supernova flux parameters from a future DUNE data set, we consider model variations thatinvolvetheapplicationofaconstantoverallscalingfactor. These variations shift a plot of σðEνÞvertically while leaving the shape unchanged (see Fig. 10). We adopt as a reference model a cross section from MARLEY version 1.2.0 [31,52]. The data-driven nuclear matrix elements in this model were obtained from a measurement of very forward ðp; nÞ scattering reported in Ref. [49]. The unaltered reference model is used together with versions changed by factors of ð5to20Þ%in 5% steps, 50%, and þ100%. This procedure yields a total of twelve unique cross-section models, and those models generate different true spectra and grids that we used as input into the forward-fitting algorithm. Figure 11 shows sensitivity regions for a 10 kpc supernova, the true scenario outlined in Sec. II F, and three different sets of assumptions. The sensitivity regions shift 10 20 30 40 50 Observed Energy (MeV) 0 20 40 60 80 100 120 140 160 180 Events per 0.5 MeV GTBD NSM+RPA MARLEY Bhattacharya (2009) QRPA-S QRPA-C FIG. 8. SNO w GL o BES event rates for select cross-section calculations from Refs. [31,41,43–46]. The initial fluence parameter values for νeare ðα0;hEνi0;ε0Þ¼ð2.5;9.5MeV;5×1052 ergsÞ, for ¯ νeare ðα0;hEνi0;ε0Þ¼ð2.5;12.0MeV;5×1052 ergsÞ, and for νxare ðα0;hEνi0;ε0Þ¼ð2.5;15.6MeV;5×1052 ergsÞ. Normal mass ordering and MSW resonance were assumed. Note that “QRPA-C”and “QRPA-S”contain the same type of calculation performed by different groups, with the former by Cheoun et al. [43] and the latter by Samana and dos Santos [44]. More details about the various models are provided in Table I. The error bars are statistical. IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-15 for changes in ε; the cross-section scaling factors affect the statistics and thus ε. The sensitivity regions shift vertically for change in cross-section normalization, with near-negligible shape change, as expected. Figure 12 shows the bias in the best-fit parameter values for each possible combination of true cross-section model (i.e., the model used to simulate the fake dataset) and assumed cross-section model (i.e., the model used to perform the parameter fits). The best fit within the grid bounds is determined, and that constraint can introduce an artificial bias to the best fit once a boundary is reached for one or more parameters. The results are shown separately for α,hEνi, and ε. For each parameter, a two-dimensional histogram is plotted in which each bin represents a particular combination of cross-section models. The color of the bin represents the bias value, i.e., the fractional difference between the best-fit parameter value and its true value. We first notice that the biases on αand hEνiare relatively small unless the assumptions significantly differ from reality. If we assume an enhanced cross section (using positive scaling factors), the large mismatch in statistics causes an εunderestimation. The difference in statistics forces the algorithm to select lower εvalues. If we assume a reduced cross section (using negative scaling factors), we expect a lower event rate than we actually observe; thus the forward-fitting algorithm prefers higher εvalues to compensate for the discrepancy. When the algorithm reaches a boundary (i.e., at the minimum or maximum εvalue allowed), the biases in αand hEνiwill increase to compensate for spectral shape differences between the true spectrum and grid elements. C. Combined cross-section normalization and shape uncertainty To characterize the impact of using an inaccurate crosssection model to extract values of the supernova flux parameters, we consider scenarios in which different combinations of the theoretical models described in Sec. III A are used to (1) simulate a fake data set, and (2) perform fits of the flux parameters. Figure 13 displays the 2D bias plots for the different combinations of assumed and true total cross-section models. A logarithmic color scale is used for εdue to the very large range of biases allowed for that parameter. In the 2D plots, the crosssection models are ordered along each histogram axis from 6 8 10 12 14 16 18 20 (MeV)² Q E¢ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H with different assumed scenarios True cross section: Bhattacharya (2009) +15% MARLEY Bhattacharya (2009) -15% = 5e52 ergH = 9.5 MeV, ² Q E¢Truth: FIG. 11. Sensitivity regions (90% C.L.) for a 10 kpc supernova to study different combinations of assumed and true total cross section normalizations. 