††thanks: also at Université Paris-Saclay††thanks: also at INFN-Laboratori
Nazionali di Legnaro††thanks: also at J-PARC, Tokai, Japan††thanks: also at
J-PARC, Tokai, Japan††thanks: also at J-PARC, Tokai, Japan††thanks: also at
J-PARC, Tokai, Japan††thanks: affiliated member at Kavli IPMU (WPI), the
University of Tokyo, Japan††thanks: affiliated member at Kavli IPMU (WPI), the
University of Tokyo, Japan††thanks: affiliated member at Kavli IPMU (WPI), the
University of Tokyo, Japan††thanks: also at J-PARC, Tokai, Japan††thanks:
affiliated member at Kavli IPMU (WPI), the University of Tokyo, Japan††thanks:
also at Moscow Institute of Physics and Technology (MIPT), Moscow region,
Russia and National Research Nuclear University ”MEPhI”, Moscow,
Russia††thanks: also at IPSA-DRII, France††thanks: also at J-PARC, Tokai,
Japan††thanks: affiliated member at Kavli IPMU (WPI), the University of Tokyo,
Japan††thanks: affiliated member at Kavli IPMU (WPI), the University of Tokyo,
Japan††thanks: also at J-PARC, Tokai, Japan††thanks: also at J-PARC, Tokai,
Japan††thanks: also at J-PARC, Tokai, Japan††thanks: also at the Graduate
University of Science and Technology, Vietnam Academy of Science and
Technology††thanks: also at J-PARC, Tokai, Japan††thanks: also at JINR, Dubna,
Russia††thanks: also at J-PARC, Tokai, Japan††thanks: affiliated member at
Kavli IPMU (WPI), the University of Tokyo, Japan††thanks: also at Nambu
Yoichiro Institute of Theoretical and Experimental Physics (NITEP)††thanks:
also at J-PARC, Tokai, Japan††thanks: affiliated member at Kavli IPMU (WPI),
the University of Tokyo, Japan††thanks: also at J-PARC, Tokai, Japan††thanks:
also at J-PARC, Tokai, Japan††thanks: affiliated member at Kavli IPMU (WPI),
the University of Tokyo, Japan††thanks: also at J-PARC, Tokai, Japan††thanks:
also at Nambu Yoichiro Institute of Theoretical and Experimental Physics
(NITEP)††thanks: also at BMCC/CUNY, Science Department, New York, New York,
U.S.A.††thanks: affiliated member at Kavli IPMU (WPI), the University of
Tokyo, Japan

The T2K Collaboration

# First measurement of muon neutrino charged-current interactions on
hydrocarbon
without pions in the final state using multiple detectors with correlated
energy spectra at T2K