20 40 60 80 100 Energy (MeV) 5 10 4 10 3 10 2 10 1 10 1 ) 2 cm -38 Cross Section (10 Bhattacharya 2009 10% r 20% r 50% r FIG. 10. νe−40Ar cross section versus energy with various scaling factors applied. Reference [31] provided the cross-section model using nuclear matrix element data from Ref. [49]. 6 8 10 12 14 16 18 (MeV)² Q E¢ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H section models are the same The grid and true spectrum cross MARLEY Bhattacharya (2009) QRPA-S GTBD = 5e52 ergH = 9.5 MeV, ² Q E¢Truth: FIG. 9. Sensitivity regions (90% C.L.) in ðhEνi;εÞspace generated from the cross-section models in Refs. [31,44,45]. Only statistical uncertainties are considered. In each case, the same cross-section model is used both to produce the fake data and to calculate the sensitivity region. A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-16 Assumed Cross Section Model True Cross Section Model 6.39 11.2 1.72 3.48 0 0.65 -0.65 FIG. 13. 2D fractional difference plots to study effects produced by different cross section models. Note that “S”stands for the cross section model implemented into SNO w GL o BES [29]. Also note that the εcolor-scale is log to account for the wide range of values. The number scale shows the raw fractional difference values to conform with the αand hEνiplots. Assumed Cross Section Scaling Factor True Cross Section Scaling Factor FIG. 12. 2D fractional difference plots to study effects produced by normalization uncertainties on the total cross section. IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-17 smallest to largest expected number of events integrated over a neutrino-energy range of [5, 15] MeV. Appendix B also contains the numerical values for the expected event counts for each model in the [5, 15] MeV range. Further insight into cross-section model effects on the extraction of supernova neutrino flux parameters can be gained from Fig. 14, which shows sensitivity regions computed based on a fake dataset produced using the MARLEY B 2009 cross-section model. When supernova flux parameters are extracted using the same cross-section model (red sensitivity regions), the best-fit values (red stars) are identical to the true ones by construction. A small bias is seen when the extraction procedure is repeated using the MARLEY L 1998 model (black stars). However, the difference between the assumed (L 1998) and true (B 2009) cross sections is small enough that the gray sensitivity regions obtained from the new fit cover the true parameter values in all cases. A more problematic bias (green stars) is seen when the fit is repeated using the PQRPA model as the assumed cross section. In this case, the difference between the PRQPA and MARLEY B 2009 predictions is large enough to lead to green sensitivity regions which do not enclose the true results. This bias would need to be corrected in the context of a real analysis by introducing a cross-section-related systematic uncertainty to inflate the sensitivity regions. The significant corresponding loss of precision can be visually estimated from Fig. 14 by examining the degree to which the green sensitivity regions “miss”the red star that represents the true parameter values. Some general trends were seen in the course of these fake data studies. If the cross-section model used for fitting gives higher values than the true one used to generate the fake data, then the fitting algorithm tends to overestimate αand hEνiwhile underestimating ε. Because εis directly proportional to the expected number of events, the best-fit value of εis driven lower for fake data sets with low statistics. D. Total cross-section uncertainty envelope The cross-section models considered above are not expected to produce results of equal quality in the energy region of interest for supernova neutrinos (see, e.g., the discussion in the supplemental materials from Ref. [16]), and furthermore, uncertainties are typically not available for them. As a means of assigning a theoretical uncertainty which neglects implausibly extreme variations, we consider the spread between three cross-section predictions; the partially data-driven MARLEY models [31], the NSM þ RPA calculation [41], and the QRPA-S calculation [44].In the absence of a direct measurement of the νecapture process on argon, we selected this subset of the available models based upon purely a priori considerations. Predictions from our chosen subset of cross-section models are shown in Fig. 15. An uncertainty envelope defined as the range between the minimum and maximum 6 8 10 12 14 16 18 20 (MeV)² Q E¢ 1 2 3 4 5 6 7 D with different assumed scenarios True cross section: Bhattacharya (2009) MARLEY Liu (1998) MARLEY Bhattacharya (2009) PQRPA 6 8 10 12 14 16 18 20 (MeV)² Q E¢ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H 1234567 D 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H FIG. 14. Sensitivity regions (90% C.L.) calculated with different assumed cross-section models for a fake data set generated using the MARLEY B 2009 model. The stars mark the best-fit measurements from the fitting algorithm. The red stars also indicate the true parameter values, i.e., when the assumed cross section model is identical to the true model. A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-18 cross-section predictions from this subset of models is also shown as the crosshatched region. Predicted supernova neutrino event rates in DUNE for each of the models used to define the envelope are displayed in Fig. 16. With a restricted range of cross-section variations defined in this way, we repeated our fake data studies using a new family of toy cross section models. The lower (Min) and upper (Max) bounds of the uncertainty envelope were treated as two of the new models, and the MARLEY B 2009 cross section [32] was treated as a midpoint. We further define four additional toy models in which three of the models attempt to cover the lower half of the envelope. The first toy model (“Lower bound toy model 1”) is an average between the MARLEY B 2009 cross section and the lower (Min) bound. The second toy model (“Lower bound toy model 2”) is defined as the average between the first toy model and the MARLEY B 2009 cross section. Finally, the third toy model (“Lower bound toy model 3”) is defined as the average between the first toy model and the lower (Min) bound. The complete set of toy cross-section models is shown in Fig. 17. Note that the two “kinks”in the Min model are artifacts from linear interpolations of the NSM þ RPA [41] and QRPA-S [44] models, respectively. Figure 18 shows the 2D fractional difference plots for the toy cross-section models within the uncertainty envelope. When compared to Fig. 13, the biases are less extreme for all three parameters. Similar to the previous fake data studies, extraction of best-fit values for αand hEνiis less affected by cross-section mismodeling while estimation of εis impacted the most. Also similar to the previous studies, assuming a cross-section higher than the true one leads to an underestimation of ε. Example sensitivity regions are shown in Fig. 19 using several assumed cross sections for fake data generated using the MARLEY B 2009 model. In this case, the black star represents the true parameter values. The observed biases are still significant for εbut relatively modest for the other supernova flux parameters. IV. DISCUSSION A proper interpretation of a DUNE supernova neutrino data set will require a good understanding of neutrinoargon scattering cross sections in the tens of MeV regime. Since direct measurements of the dominant charged-current νeabsorption process on argon are currently unavailable, our present consideration of cross-section uncertainties necessarily relies on calculations available in the theoretical literature. Furthermore, because few published calculations of observables beyond energy-dependent total cross sections σðEνÞare available for CC νe−40Ar scattering, we focus entirely upon variations to the total cross section. For the studies reported here, the remaining aspects of the interaction modeling needed to connect the true neutrino energy to the observed energy distribution in DUNE are 5 1015202530 Energy (MeV) 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 MARLEY Bhattacharya 1998 MARLEY Bhattacharya 2009 MARLEY Liu 1998 NSM+RPA QRPA-S Envelope ) 2 cm -38 Cross Section (10 FIG. 15. Total cross section predictions for the νe−40Ar interaction from the selected subset of models discussed in Sec. III D. The shaded region represents the adopted uncertainty envelope based on the spread of these models. 5 1015202530 Energy (MeV) 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 ) 2 cm -38 Cross Section (10 Lower bound Lower bound toy model 3 Lower bound toy model 2 Lower bound toy model 1 Bhattacharya 2009 Between B 2009 and upper bound Upper bound FIG. 17. Toy total cross-section models for the νe−40Ar interaction covering portions of the uncertainty envelope shown in Fig. 15. 