K. Abe  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  N. Akhlaq  Queen Mary University of London,
School of Physics and Astronomy, London, United Kingdom  R. Akutsu  High
Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  H.
Alarakia-Charles  Lancaster University, Physics Department, Lancaster, United
Kingdom  A. Ali  University of Winnipeg, Department of Physics, Winnipeg,
Manitoba, Canada  TRIUMF, Vancouver, British Columbia, Canada  Y.I. Alj Hakim
Imperial College London, Department of Physics, London, United Kingdom  S.
Alonso Monsalve  ETH Zurich, Institute for Particle Physics and Astrophysics,
Zurich, Switzerland  C. Alt  ETH Zurich, Institute for Particle Physics and
Astrophysics, Zurich, Switzerland  C. Andreopoulos  University of Liverpool,
Department of Physics, Liverpool, United Kingdom  M. Antonova  IFIC (CSIC &
University of Valencia), Valencia, Spain  S. Aoki  Kobe University, Kobe,
Japan  T. Arihara  Tokyo Metropolitan University, Department of Physics,
Tokyo, Japan  Y. Asada  Yokohama National University, Department of Physics,
Yokohama, Japan  Y. Ashida  Kyoto University, Department of Physics, Kyoto,
Japan  E.T. Atkin  Imperial College London, Department of Physics, London,
United Kingdom  M. Barbi  University of Regina, Department of Physics, Regina,
Saskatchewan, Canada  G.J. Barker  University of Warwick, Department of
Physics, Coventry, United Kingdom  G. Barr  Oxford University, Department of
Physics, Oxford, United Kingdom  D. Barrow  Oxford University, Department of
Physics, Oxford, United Kingdom  M. Batkiewicz-Kwasniak  H. Niewodniczanski
Institute of Nuclear Physics PAN, Cracow, Poland  F. Bench  University of
Liverpool, Department of Physics, Liverpool, United Kingdom  V. Berardi  INFN
Sezione di Bari and Università e Politecnico di Bari, Dipartimento
Interuniversitario di Fisica, Bari, Italy  L. Berns  Tohoku University,
Faculty of Science, Department of Physics, Miyagi, Japan  S. Bhadra  York
University, Department of Physics and Astronomy, Toronto, Ontario, Canada  A.
Blanchet  University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
A. Blondel  Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire
et de Hautes Energies (LPNHE), Paris, France  University of Geneva, Section de
Physique, DPNC, Geneva, Switzerland  S. Bolognesi  IRFU, CEA, Université
Paris-Saclay, F-91191 Gif-sur-Yvette, France  T. Bonus  Wroclaw University,
Faculty of Physics and Astronomy, Wroclaw, Poland  S. Bordoni  University of
Geneva, Section de Physique, DPNC, Geneva, Switzerland  S.B. Boyd  University
of Warwick, Department of Physics, Coventry, United Kingdom  A. Bravar
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland  C.
Bronner  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  S. Bron  TRIUMF, Vancouver, British Columbia,
Canada  A. Bubak  University of Silesia, Institute of Physics, Katowice,
Poland  M. Buizza Avanzini  Ecole Polytechnique, IN2P3-CNRS, Laboratoire
Leprince-Ringuet, Palaiseau, France  J.A. Caballero  Departamento de Física
Atómica, Molecular y Nuclear, Universidad de Sevilla, 41080 Sevilla, Spain
N.F. Calabria  INFN Sezione di Bari and Università e Politecnico di Bari,
Dipartimento Interuniversitario di Fisica, Bari, Italy  S. Cao  Institute For
Interdisciplinary Research in Science and Education (IFIRSE), ICISE, Quy Nhon,
Vietnam  D. Carabadjac  Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-
Ringuet, Palaiseau, France  A.J. Carter  Royal Holloway University of London,
Department of Physics, Egham, Surrey, United Kingdom  S.L. Cartwright
University of Sheffield, Department of Physics and Astronomy, Sheffield,
United Kingdom  M.P. Casado  Institut de Fisica d’Altes Energies (IFAE) - The
Barcelona Institute of Science and Technology, Campus UAB, Bellaterra
(Barcelona) Spain  M.G. Catanesi  INFN Sezione di Bari and Università e
Politecnico di Bari, Dipartimento Interuniversitario di Fisica, Bari, Italy
A. Cervera  IFIC (CSIC & University of Valencia), Valencia, Spain  J. Chakrani
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau,
France  D. Cherdack  University of Houston, Department of Physics, Houston,
Texas, U.S.A.  P.S. Chong  University of Pennsylvania, Department of Physics
and Astronomy, Philadelphia, PA, 19104, USA.  G. Christodoulou  CERN European
Organization for Nuclear Research, CH-1211 Genéve 23, Switzerland  A. Chvirova
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  M. Cicerchia  INFN Sezione di Padova and Università di Padova,
Dipartimento di Fisica, Padova, Italy  J. Coleman  University of Liverpool,
Department of Physics, Liverpool, United Kingdom  G. Collazuol  INFN Sezione
di Padova and Università di Padova, Dipartimento di Fisica, Padova, Italy  L.
Cook  Oxford University, Department of Physics, Oxford, United Kingdom  Kavli
Institute for the Physics and Mathematics of the Universe (WPI), The
University of Tokyo Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba, Japan  A. Cudd  University of Colorado at Boulder, Department
of Physics, Boulder, Colorado, U.S.A.  C. Dalmazzone  Sorbonne Université,
CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE),
Paris, France  T. Daret  IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-
Yvette, France  P. Dasgupta  Eötvös Loránd University, Department of Atomic
Physics, Budapest, Hungary  Yu.I. Davydov  Joint Institute for Nuclear
Research, Dubna, Moscow Region, Russia  A. De Roeck  CERN European
Organization for Nuclear Research, CH-1211 Genéve 23, Switzerland  G. De Rosa
INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica,
Napoli, Italy  T. Dealtry  Lancaster University, Physics Department,
Lancaster, United Kingdom  C.C. Delogu  INFN Sezione di Padova and Università
di Padova, Dipartimento di Fisica, Padova, Italy  C. Densham  STFC, Rutherford
Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington,
United Kingdom  A. Dergacheva  Institute for Nuclear Research of the Russian
Academy of Sciences, Moscow, Russia  F. Di Lodovico  King’s College London,
Department of Physics, Strand, London WC2R 2LS, United Kingdom  S. Dolan  CERN
European Organization for Nuclear Research, CH-1211 Genéve 23, Switzerland  D.
Douqa  University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
T.A. Doyle  State University of New York at Stony Brook, Department of Physics
and Astronomy, Stony Brook, New York, U.S.A.  O. Drapier  Ecole Polytechnique,
IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France  J. Dumarchez
Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de
Hautes Energies (LPNHE), Paris, France  P. Dunne  Imperial College London,
Department of Physics, London, United Kingdom  K. Dygnarowicz  Warsaw
University of Technology, Institute of Radioelectronics and Multimedia
Technology, Warsaw, Poland  A. Eguchi  University of Tokyo, Department of
Physics, Tokyo, Japan  S. Emery-Schrenk  IRFU, CEA, Université Paris-Saclay,
F-91191 Gif-sur-Yvette, France  G. Erofeev  Institute for Nuclear Research of
the Russian Academy of Sciences, Moscow, Russia  A. Ershova  IRFU, CEA,
Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  G. Eurin  IRFU, CEA,
Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  D. Fedorova
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  S. Fedotov  Institute for Nuclear Research of the Russian Academy of
Sciences, Moscow, Russia  M. Feltre  INFN Sezione di Padova and Università di
Padova, Dipartimento di Fisica, Padova, Italy  A.J. Finch  Lancaster
University, Physics Department, Lancaster, United Kingdom  G.A. Fiorentini
Aguirre  York University, Department of Physics and Astronomy, Toronto,
Ontario, Canada  G. Fiorillo  INFN Sezione di Napoli and Università di Napoli,
Dipartimento di Fisica, Napoli, Italy  M.D. Fitton  STFC, Rutherford Appleton
Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United
Kingdom  J.M. Franco Patiño  Departamento de Física Atómica, Molecular y
Nuclear, Universidad de Sevilla, 41080 Sevilla, Spain  M. Friend  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  Y. Fujii
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
Y. Fukuda  Miyagi University of Education, Department of Physics, Sendai,
Japan  Y. Furui  Tokyo Metropolitan University, Department of Physics, Tokyo,
Japan  K. Fusshoeller  ETH Zurich, Institute for Particle Physics and
Astrophysics, Zurich, Switzerland  L. Giannessi  University of Geneva, Section
de Physique, DPNC, Geneva, Switzerland  C. Giganti  Sorbonne Université,
CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE),
Paris, France  V. Glagolev  Joint Institute for Nuclear Research, Dubna,
Moscow Region, Russia  M. Gonin  ILANCE, CNRS – University of Tokyo
International Research Laboratory, Kashiwa, Chiba 277-8582, Japan  J. González
Rosa  Departamento de Física Atómica, Molecular y Nuclear, Universidad de
Sevilla, 41080 Sevilla, Spain  E.A.G. Goodman  University of Glasgow, School
of Physics and Astronomy, Glasgow, United Kingdom  A. Gorin  Institute for
Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  M. Grassi
INFN Sezione di Padova and Università di Padova, Dipartimento di Fisica,
Padova, Italy  M. Guigue  Sorbonne Université, CNRS/IN2P3, Laboratoire de
Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France  D.R. Hadley
University of Warwick, Department of Physics, Coventry, United Kingdom  J.T.
Haigh  University of Warwick, Department of Physics, Coventry, United Kingdom
P. Hamacher-Baumann  RWTH Aachen University, III. Physikalisches Institut,
Aachen, Germany  D.A. Harris  York University, Department of Physics and
Astronomy, Toronto, Ontario, Canada  M. Hartz  TRIUMF, Vancouver, British
Columbia, Canada  Kavli Institute for the Physics and Mathematics of the