10 20 30 40 50 Observed Energy (MeV) 0 20 40 60 80 100 120 140 160 Events per 0.5 MeV MARLEY Bhattacharya (2009) NSM+RPA MARLEY Bhattacharya (1998) MARLEY Liu (1998) QRPA-S FIG. 16. SNO w GL o BES event rates for the selected cross-section calculations discussed in the text. The error bars are statistical. IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-19 provided by the MARLEY event generator, which currently implements the only realistic predictions of complete final states for low-energy CC neutrino-argon scattering. We expect the theoretical uncertainties on these additional modeling details to be significant, and future work will be needed to reliably quantify them. To examine the impact of total cross-section mismodeling on the interpretation of DUNE supernova neutrino data, we employed three strategies for model variations; applying a constant scaling factor to the MARLEY B 2009 model (Sec. III B), considering the full range of a variety of crosssection predictions (Sec. III C), and defining an uncertainty envelope based on the spread of a subset of selected predictions (Sec. III D). Beyond the phenomenological models available in MARLEY , the theoretical calculations that we reviewed and employed for the latter two strategies included theglobalGTBDtreatmentandmicroscopicevaluationssuch as the QRPA, PQRPA, NSM, and hybrid approaches. All of these models have significant differences coming from the description of nuclear correlations, the residual interaction, and the value of the nucleon axial-vector coupling. Nevertheless, these models reasonably describe the main features of measured weak interaction observables such as β-decay strengths and inclusive muon capture rates. For all three strategies, the cross-section model variations were applied to toy measurements of supernova neutrino flux parameters performed using fake data sets produced using the SNO w GL o BES framework. Different combinations of true and assumed cross-section models (used to create the fake data and interpret the toy measurement results, respectively) were employed, and the impact on the extracted values of the flux parameters was assessed. Table II provides a high-level summary of the conclusions from our fake data studies. For each of the three supernova neutrino flux parameters that we considered, an uncertainty on the total CC neutrino-argon cross-section of −50=þ100% and 20% is translated into a corresponding range of observed biases on the best-fit parameter value extracted from the toy measurements. The values of the bias were read directly off the 2D fractional difference plots. For the −50=þ100% combination, the forward-fitting algorithm reached the most extreme allowed values of ε, causing the biases in αand hEνito increase in an attempt to compensate for the spectral shape differences between the true spectrum and grid elements. For total cross section known at about the 20% level, bias on best-fit αand hEνiis in the 3–8% range. Achieving less than 10% bias on the best-fit value of εrequires the cross section to be known to about 5%. These requirements may be somewhat relaxed in light of possible constraints from simultaneous observations of the supernova by other detectors, which we do not consider here. On the other hand, more stringent requirements may ultimately be needed when additional interaction modeling uncertainties (beyond those on the total cross section) are fully taken into account. While we are optimistic that the theoretical understanding of low-energy neutrino-argon cross sections will continue to improve, there is no substitute for actually measuring the cross sections with a well-characterized neutrino flux. Pions decaying at rest represent a near-ideal source of neutrinos for such measurements. Decays of πþ produce monochromatic νμon a short timescale, plus ¯ νμ and νefrom delayed decay of the stopped daughter muon on a 2.2μs timescale. The spectrum and timing are very well understood. The neutrino energies extend to 52 MeV, overlapping nicely with the supernova spectrum. It is also possible to study neutral-current argon inelastic events given the time structure of the beam. Spallation-based neutron beams such as the Spallation Neutron Source at Oak Ridge National Laboratory [53], the Lujan Neutron Science Center at Los Alamos National Laboratory [54], the J-PARC Spallation Neutron Source [55], and the future European Spallation Source [56] (currently under construction) are intense sources of pion decay-at-rest neutrinos. Measurements of these neutrinos may also be possible at high-energy physics facilities including the Large Hadron Collider beam dump [57] and the meson decay-in-flight neutrino beams at Fermilab [58]. Future direct measurements of CC νe-argon cross sections using a pion decay-at-rest source could pursue several distinct observables to better constrain interaction modeling uncertainties for the DUNE supernova neutrino program. The most straightforward of these (and most directly relevant to the specific uncertainties considered in this paper) would be an inclusive total cross section hσi averaged over the νeflux ϕðEνÞfrom πþdecays at rest, hσi≡Rmμ=2 0σðEνÞϕðEνÞdEν Rmμ=2 0ϕðEνÞdEν ;ð9Þ where mμis the muon mass and ϕðEνÞ∝E2 νm−4 μðmμ−2EνÞ:ð10Þ Measurements of both hσiand a differential cross section as a function of the total visible energy would likely be TABLE II. Parameter biases caused by normalization uncertainties on the total cross section. σðEνÞuncertainty Parameter Measurement bias −50=þ100% α−80% to þ176% hEνi−41.1% to þ47.4% ε−60% to þ100% 20% α0% to þ8% hEνi−3% to 0% ε−45% to þ50% A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-20 Assumed Cross Section Model True Cross Section Model 6.39 11.2 1.72 3.48 0 0.65 -0.65 FIG. 18. 2D fractional difference plots to study effects produced by toy models within the cross-section uncertainty envelope discussed in Sec. III D. 6 8 10 12 14 16 18 20 (MeV)² Q E¢ 1 2 3 4 5 6 7 D with different assumed scenarios True cross section: Bhattacharya (2009) MARLEY Bhattacharya (2009) Low 2 Low 1 6 8 10 12 14 16 18 20 (MeV)² Q E¢ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H 1234567 D 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H FIG. 19. Sensitivity regions (90% C.L.) with different combinations of assumed and true cross-section models. Two of the models are toy models generated from the midpoint (B 2009) and minimum cross-section values from the set of selected models. The stars mark the best-fit values from the fitting algorithm. The black stars also represent the true parameter values. IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-21 obtainable with a suitably large (several-ton-scale) argon detector. As an example, 5–10% statistical uncertainty on the total cross section could be obtained in a few years with a ton-scale detector a few tens of meters from the Spallation Neutron Source. The fine spatial resolution of a LArTPC detector would potentially allow for more detailed measurements. In particular, topological separation between the outgoing electron and γ-rays emitted due to neutrino-induced nuclear deexcitations could allow separate measurements of differential distributions for both particle species. Recent studies (e.g., Ref. [59]) suggest that such a separation would be feasible, and a successful implementation would yield a rich data set; the inclusive electron energy and angular distributions are known to be sensitive to the modeling of forbidden contributions to the cross section [60], while the γ-rays would provide a helpful constraint on deexcitation modeling and, in principle, the opportunity to measure partial cross sections for specific nuclear transitions. Measuring the neutrino angular distribution is particularly important for supernova pointing measurements relevant for prompt multimessenger astrophysics [12,61]. An especially impactful but highly challenging measurement would involve the detection of final-state neutrons produced by CC νe-argon interactions. Missing energy attributable to these neutrons is expected to have a significant impact on neutrino energy reconstruction at supernova energies [31], and the modeling needed to account for it is complicatedandpoorlyconstrained byexperimentaldata.In the absence of any new experimental techniques to increase the sensitivity of argon-based detectors to neutrons at and below MeV energies, external instrumentation designed to capture and detect escaping neutrons would likely be the only means of attempting such a measurement. V. CONCLUSION A possible future observation by DUNE of neutrinos from acore-collapsesupernovawouldrepresentarareandvaluable scientific opportunity. In particular, the unique sensitivity of DUNE’s LArTPC detectors to the νecomponent of the supernova neutrino flux would be highly complementary to other current andanticipated largeneutrino experiments. In the studies reported in this paper, we have examined the effects of cross-section