Universe (WPI), The University of Tokyo Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba, Japan  T. Hasegawa  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  S. Hassani
IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  N.C.
Hastings  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki, Japan  Y. Hayato  University of Tokyo, Institute for Cosmic Ray
Research, Kamioka Observatory, Kamioka, Japan  Kavli Institute for the Physics
and Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan  D. Henaff  IRFU,
CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  A. Hiramoto
Kyoto University, Department of Physics, Kyoto, Japan  M. Hogan  Colorado
State University, Department of Physics, Fort Collins, Colorado, U.S.A.  J.
Holeczek  University of Silesia, Institute of Physics, Katowice, Poland  A.
Holin  STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury
Laboratory, Warrington, United Kingdom  T. Holvey  Oxford University,
Department of Physics, Oxford, United Kingdom  N.T. Hong Van  International
Centre of Physics, Institute of Physics (IOP), Vietnam Academy of Science and
Technology (VAST), 10 Dao Tan, Ba Dinh, Hanoi, Vietnam  T. Honjo  Osaka
Metropolitan University, Department of Physics, Osaka, Japan  F. Iacob  INFN
Sezione di Padova and Università di Padova, Dipartimento di Fisica, Padova,
Italy  A.K. Ichikawa  Tohoku University, Faculty of Science, Department of
Physics, Miyagi, Japan  M. Ikeda  University of Tokyo, Institute for Cosmic
Ray Research, Kamioka Observatory, Kamioka, Japan  T. Ishida  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  M. Ishitsuka
Tokyo University of Science, Faculty of Science and Technology, Department of
Physics, Noda, Chiba, Japan  H.T. Israel  University of Sheffield, Department
of Physics and Astronomy, Sheffield, United Kingdom  A. Izmaylov  Institute
for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  N.
Izumi  Tokyo University of Science, Faculty of Science and Technology,
Department of Physics, Noda, Chiba, Japan  M. Jakkapu  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  B. Jamieson  University
of Winnipeg, Department of Physics, Winnipeg, Manitoba, Canada  S.J. Jenkins
University of Liverpool, Department of Physics, Liverpool, United Kingdom  C.
Jesús-Valls  Kavli Institute for the Physics and Mathematics of the Universe
(WPI), The University of Tokyo Institutes for Advanced Study, University of
Tokyo, Kashiwa, Chiba, Japan  J.J. Jiang  State University of New York at
Stony Brook, Department of Physics and Astronomy, Stony Brook, New York,
U.S.A.  J.Y. Ji  State University of New York at Stony Brook, Department of
Physics and Astronomy, Stony Brook, New York, U.S.A.  P. Jonsson  Imperial
College London, Department of Physics, London, United Kingdom  S. Joshi  IRFU,
CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  C.K. Jung  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  P.B. Jurj  Imperial College London, Department
of Physics, London, United Kingdom  M. Kabirnezhad  Imperial College London,
Department of Physics, London, United Kingdom  A.C. Kaboth  Royal Holloway
University of London, Department of Physics, Egham, Surrey, United Kingdom
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury
Laboratory, Warrington, United Kingdom  T. Kajita  University of Tokyo,
Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos,
Kashiwa, Japan  H. Kakuno  Tokyo Metropolitan University, Department of
Physics, Tokyo, Japan  J. Kameda  University of Tokyo, Institute for Cosmic
Ray Research, Kamioka Observatory, Kamioka, Japan  S.P. Kasetti  Louisiana
State University, Department of Physics and Astronomy, Baton Rouge, Louisiana,
U.S.A.  Y. Kataoka  University of Tokyo, Institute for Cosmic Ray Research,
Kamioka Observatory, Kamioka, Japan  T. Katori  King’s College London,
Department of Physics, Strand, London WC2R 2LS, United Kingdom  M. Kawaue
Kyoto University, Department of Physics, Kyoto, Japan  E. Kearns  Boston
University, Department of Physics, Boston, Massachusetts, U.S.A.  M.
Khabibullin  Institute for Nuclear Research of the Russian Academy of
Sciences, Moscow, Russia  A. Khotjantsev  Institute for Nuclear Research of
the Russian Academy of Sciences, Moscow, Russia  T. Kikawa  Kyoto University,
Department of Physics, Kyoto, Japan  S. King  King’s College London,
Department of Physics, Strand, London WC2R 2LS, United Kingdom  V. Kiseeva
Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia  J. Kisiel
University of Silesia, Institute of Physics, Katowice, Poland  T. Kobata
Osaka Metropolitan University, Department of Physics, Osaka, Japan  H.
Kobayashi  University of Tokyo, Department of Physics, Tokyo, Japan  T.
Kobayashi  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki, Japan  L. Koch  Institut für Physik, Johannes Gutenberg-Universität
Mainz, Staudingerweg 7, 55128 Mainz, Germany  S. Kodama  University of Tokyo,
Department of Physics, Tokyo, Japan  A. Konaka  TRIUMF, Vancouver, British
Columbia, Canada  L.L. Kormos  Lancaster University, Physics Department,
Lancaster, United Kingdom  Y. Koshio  Okayama University, Department of
Physics, Okayama, Japan  A. Kostin  Institute for Nuclear Research of the
Russian Academy of Sciences, Moscow, Russia  T. Koto  Tokyo Metropolitan
University, Department of Physics, Tokyo, Japan  K. Kowalik  National Centre
for Nuclear Research, Warsaw, Poland  Y. Kudenko  Institute for Nuclear
Research of the Russian Academy of Sciences, Moscow, Russia  Y. Kudo  Yokohama
National University, Department of Physics, Yokohama, Japan  S. Kuribayashi
Kyoto University, Department of Physics, Kyoto, Japan  R. Kurjata  Warsaw
University of Technology, Institute of Radioelectronics and Multimedia
Technology, Warsaw, Poland  T. Kutter  Louisiana State University, Department
of Physics and Astronomy, Baton Rouge, Louisiana, U.S.A.  M. Kuze  Tokyo
Institute of Technology, Department of Physics, Tokyo, Japan  M. La Commara
INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica,
Napoli, Italy  L. Labarga  University Autonoma Madrid, Department of
Theoretical Physics, 28049 Madrid, Spain  K. Lachner  University of Warwick,
Department of Physics, Coventry, United Kingdom  J. Lagoda  National Centre
for Nuclear Research, Warsaw, Poland  S.M. Lakshmi  National Centre for
Nuclear Research, Warsaw, Poland  M. Lamers James  Lancaster University,
Physics Department, Lancaster, United Kingdom  STFC, Rutherford Appleton
Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United
Kingdom  M. Lamoureux  INFN Sezione di Padova and Università di Padova,
Dipartimento di Fisica, Padova, Italy  A. Langella  INFN Sezione di Napoli and
Università di Napoli, Dipartimento di Fisica, Napoli, Italy  J.-F. Laporte
IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  D. Last
University of Pennsylvania, Department of Physics and Astronomy, Philadelphia,
PA, 19104, USA.  N. Latham  University of Warwick, Department of Physics,
Coventry, United Kingdom  M. Laveder  INFN Sezione di Padova and Università di
Padova, Dipartimento di Fisica, Padova, Italy  L. Lavitola  INFN Sezione di
Napoli and Università di Napoli, Dipartimento di Fisica, Napoli, Italy  M.
Lawe  Lancaster University, Physics Department, Lancaster, United Kingdom  Y.
Lee  Kyoto University, Department of Physics, Kyoto, Japan  C. Lin  Imperial
College London, Department of Physics, London, United Kingdom  S.-K. Lin
Louisiana State University, Department of Physics and Astronomy, Baton Rouge,
Louisiana, U.S.A.  R.P. Litchfield  University of Glasgow, School of Physics
and Astronomy, Glasgow, United Kingdom  S.L. Liu  State University of New York
at Stony Brook, Department of Physics and Astronomy, Stony Brook, New York,
U.S.A.  W. Li  Oxford University, Department of Physics, Oxford, United
Kingdom  A. Longhin  INFN Sezione di Padova and Università di Padova,
Dipartimento di Fisica, Padova, Italy  K.R. Long  Imperial College London,
Department of Physics, London, United Kingdom  STFC, Rutherford Appleton
Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United
Kingdom  A. Lopez Moreno  King’s College London, Department of Physics,
Strand, London WC2R 2LS, United Kingdom  L. Ludovici  INFN Sezione di Roma and
Università di Roma “La Sapienza”, Roma, Italy  X. Lu  University of Warwick,
Department of Physics, Coventry, United Kingdom  T. Lux  Institut de Fisica
d’Altes Energies (IFAE) - The Barcelona Institute of Science and Technology,
Campus UAB, Bellaterra (Barcelona) Spain  L.N. Machado  University of Glasgow,
School of Physics and Astronomy, Glasgow, United Kingdom  L. Magaletti  INFN
Sezione di Bari and Università e Politecnico di Bari, Dipartimento
Interuniversitario di Fisica, Bari, Italy  K. Mahn  Michigan State University,
Department of Physics and Astronomy, East Lansing, Michigan, U.S.A.  M. Malek
University of Sheffield, Department of Physics and Astronomy, Sheffield,
United Kingdom  M. Mandal  National Centre for Nuclear Research, Warsaw,
Poland  S. Manly  University of Rochester, Department of Physics and
Astronomy, Rochester, New York, U.S.A.  A.D. Marino  University of Colorado at
Boulder, Department of Physics, Boulder, Colorado, U.S.A.  L. Marti-Magro
Yokohama National University, Department of Physics, Yokohama, Japan  D.G.R.
Martin  Imperial College London, Department of Physics, London, United Kingdom
M. Martini  Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire
et de Hautes Energies (LPNHE), Paris, France  J.F. Martin  University of
Toronto, Department of Physics, Toronto, Ontario, Canada  T. Maruyama  High
Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  T.