modeling uncertainties on a simulated analysis of supernova neutrinos in DUNE. Significant experimental and theoretical challenges remain before a precise understanding of tens of MeV neutrino-argon scattering can be achieved. Nevertheless, pursuing this understanding will be essential to maximize the discovery potential from a core-collapse supernova observation (and a potentially broader program of lowenergy physics) in DUNE.We hope that the initial studies of neutrino-argon interaction modeling uncertainties reported here may serve as a useful foundation for the more comprehensive investigations that will be required in the future. ACKNOWLEDGMENTS This document was prepared by the DUNE Collaboration using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. This work was supported by CNPq, FAPERJ, FAPEG and FAPESP, Brazil; CFI, IPP and NSERC, Canada; CERN; MŠMT, Czech Republic; ERDF, H2020-EU and MSCA, European Union; CNRS/IN2P3 and CEA, France; INFN, Italy; FCT, Portugal; NRF, South Korea; CAM, Fundación “La Caixa,” Junta de Andalucía-FEDER, MICINN, and Xunta de Galicia, Spain; SERI and SNSF, Switzerland; TÜBİTAK, Turkey; The Royal Society and UKRI/STFC, United Kingdom; DOE and NSF, United States of America. This work was also supported by FAPESB T. O. PIE 0013/2016 and UESC/PROPP 0010299-61. APPENDIX A: INTERPOLATION/ EXTRAPOLATION METHODS USED ON CROSS SECTION MODELS In order to study the measurement biases introduced by the cross-section modeling, we obtained numerical tables of model predictions for the total charged-current νe−40Ar cross section (see Table I). SNO w GL o BES requires 1001 data points in a cross-section file for neutrino energies between 5–100 MeV. While some of the models of interest are already available within SNO w GL o BES (including its default cross-section model, along with some MARLEY crosssection models from Ref. [31]), input files for the other models required extra preparation to conform to the requirements of the SNO w GL o BES format. Table III summarizes the interpolation and extrapolation methods used for the various models. Excluding the crosssection models already available within SNO w GL o BES , all models required interpolation between their tabulated data points to obtain cross-section values at intermediate neutrino energies. For models which were tabulated over the entire energy range of interest, either a cubic spline or a linear spline was used to interpolate between the given data points. A cubic spline was generally preferred, but the linear spline was used in cases where the cubic spline caused unphysical fluctuations in the interpolated total cross section. The available cross-section tables for some models did not cover the entire 5–100 MeV energy range required by SNO w GL o BES . In such cases, extrapolation techniques were used to extend the existing predictions. The models from Refs. [38,39,41,45,46] required extrapolation down to 5 MeV, while the model from Ref. [43] required A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-22 extrapolation down to 5 MeVand up to 100 MeV. All of the extrapolations used to prepare the SNO w GL o BES input files employed a quadratic fit of the form σðEνÞ¼p0ðEν−p1Þ2;ðA1Þ where p0and p1are the free parameters used for fitting. All extrapolation fits used five data points. In the fits for low energies, p1(which has units of MeV) holds special significance as the “endpoint”of the crosssection model because it is the minimum of the quadratic function. For p1>5MeV, the fit would introduce unphysical behavior into the model in the form of an increasing cross section as the neutrino energy Eνapproaches 5 MeV from above. To prevent this behavior, the total cross section σðEνÞwas zeroed out for all energies Eν<p 1whenever p1>5MeV. The same quadratic functional form was also fit to the last five data points of the model from Ref. [43] to extrapolate up to 100 MeV. In this case, the lowand highenergy fits were handled independently. In order to avoid discontinuities between the interpolation and extrapolation methods, the fits performed at low (high) neutrino energy were required to pass through the first (last) tabulated data point for the cross-section model of interest. Figure 20 shows the cross section model from Refs. [45,46] as an example of the interpolation between points (in this case, with a linear spline) as well as an extrapolation to low energies. APPENDIX B: SNO w GL o BES EVENT RATES FOR DIFFERENT CROSS-SECTION MODELS TABLE III. Table summarizing the interpolation and extrapolation methods performed on the various cross-section models to format them for usage in SNO w GL o BES [29]. Parameters from the quadratic fits described in the text are also given when extrapolation was used. Cross-section model Interpolation method used Extrapolation method used SNO w GL o BES [29] Not applicable Not applicable RPA [38,39] Linear spline Low-energy quadratic fit: σ¼1.35027 ×10−5ðE−0.567063Þ2 QRPA-C [43] Linear spline Low-energy quadratic fit: σ¼7.29830 ×10−6ðE−6.67699Þ2; for all energy values below p1¼6.68 MeV, the cross section was set to zero. High-energy quadratic fit: σ¼1.83273 ×10−5ðE−12.3510Þ2 GTBD [45,46] Linear spline Low-energy quadratic fit: σ¼2.26358 ×10−5ðEþ0.761242Þ2 NSM þRPA [41] Linear spline Low-energy quadratic fit: σ¼1.49812 ×10−4ðE−7.45969Þ2; for all energy values below p1¼7.46 MeV, the cross section was set to zero. QRPA-S [44] Linear spline Not applicable RQRPA [40] Cubic spline Not applicable PQRPA [42] Cubic spline Not applicable B 1998 [32] Cubic spline Not applicable B 2009 [32] Cubic spline Not applicable L 2009 [32] Cubic spline Not applicable FIG. 20. Cross-section model from Refs. [45,46] with the interpolation (with a linear spline) and extrapolation (using a quadratic fit) shown. See Table III for the quadratic fit parameters for the low-energy fit. TABLE IV. SNO w GL o BES estimated number of νeCC events in the DUNE far detectors for pinched-thermal flux parameters ðα;hEνi;εÞ¼ð2.5;9.5;5×1052Þfor the νeflavor, a 10 kpc supernova, and assuming NMO and MSW oscillations via Eq. (5). Cross-section model Number of νeCC events Number of νeCC events between [5, 15] MeV QRPA-C [43] 1383 134 RQRPA [40] 2243 220 QRPA-S [44] 2791 243 SNO w GL o BES [29] 4486 624 B 1998 [32] 6307 874 L 1998 [32] 6390 883 NSM þRPA [41] 6391 897 B 2009 [32] 6852 988 PQRPA [42] 4562 909 RPA [38,39] 5064 998 GTBD [45,46] 7770 2070 IMPACT OF CROSS-SECTION UNCERTAINTIES ON …PHYS. REV. D 107, 112012 (2023) 112012-23 APPENDIX C: INTERPOLATING SENSITIVITY REGIONS To keep computation time reasonable, the algorithm used to compute flux parameter sensitivity regions (see Sec. II D) uses a limited number of elements in the grid of reference ðα;hEνi;εÞvalues. The limited number of grid elements leads to unphysical jagged edges in plots of the 90% confidence contours used in this paper to estimate DUNE sensitivity regions for the supernova spectral parameters. To remove these artifacts from the sensitivity region plots, we developed an interpolation technique to smooth the contour edges. Each contour was stored as a two-dimensional histogram, where the weight in each bin was calculated as the minimum χ2value obtained in that region of 2D flux parameter space. Bilinear interpolation [62] between histogram bins was then used to increase the number of bins along each axis to 1000. Example sensitivity regions for the MARLEY B 2009 model are shown in Fig. 21 before (black) and after (blue) applying the smoothing procedure. The impact of the smoothing is most noticeable in the plots involving εsince the reference grid is coarsest for that parameter. Specifically, the interpolated contours are slightly smaller than the original contours. [1] A core collapse leaving behind a black hole may not result in a visible supernova, but will still emit a bright burst of neutrinos. [2] J. F. Cherry, J. Carlson, A. Friedland, G. M. Fuller, and A. Vlasenko, Phys. Rev. D 87, 085037 (2013). [3] J. F. Beacom, R. N. Boyd, and A. Mezzacappa, Phys. Rev. D 63, 073011 (2001). [4] R. C. Schirato and G. M. Fuller, arXiv:astro-ph/0205390. [5] F. Hanke, A. Marek, B. Müller, and H.-T. Janka, Astrophys. J. 755, 138 (2012). [6] A. Friedland and A. Gruzinov, arXiv:astro-ph/0607244. [7] R. M. Bionta et al.,Phys. Rev. Lett. 58, 1494 (1987). [8] K. Hirata et al. (KAMIOKANDE-II Collaboration), Phys. Rev. Lett. 58, 1490 (1987). 6 8 10 12 14 16 18 (MeV)² Q E¢ 1 2 3 4 5 6 D 10 kpc supernova Bhattacharya (2009) cross section TH2D Interpolate 6 8 10 12 14 16 18 (MeV)² Q E¢ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H 123456 D 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10H FIG. 21. 90% C.L. contours for the three parameter spaces with NMO assumptions and the MARLEY B 2009 cross-section model [32]. The contours before interpolation have prominent jagged edges due to a limited number of reference grid points. The edges are most noticeable for the εparameter. A. ABED ABUD et al. PHYS. REV. D 107, 112012 (2023) 112012-24