Matsubara  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki, Japan  V. Matveev  Institute for Nuclear Research of the Russian
Academy of Sciences, Moscow, Russia  C. Mauger  University of Pennsylvania,
Department of Physics and Astronomy, Philadelphia, PA, 19104, USA.  K.
Mavrokoridis  University of Liverpool, Department of Physics, Liverpool,
United Kingdom  E. Mazzucato  IRFU, CEA, Université Paris-Saclay, F-91191 Gif-
sur-Yvette, France  N. McCauley  University of Liverpool, Department of
Physics, Liverpool, United Kingdom  J. McElwee  University of Sheffield,
Department of Physics and Astronomy, Sheffield, United Kingdom  K.S. McFarland
University of Rochester, Department of Physics and Astronomy, Rochester, New
York, U.S.A.  C. McGrew  State University of New York at Stony Brook,
Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  J. McKean
Imperial College London, Department of Physics, London, United Kingdom  A.
Mefodiev  Institute for Nuclear Research of the Russian Academy of Sciences,
Moscow, Russia  G.D. Megias  Departamento de Física Atómica, Molecular y
Nuclear, Universidad de Sevilla, 41080 Sevilla, Spain  P. Mehta  University of
Liverpool, Department of Physics, Liverpool, United Kingdom  L. Mellet
Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de
Hautes Energies (LPNHE), Paris, France  C. Metelko  University of Liverpool,
Department of Physics, Liverpool, United Kingdom  M. Mezzetto  INFN Sezione di
Padova and Università di Padova, Dipartimento di Fisica, Padova, Italy  E.
Miller  King’s College London, Department of Physics, Strand, London WC2R 2LS,
United Kingdom  A. Minamino  Yokohama National University, Department of
Physics, Yokohama, Japan  O. Mineev  Institute for Nuclear Research of the
Russian Academy of Sciences, Moscow, Russia  S. Mine  University of Tokyo,
Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
University of California, Irvine, Department of Physics and Astronomy, Irvine,
California, U.S.A.  M. Miura  University of Tokyo, Institute for Cosmic Ray
Research, Kamioka Observatory, Kamioka, Japan  L. Molina Bueno  IFIC (CSIC &
University of Valencia), Valencia, Spain  S. Moriyama  University of Tokyo,
Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  S.
Moriyama  Yokohama National University, Department of Physics, Yokohama, Japan
P. Morrison  University of Glasgow, School of Physics and Astronomy, Glasgow,
United Kingdom  Th.A. Mueller  Ecole Polytechnique, IN2P3-CNRS, Laboratoire
Leprince-Ringuet, Palaiseau, France  D. Munford  University of Houston,
Department of Physics, Houston, Texas, U.S.A.  L. Munteanu  CERN European
Organization for Nuclear Research, CH-1211 Genéve 23, Switzerland  K. Nagai
Yokohama National University, Department of Physics, Yokohama, Japan  Y. Nagai
Eötvös Loránd University, Department of Atomic Physics, Budapest, Hungary  T.
Nakadaira  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki, Japan  K. Nakagiri  University of Tokyo, Department of Physics,
Tokyo, Japan  M. Nakahata  University of Tokyo, Institute for Cosmic Ray
Research, Kamioka Observatory, Kamioka, Japan  Kavli Institute for the Physics
and Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan  Y. Nakajima
University of Tokyo, Department of Physics, Tokyo, Japan  A. Nakamura  Okayama
University, Department of Physics, Okayama, Japan  H. Nakamura  Tokyo
University of Science, Faculty of Science and Technology, Department of
Physics, Noda, Chiba, Japan  K. Nakamura  Kavli Institute for the Physics and
Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  K.D.
Nakamura  Tohoku University, Faculty of Science, Department of Physics,
Miyagi, Japan  Y. Nakano  University of Tokyo, Institute for Cosmic Ray
Research, Kamioka Observatory, Kamioka, Japan  S. Nakayama  University of
Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The
University of Tokyo Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba, Japan  T. Nakaya  Kyoto University, Department of Physics,
Kyoto, Japan  Kavli Institute for the Physics and Mathematics of the Universe
(WPI), The University of Tokyo Institutes for Advanced Study, University of
Tokyo, Kashiwa, Chiba, Japan  K. Nakayoshi  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki, Japan  C.E.R. Naseby  Imperial College
London, Department of Physics, London, United Kingdom  T.V. Ngoc  Institute
For Interdisciplinary Research in Science and Education (IFIRSE), ICISE, Quy
Nhon, Vietnam  V.Q. Nguyen  Ecole Polytechnique, IN2P3-CNRS, Laboratoire
Leprince-Ringuet, Palaiseau, France  K. Niewczas  Wroclaw University, Faculty
of Physics and Astronomy, Wroclaw, Poland  S. Nishimori  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  Y. Nishimura
Keio University, Department of Physics, Kanagawa, Japan  K. Nishizaki  Osaka
Metropolitan University, Department of Physics, Osaka, Japan  T. Nosek
National Centre for Nuclear Research, Warsaw, Poland  F. Nova  STFC,
Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory,
Warrington, United Kingdom  P. Novella  IFIC (CSIC & University of Valencia),
Valencia, Spain  J.C. Nugent  Tohoku University, Faculty of Science,
Department of Physics, Miyagi, Japan  H.M. O’Keeffe  Lancaster University,
Physics Department, Lancaster, United Kingdom  L. O’Sullivan  Institut für
Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz,
Germany  T. Odagawa  Kyoto University, Department of Physics, Kyoto, Japan  T.
Ogawa  High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki,
Japan  W. Okinaga  University of Tokyo, Department of Physics, Tokyo, Japan
K. Okumura  University of Tokyo, Institute for Cosmic Ray Research, Research
Center for Cosmic Neutrinos, Kashiwa, Japan  Kavli Institute for the Physics
and Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan  T. Okusawa  Osaka
Metropolitan University, Department of Physics, Osaka, Japan  N. Ospina
University Autonoma Madrid, Department of Theoretical Physics, 28049 Madrid,
Spain  L. Osu  Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet,
Palaiseau, France  R.A. Owen  Queen Mary University of London, School of
Physics and Astronomy, London, United Kingdom  Y. Oyama  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  V. Palladino
INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica,
Napoli, Italy  V. Paolone  University of Pittsburgh, Department of Physics and
Astronomy, Pittsburgh, Pennsylvania, U.S.A.  M. Pari  INFN Sezione di Padova
and Università di Padova, Dipartimento di Fisica, Padova, Italy  J. Parlone
University of Liverpool, Department of Physics, Liverpool, United Kingdom  S.
Parsa  University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
J. Pasternak  Imperial College London, Department of Physics, London, United
Kingdom  M. Pavin  TRIUMF, Vancouver, British Columbia, Canada  D. Payne
University of Liverpool, Department of Physics, Liverpool, United Kingdom
G.C. Penn  University of Liverpool, Department of Physics, Liverpool, United
Kingdom  D. Pershey  Duke University, Department of Physics, Durham, North
Carolina, U.S.A.  L. Pickering  STFC, Rutherford Appleton Laboratory, Harwell
Oxford, and Daresbury Laboratory, Warrington, United Kingdom  C. Pidcott
University of Sheffield, Department of Physics and Astronomy, Sheffield,
United Kingdom  G. Pintaudi  Yokohama National University, Department of
Physics, Yokohama, Japan  C. Pistillo  University of Bern, Albert Einstein
Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP),
Bern, Switzerland  B. Popov  Sorbonne Université, CNRS/IN2P3, Laboratoire de
Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France  A.J.
Portocarrero Yrey  High Energy Accelerator Research Organization (KEK),
Tsukuba, Ibaraki, Japan  K. Porwit  University of Silesia, Institute of
Physics, Katowice, Poland  M. Posiadala-Zezula  University of Warsaw, Faculty
of Physics, Warsaw, Poland  Y.S. Prabhu  National Centre for Nuclear Research,
Warsaw, Poland  F. Pupilli  INFN Sezione di Padova and Università di Padova,
Dipartimento di Fisica, Padova, Italy  B. Quilain  Ecole Polytechnique,
IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France  T. Radermacher
RWTH Aachen University, III. Physikalisches Institut, Aachen, Germany  E.
Radicioni  INFN Sezione di Bari and Università e Politecnico di Bari,
Dipartimento Interuniversitario di Fisica, Bari, Italy  B. Radics  York
University, Department of Physics and Astronomy, Toronto, Ontario, Canada
M.A. Ramírez  University of Pennsylvania, Department of Physics and Astronomy,
Philadelphia, PA, 19104, USA.  P.N. Ratoff  Lancaster University, Physics
Department, Lancaster, United Kingdom  M. Reh  University of Colorado at
Boulder, Department of Physics, Boulder, Colorado, U.S.A.  C. Riccio  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  E. Rondio  National Centre for Nuclear
Research, Warsaw, Poland  S. Roth  RWTH Aachen University, III. Physikalisches
Institut, Aachen, Germany  N. Roy  York University, Department of Physics and
Astronomy, Toronto, Ontario, Canada  A. Rubbia  ETH Zurich, Institute for
Particle Physics and Astrophysics, Zurich, Switzerland  A.C. Ruggeri  INFN
Sezione di Napoli and Università di Napoli, Dipartimento di Fisica, Napoli,
Italy  C.A. Ruggles  University of Glasgow, School of Physics and Astronomy,
Glasgow, United Kingdom  A. Rychter  Warsaw University of Technology,
Institute of Radioelectronics and Multimedia Technology, Warsaw, Poland  K.
Sakashita  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki, Japan  F. Sánchez  University of Geneva, Section de Physique, DPNC,
Geneva, Switzerland  G. Santucci  York University, Department of Physics and
Astronomy, Toronto, Ontario, Canada  T. Schefke  Louisiana State University,
Department of Physics and Astronomy, Baton Rouge, Louisiana, U.S.A.  C.M.
Schloesser  University of Geneva, Section de Physique, DPNC, Geneva,
Switzerland  K. Scholberg  Duke University, Department of Physics, Durham,
North Carolina, U.S.A.  M. Scott  Imperial College London, Department of
Physics, London, United Kingdom  Y. Seiya  Osaka Metropolitan University,
Department of Physics, Osaka, Japan  T. Sekiguchi  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  H. Sekiya  University of
Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The
University of Tokyo Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba, Japan  D. Sgalaberna  ETH Zurich, Institute for Particle
Physics and Astrophysics, Zurich, Switzerland  A. Shaikhiev  Institute for
Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  F. Shaker
York University, Department of Physics and Astronomy, Toronto, Ontario, Canada
M. Shiozawa  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  Kavli Institute for the Physics and Mathematics
of the Universe (WPI), The University of Tokyo Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba, Japan  W. Shorrock  Imperial College
London, Department of Physics, London, United Kingdom  A. Shvartsman
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  N. Skrobova  Institute for Nuclear Research of the Russian Academy of
Sciences, Moscow, Russia  K. Skwarczynski  Royal Holloway University of
London, Department of Physics, Egham, Surrey, United Kingdom  D. Smyczek  RWTH
Aachen University, III. Physikalisches Institut, Aachen, Germany  M. Smy
University of California, Irvine, Department of Physics and Astronomy, Irvine,
California, U.S.A.  J.T. Sobczyk  Wroclaw University, Faculty of Physics and
Astronomy, Wroclaw, Poland  H. Sobel  University of California, Irvine,
Department of Physics and Astronomy, Irvine, California, U.S.A.  Kavli
Institute for the Physics and Mathematics of the Universe (WPI), The
University of Tokyo Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba, Japan  F.J.P. Soler  University of Glasgow, School of Physics
and Astronomy, Glasgow, United Kingdom  Y. Sonoda  University of Tokyo,
Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  A.J.
Speers  Lancaster University, Physics Department, Lancaster, United Kingdom
R. Spina  INFN Sezione di Bari and Università e Politecnico di Bari,
Dipartimento Interuniversitario di Fisica, Bari, Italy  I.A. Suslov  Joint
Institute for Nuclear Research, Dubna, Moscow Region, Russia  S. Suvorov
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et
de Hautes Energies (LPNHE), Paris, France  A. Suzuki  Kobe University, Kobe,
Japan  S.Y. Suzuki  High Energy Accelerator Research Organization (KEK),
Tsukuba, Ibaraki, Japan  Y. Suzuki  Kavli Institute for the Physics and
Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan  A.A. Sztuc
Imperial College London, Department of Physics, London, United Kingdom  M.
Tada  High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki,
Japan  S. Tairafune  Tohoku University, Faculty of Science, Department of
Physics, Miyagi, Japan  S. Takayasu  Osaka Metropolitan University, Department
of Physics, Osaka, Japan  A. Takeda  University of Tokyo, Institute for Cosmic
Ray Research, Kamioka Observatory, Kamioka, Japan  Y. Takeuchi  Kobe
University, Kobe, Japan  Kavli Institute for the Physics and Mathematics of
the Universe (WPI), The University of Tokyo Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba, Japan  K. Takifuji  Tohoku University,
Faculty of Science, Department of Physics, Miyagi, Japan  H.K. Tanaka
University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory,
Kamioka, Japan  H. Tanigawa  High Energy Accelerator Research Organization
(KEK), Tsukuba, Ibaraki, Japan  M. Tani  Kyoto University, Department of
Physics, Kyoto, Japan  A. Teklu  State University of New York at Stony Brook,
Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  V.V.
Tereshchenko  Joint Institute for Nuclear Research, Dubna, Moscow Region,
Russia  N. Teshima  Osaka Metropolitan University, Department of Physics,
Osaka, Japan  N. Thamm  RWTH Aachen University, III. Physikalisches Institut,
Aachen, Germany  L.F. Thompson  University of Sheffield, Department of Physics
and Astronomy, Sheffield, United Kingdom  W. Toki  Colorado State University,
Department of Physics, Fort Collins, Colorado, U.S.A.  C. Touramanis
University of Liverpool, Department of Physics, Liverpool, United Kingdom  T.
Towstego  University of Toronto, Department of Physics, Toronto, Ontario,
Canada  K.M. Tsui  University of Liverpool, Department of Physics, Liverpool,
United Kingdom  T. Tsukamoto  High Energy Accelerator Research Organization
(KEK), Tsukuba, Ibaraki, Japan  M. Tzanov  Louisiana State University,
Department of Physics and Astronomy, Baton Rouge, Louisiana, U.S.A.  Y. Uchida
Imperial College London, Department of Physics, London, United Kingdom  M.
Vagins  Kavli Institute for the Physics and Mathematics of the Universe (WPI),
The University of Tokyo Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba, Japan  University of California, Irvine, Department of Physics
and Astronomy, Irvine, California, U.S.A.  D. Vargas  Institut de Fisica
d’Altes Energies (IFAE) - The Barcelona Institute of Science and Technology,
Campus UAB, Bellaterra (Barcelona) Spain  M. Varghese  Institut de Fisica
d’Altes Energies (IFAE) - The Barcelona Institute of Science and Technology,
Campus UAB, Bellaterra (Barcelona) Spain  G. Vasseur  IRFU, CEA, Université
Paris-Saclay, F-91191 Gif-sur-Yvette, France  C. Vilela  CERN European
Organization for Nuclear Research, CH-1211 Genéve 23, Switzerland  E. Villa
CERN European Organization for Nuclear Research, CH-1211 Genéve 23,
Switzerland  University of Geneva, Section de Physique, DPNC, Geneva,
Switzerland  W.G.S. Vinning  University of Warwick, Department of Physics,
Coventry, United Kingdom  U. Virginet  Sorbonne Université, CNRS/IN2P3,
Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France
T. Vladisavljevic  STFC, Rutherford Appleton Laboratory, Harwell Oxford, and
Daresbury Laboratory, Warrington, United Kingdom  T. Wachala  H.
Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland  D.
Wakabayashi  Tohoku University, Faculty of Science, Department of Physics,
Miyagi, Japan  J.G. Walsh  Michigan State University, Department of Physics
and Astronomy, East Lansing, Michigan, U.S.A.  Y. Wang  State University of
New York at Stony Brook, Department of Physics and Astronomy, Stony Brook, New
York, U.S.A.  L. Wan  Boston University, Department of Physics, Boston,
Massachusetts, U.S.A.  D. Wark  STFC, Rutherford Appleton Laboratory, Harwell
Oxford, and Daresbury Laboratory, Warrington, United Kingdom  Oxford
University, Department of Physics, Oxford, United Kingdom  M.O. Wascko
Imperial College London, Department of Physics, London, United Kingdom  A.
Weber  Institut für Physik, Johannes Gutenberg-Universität Mainz,
Staudingerweg 7, 55128 Mainz, Germany  R. Wendell  Kyoto University,
Department of Physics, Kyoto, Japan  M.J. Wilking  State University of New
York at Stony Brook, Department of Physics and Astronomy, Stony Brook, New
York, U.S.A.  C. Wilkinson  Lawrence Berkeley National Laboratory, Berkeley,
CA 94720, USA  J.R. Wilson  King’s College London, Department of Physics,
Strand, London WC2R 2LS, United Kingdom  K. Wood  Lawrence Berkeley National
Laboratory, Berkeley, CA 94720, USA  C. Wret  Oxford University, Department of
Physics, Oxford, United Kingdom  J. Xia  Kavli Institute for the Physics and
Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan  Y.-h. Xu
Lancaster University, Physics Department, Lancaster, United Kingdom  K.
Yamamoto  Osaka Metropolitan University, Department of Physics, Osaka, Japan
T. Yamamoto  Osaka Metropolitan University, Department of Physics, Osaka,
Japan  C. Yanagisawa  State University of New York at Stony Brook, Department
of Physics and Astronomy, Stony Brook, New York, U.S.A.  G. Yang  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  T. Yano  University of Tokyo, Institute for
Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  K. Yasutome  Kyoto
University, Department of Physics, Kyoto, Japan  N. Yershov  Institute for
Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  U.
Yevarouskaya  Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique
Nucléaire et de Hautes Energies (LPNHE), Paris, France  M. Yokoyama
University of Tokyo, Department of Physics, Tokyo, Japan  Y. Yoshimoto
University of Tokyo, Department of Physics, Tokyo, Japan  N. Yoshimura  Kyoto
University, Department of Physics, Kyoto, Japan  M. Yu  York University,
Department of Physics and Astronomy, Toronto, Ontario, Canada  R. Zaki  York
University, Department of Physics and Astronomy, Toronto, Ontario, Canada  A.
Zalewska  H. Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland
J. Zalipska  National Centre for Nuclear Research, Warsaw, Poland  K. Zaremba
Warsaw University of Technology, Institute of Radioelectronics and Multimedia
Technology, Warsaw, Poland  G. Zarnecki  H. Niewodniczanski Institute of
Nuclear Physics PAN, Cracow, Poland  X. Zhao  ETH Zurich, Institute for
Particle Physics and Astrophysics, Zurich, Switzerland  T. Zhu  Imperial
College London, Department of Physics, London, United Kingdom  M. Ziembicki
Warsaw University of Technology, Institute of Radioelectronics and Multimedia
Technology, Warsaw, Poland  E.D. Zimmerman  University of Colorado at Boulder,
Department of Physics, Boulder, Colorado, U.S.A.  M. Zito  Sorbonne
Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes
Energies (LPNHE), Paris, France  S. Zsoldos  King’s College London, Department
of Physics, Strand, London WC2R 2LS, United Kingdom

###### Abstract

This paper reports the first measurement of muon neutrino charged-current
interactions without pions in the final state using multiple detectors with
correlated energy spectra at T2K. The data was collected on hydrocarbon
targets using the off-axis T2K near detector (ND280) and the on-axis T2K near
detector (INGRID) with neutrino energy spectra peaked at 0.6 GeV and 1.1 GeV
respectively. The correlated neutrino flux presents an opportunity to reduce
the impact of the flux uncertainty and to study the energy dependence of
neutrino interactions. The extracted double-differential cross sections are
compared to several Monte Carlo neutrino-nucleus interaction event generators
showing the agreement between both detectors individually and with the
correlated result.

##  I Introduction

In the last decade, neutrino oscillations experiments have continued to
collect more statistics and reduce their systematic uncertainties, moving
forward to the precision era of neutrino oscillation physics [1, 2, 3, 4, 5,
6, 7]. For this reason, the next generation of long-baseline (LBL) neutrino
oscillations experiments, DUNE (Deep Underground Neutrino Experiment) [8] and
Hyper-Kamiokande [9], require systematic errors reduced to a few percent to
achieve their physics goals, including precise measurements of the neutrino
mass hierarchy and leptonic CP-violation [10, 11]. In order to reach this
unprecedented reduction of systematic uncertainties, our knowledge of
neutrino–nucleus interaction cross sections must be improved. In the range of
energies used in current LBL neutrino oscillation experiments, a precise
knowledge of neutrino interactions with nucleons is crucial for the
extrapolation from the near to the far detector. Incorrect modeling of
neutrino interactions can affect the reconstructed neutrino energy, which can
introduce bias in the measurement of neutrino oscillation parameters. This
reduction of interaction uncertainty in part will be accomplished through
measurements using the planned near detectors for DUNE and Hyper-Kamiokande,
but can also be achieved through performing measurements and exploring new
techniques with current generation neutrino experiments.

Neutrino charged-current quasielastic (CCQE) interactions, also referred to as
one-particle-one-hole (1p1h) excitations, can be written as:

$\nu_{\ell}+n\rightarrow\ell^{-}+p,$ (1)

where $\nu_{\ell}$ is the incident neutrino of flavor $\ell$, $n$ and $p$ are
the struck neutron and outgoing proton respectively, and $\ell$ is the charged
lepton. CCQE interactions are the dominant reaction at the T2K (Tōkai-to-
Kamioka) neutrino beam energy (peaked at 0.6 GeV). Modelling these
interactions with a bound nucleon inside a nucleus is complex, requiring
treatment of the Fermi motion, removal energy, and nucleon-nucleon
correlations. Various models exist for predicting the initial state nucleon
momentum and removal energy, such as Fermi gas models or relativistic mean
field models, and for modelling correlations between nucleons, for example the
random phase approximation method [12, 13, 14, 15, 16]. Interactions with
correlated pairs of nucleons, referred to as multi-nucleon or two-particle-
two-hole (2p2h) excitations, are possible due to meson-exchange currents or
short range correlations in the nucleus [16, 17, 18, 19, 20, 21, 22]. These
multi-nucleon interactions enhance the neutrino cross section in the energy
range of T2K and can easily be confused for CCQE interactions, which can then
bias the oscillation analysis if not considered. The global picture of
neutrino cross-section data is still complicated as many results are in
tension with each other, and the available models and Monte Carlo (MC)
generators cannot accurately describe many different results across
experiments [23, 24]. In recent T2K oscillation results [25], the dominant
systematic uncertainty is from the nucleon removal energy on charged current
quasielastic interactions, showcasing the need for further study of neutrino
cross sections and cross-section modelling.

The near detectors (close to the neutrino source) used by T2K provide a unique
opportunity to perform a combined measurement using the same neutrino beam
with two detectors exposed to different but correlated spectra of incident
neutrinos, and is the subject of the analysis presented in this paper.
Neutrino detectors measure the rate of neutrino interactions, which is
primarily a product of the neutrino flux and neutrino cross section. Changes
in both the flux and cross-section models can cause the observed event rate to
change, often in similar ways, and this degeneracy limits the ability to
separate individual effects due to either the flux or cross section. The
correlation between the different fluxes at the near detectors provides
additional information that can be used to constrain the flux uncertainty and
break some of the degeneracy between flux and cross section. The different
neutrino energy spectra seen at each detector also presents an opportunity to
study the energy dependence of neutrino interactions within the same analysis
framework. An example is the energy dependence of multi-nucleon interactions,
which comprise a non-negligible fraction of the samples used to measure the
cross section presented in this paper (on average 10% across all samples). The
multi-nucleon cross-section prediction as a function of energy for the Nieves
et al. model [20], which is the default multi-nucleon model used in T2K, and
the Martini et al. model [16] shows differences mainly related to
normalization of by about a factor of two to three across the neutrino energy
range used at T2K (shown in Fig. 1 from [26]). This variation between models
motivated an additional systematic uncertainty for the T2K oscillation
analysis [1]. The analysis presented in this paper takes advantage of the T2K
near detector setup to perform the first measurement using multiple detectors
with different neutrino energy spectra.

Figure 1: Multi-nucleon cross section on 12C as a function of energy for the
Nieves et al. and the Martini et al. models.

##  II The T2K experiment

T2K [27] is a second-generation long-baseline neutrino oscillation experiment
based in Japan, which is able to measure neutrino oscillations with a
$\nu_{\mu}$ ($\bar{\nu}_{\mu}$) beam. The neutrino beam is produced at the
Japan Proton Accelerator Research Complex (J-PARC) in Tōkai. It is first
detected 280 m downstream from the source at the near detector complex, where
the flavor composition of the incoming neutrino flux is not expected to be
affected by oscillations, and then it travels 295 km to the Super-Kamiokande
(SK) far detector [28, 29], located in Hida, where oscillations significantly
affect the flavor composition. The near detector complex houses the two
detectors of primary interest for the analysis presented in this paper: a
detector on the axis of the neutrino beam, called INGRID [30] (Interactive
Neutrino GRID), and a detector located 2.5 degrees off-axis, called ND280 [31]
(Near Detector at 280 meters). INGRID primarily serves as a neutrino beam and
flux monitor, measuring the total rate of neutrino interactions and the beam
direction. ND280 is dedicated to the study of the un-oscillated spectrum of
neutrinos at 280 meters from the production point and neutrino interaction
cross-section properties.

The Super-Kamiokande far detector is a deep underground 50 kton water
Cherenkov detector. The SK detector, as with ND280, is situated at 2.5 degrees
off-axis, meaning that it is exposed to the same relatively narrow energy band
neutrino flux, peaked at the oscillation maximum, around 0.6 GeV.

###  II.1 Neutrino beam

T2K neutrinos come from in-flight decays of focused hadrons emitted from an
extended, 91.4 cm long, monolithic graphite target. The target is bombarded
with a 30 GeV proton beam produced at J-PARC. Interactions of beam protons
inside the target initiate a chain of hadronic interactions, the charged
products of which are focused upon exit from the target using a series of
three magnetic horns. The polarity of the horn current determines whether a
$\nu_{\mu}$ (neutrino mode) or $\bar{\nu}_{\mu}$ (anti-neutrino mode) enhanced
beam is produced, by focusing predominantly positively or negatively charged
pions and kaons, respectively. These mesons are then left to decay, e.g. via
$\pi^{\pm}\rightarrow\mu^{\pm}+\nu_{\mu}(\bar{\nu}_{\mu})$, in a 96 m long
decay volume, capped with a concrete beam dump at the downstream end. Behind
the beam dump, a muon monitor [32, 33] is used to measure the secondary beam
stability. INGRID and ND280 are exposed to the same neutrino beam, but are
placed at different angles relative to the beam center which gives a different
integrated flux and energy spectrum for each detector. The neutrino flux peaks
around 0.6 GeV at ND280 and around 1.1 GeV at INGRID, and the nominal
$\nu_{\mu}$ fluxes are shown in Fig. 2. The beam composition at INGRID and
ND280 when running in neutrino mode is shown in Tab. 1.

| $\nu_{\mu}$ | $\bar{\nu}_{\mu}$ |  $\nu_{e}$ \+ $\bar{\nu}_{e}$
---|---|---|---
INGRID | 95.3% | 3.9% | 0.8%
ND280 | 92.9% | 5.9% | 1.2%
Table 1: Neutrino beam composition at INGRID and ND280.

Figure 2: Nominal neutrino mode flux prediction at ND280 (top) and INGRID
(bottom) separated by neutrino flavor.

###  II.2 INGRID

The INGRID detector is an on-axis neutrino detector located 280 m downstream
of the proton target. It consists of 14 identical detector modules (referred
to as standard modules) and an extra module called the Proton Module (PM).

The main purpose of the standard modules is to monitor the neutrino beam
direction. The 14 identical standard modules are arranged in two identical
groups along the horizontal and vertical axes, as shown in Fig. 3. Each of the
modules consists of nine iron target plates and eleven tracking scintillator
planes surrounded by veto scintillator planes to reject charged particles
coming from outside the modules [34], as shown in Fig. 4.

Figure 3: Overview of the 14 standard modules and cross configuration. Figure
4: An exploded view of a standard module.

By contrast, the Proton Module was specifically developed for neutrino cross-
section measurements. It is located at the beam center between the horizontal
and vertical standard modules as shown in Fig 5. It is a fully-active tracking
detector consisting of 36 tracking layers surrounded by veto planes (shown in
Fig. 6), where each tracking layer is an array of two types of scintillator
bars [35]. Each scintillator plane covers an area of $120\times
120\;\text{cm}^{2}$ transverse to the beam direction. The tracking layers also
serve as the neutrino interaction target, with the total target mass of the
scintillator and fibers in the fiducial volume being 292.1 kg.

Figure 5: A schematic view of the Proton Module and the standard modules.
Figure 6: An exploded view of the Proton Module.

###  II.3 ND280

The off-axis near detector ND280 (Fig. 7), is a magnetized particle tracking
device.

Figure 7: An exploded view of the ND280 off-axis detector.

It consists of a number of sub-detectors installed inside the refurbished
UA1/NOMAD magnet, which provides a 0.2 T field used to measure the charge and
momentum of particles passing through ND280. Inside the UA1 magnet, the
neutrino beam first passes through the $\pi^{0}$ detector (P0D) [36] and then
the inner tracker, both of which are surrounded by an electromagnetic
calorimeter (ECal) [37]. Moreover the UA1 magnet yoke is instrumented with
plastic scintillator to perform as a muon range detector (SMRD) [38] in order
to track high angle muons and “sand muons” coming from neutrino interactions
in the rock upstream of the detector. The tracker region of ND280 consists of
three Time Projection Chambers (TPC1, 2, 3) [39], interleaved with two Fine-
Grained Detectors (FGD1, 2) [40]. The upstream FGD1 detector is made of
fifteen XY planes of polystyrene scintillator with each plane having 2
$\times$ 192 bars, while the downstream FGD2 contains seven polystyrene
scintillator modules interleaved with six modules of water in between. The
FGDs provide 1.1 tons target mass each for neutrino interactions and tracking
of the charged particles coming from the interaction vertex, while the TPCs
provide 3D tracking and determine the momentum and energy loss of each charged
particle traversing them. The observed energy loss in the TPCs, combined with
the measurement of the momentum, is used for particle identification (PID).
The analysis presented here is focused on neutrino interactions on carbon,
including only events occurring in FGD1.

##  III Event simulation and selection

The goal of this analysis was to perform a simultaneous fit to ND280 and
INGRID data, extracting the muon neutrino flux-integrated differential cross
section on hydrocarbon without pions in the final state as a function of the
outgoing muon kinematics for both the off- and on-axis T2K flux. Signal events
are defined by a neutrino interaction with an outgoing muon, zero pions, and
any number of other hadrons in the final state and are referred to as
CC-$0\pi$ events (or topology). This signal definition is chosen because it is
the most common interaction for the T2K oscillation analysis and to match what
is accessible to the detectors: the outgoing final-state particles that exit
the nucleus. Particles produced in the neutrino interaction can re-interact as
they leave the nucleus, potentially producing new particles or being absorbed,
referred to as final-state interactions (FSI). Defining the signal in terms of
the final-state particles reduces the model dependence of attempting to
correct for FSI effects. Similarly, the cross section is measured as a
function of the outgoing muon kinematics as opposed to using the reconstructed
neutrino energy or momentum transfer to avoid as much model dependence as
possible.

###  III.1 Event simulation

The T2K neutrino flux simulation [41] is based on the modeling of proton
interactions with the graphite target and propagating the produced particles
through the target station, allowing for further interactions. Interactions
within the target are simulated using the fluka 2011 package [42, 43] while
out-of-target interactions and decays are handled by the geant3 [44] and
gcalor [45] packages. Hadronic interactions and multiplicities are tuned using
NA61/SHINE thin-target data [46, 47, 48] and data from other experiments [49,
50, 51]. The proton beam conditions, horn current, and neutrino beam position
are monitored and used as inputs to the flux simulation to provide additional
constraints. Combined, this data-driven procedure gives an overall flux
normalization prior uncertainty of about $8.5\%$ at ND280 and $9.9\%$ at
INGRID for this analysis, which is dominated by hadron production and
interaction uncertainties. The ND280 and INGRID flux predictions are produced
simultaneously using the same input parameters, and this results in correlated
uncertainties that are included in this analysis (and described further in
Sec. IV.2).

Neutrino interactions in the detectors and the outgoing kinematics of the
produced final-state particles are simulated using the NEUT neutrino event
generator [52, 53]. NEUT describes charged-current quasi-elastic (CCQE)
neutrino-nucleon interactions using the spectral function (SF) approach from
[54] with the quasi-elastic axial mass ($M^{QE}_{A}$) set to 1.21
$\mathrm{GeV}/c^{2}$ based on the K2K CCQE cross-section measurement in [55].
Multi-nucleon correlations (also referred to as 2p2h interactions) are based
on the model from Nieves et. al. [20]. Resonant pion production (RES) is
described by the Rein–Sehgal model [56] using updated nucleon form factors
[57] and the resonant axial mass ($M^{RES}_{A}$) set to 0.95
$\mathrm{GeV/}c^{2}$. Coherent pion production uses the updated Berger–Sehgal
model [58]. Deep inelastic scattering (DIS) interactions are modeled using the
GRV98 parton distribution functions [59] with corrections from Bodek and Yang
[60] to extend the validity of the treatment to lower four-momentum transfer
($Q^{2}\lesssim 1.5\,\mathrm{GeV}^{2}$). NEUT begins modeling DIS processes
for interactions with hadronic invariant mass $W>1.3\,\mathrm{GeV}/c^{2}$. For
interactions with $1.3<W<2.0\,\mathrm{GeV}/c^{2}$ a custom hadronization model
[61] is used to interpolate between RES and DIS processes, while for
$W>2.0\,\mathrm{GeV}/c^{2}$, pythia/jetset [62] is used for the hadronization
model. Hadrons produced in the primary neutrino–nucleon interaction must
propagate through the nuclear remnant before they can be detected.
Interactions before the hadrons leave are referred to as final-state
interactions (FSI), and are simulated using a semi-classical intra-nuclear
cascade model [63, 64]. The MC productions for each detector use the same
physics models in NEUT, but are based on slightly different versions, with
ND280 using version 5.3.2 and INGRID using version 5.3.3, however this has a
negligible impact on the analysis.

The propagation of the final-state particles through the detector medium after
exiting the nucleus is performed using a geant4 [65] simulation. Both detector
simulations use qgsp_bert for the hadronic physics list [66]. The detector
readout simulation is handled by a custom electronics simulation separately
for ND280 and INGRID [27].

###  III.2 Data samples

This analysis uses neutrino-mode data collected between 2010 and 2017 during
T2K Runs 2 through 8. The ND280 sample corresponds to a total of $11.53\times
10^{20}$ POT (protons on target), while the INGRID sample corresponds to a
total of $6.04\times 10^{20}$ POT. The breakdown of collected data by run
period is listed in Tab. 2. The INGRID detector configuration was changed
after Run 4 where the Proton Module was moved to a different location in the
detector hall, which limits the usable data for this analysis and is the main
reason for the difference in total POT between the ND280 and INGRID samples.
T2K Run 3b used a lower horn current (205 kA instead of 250 kA) during data-
taking, and is included in the ND280 data set but excluded from the INGRID
data set. This is what was done in previous ND280 [67, 68, 69] and INGRID
analyses [70], and kept the same for this analysis for consistency and could
be revisited for future versions.

T2K Run | ND280 | INGRID | Date Range
---|---|---|---
Run 2 | 0.792 | 1.115 | Nov. 2010 – Mar. 2011
Run 3b | 0.217 | —– | Mar. 2012 – Mar. 2012
Run 3c | 1.364 | 1.373 | Apr. 2012 – Jun. 2012
Run 4 | 3.426 | 3.551 | Oct. 2012 – May 2013
Run 8 | 5.730 | —– | Oct. 2016 – Apr. 2017
Total | 11.529 | 6.039 |
Table 2: Recorded POT in units of $10^{20}$ after accounting for detector up-
time separated by run period for ND280 and INGRID that are included in this
analysis. The proton module was moved from its on-axis position before Run 8.

###  III.3 Signal selection

The signal selection for this analysis is designed to select muon neutrino
events with no detected pions in the final state and any number of visible
protons, referred to as the CC-$0\pi$ topology. The target material is the
plastic scintillator in either FGD1 (for ND280) or the Proton Module (for
INGRID). The individual selections for ND280 and INGRID were developed for
previous analyses, described in Refs. [67, 68, 69] and Ref. [70] for ND280 and
INGRID respectively, and minor updates necessary for the joint fit and the
addition of new data were made for the analysis presented in this paper.

####  III.3.1 ND280

The ND280 selection first requires passing a set of data quality cuts, and
then requires the interaction vertex to be within the FGD1 fiducial volume
(FV). The FV is defined to include events with a vertex at least five
scintillator bars from the edge in the X and Y directions, and excludes the
first XY module as an upstream veto. Events with a single negatively charged
muon candidate and any number of proton candidates sharing a common vertex are
identified and classified into different samples based on the detectors (FGD1
or TPCs) used to measure the momentum of the muon candidate and the proton
candidate(s), if any. This sample separation by detector and particle content
allows for a more precise treatment of the detector systematics due to the
different detector responses. Tracks are identified by their energy deposition
and curvature compared to the expected distributions for each particle
hypothesis. The momentum of each reconstructed track is measured either by
curvature in the TPCs or by range in FGD1 (and ECAL). Events with a detected
associated decay electron in FGD1 are treated as background as these events
are likely to have produced an untracked stopped pion decaying into a muon
followed by a Michel electron from the muon decay. The signal events are
classified into the following samples:

  * •

Sample I ($\mu$TPC): defined by a single muon candidate in the TPCs and no
other tracks;

  * •

Sample II ($\mu$TPC+pTPC): a muon candidate in the TPCs with one or more
proton candidates in the TPC;

  * •

Sample III ($\mu$TPC+pFGD): a muon candidate in the TPCs and a proton
candidate in FGD1;

  * •

Sample IV ($\mu$FGD+pTPC): a muon candidate in FGD1 (possibly reaching the
ECAL) and a proton candidate in the TPC;

  * •

Sample V ($\mu$FGD): a muon candidate in FGD1 (possibly reaching the ECAL) and
no other tracks.

The majority of events in the signal sample ($\sim 62\%$) are events with a
single reconstructed muon and no other tracks, with most muons reaching the
TPCs. The kinematic distributions of each sample separated by true topology
are shown in Figs. 8 and 9 with data plus statistical errors overlaid. Most
samples achieve a high purity of CC-$0\pi$ events (approximately 82% pure when
integrated over all signal samples) with the main background coming from
misidentified or unidentified pions from CC-$1\pi^{+}$ (events with a muon and
single positive pion track) or CC-Other (events with a muon and multiple pion
tracks) events. The normalization of the data and nominal MC is very similar
when integrated across all the samples, but varies within 15% per sample. A
noticeable feature is the slight deficit of data events compared to the
nominal MC at very forward angles for the combined $\mu$TPC sample
(representing $\sim 85\%$ of the total event sample). The selected events are
binned using the reconstructed muon momentum and cosine of the angle with
respect to the beam direction (list of bin edges available in Appendix A). The
binning scheme is designed such that bins are not finer than the detector
resolution.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 8: Event distribution for measured data and MC prediction in
reconstructed muon momentum and angle for the ND280 signal samples stacked by
true topology. The purity of each topology is listed in the legend, and the
last bin for muon momentum contains all events with momentum greater than 5
GeV/c.

(a)

(b)

(c)

(d)

Figure 9: Event distribution for measured data and MC prediction in
reconstructed muon momentum and angle for the ND280 signal samples stacked by
true topology. The purity of each topology is listed in the legend.

The cross section is extracted by adding the contributions from each sample,
but the samples are kept separate in the analysis. This is important because
events with and without protons and which subdetectors were used in the
reconstruction are affected by different systematics and backgrounds.

####  III.3.2 INGRID

The INGRID selection first requires passing a set of data quality cuts, and
then requires the interaction vertex to be within the Proton Module fiducial
volume. The FV is defined to be the transverse central $\pm 50\times\pm
50\;\mathrm{cm}^{2}$ region of the Proton Module and excludes the first four
scintillator layers as an upstream veto. Events with exactly one or two tracks
sharing a common vertex are selected where one track must be minimum ionizing
– the muon candidate – and the second track, if present, must be proton-like
according to the PID. The INGRID PID algorithm is based on a boosted decision
tree that uses the dE/dx along the track and the distribution of deposited
energy with respect to distance from the end point of the track. Protons will
tend to deposit more energy at the end of the track compared to muons or pions
(referred to as a Bragg peak). The muon candidate track must either stop in
the Proton Module or reach the standard module directly downstream, where it
may also stop or traverse the entire module and escape. Events where the muon
escapes out the side of the Proton Module are rejected. The momentum of a
stopping muon candidate track is measured by calculating an equivalent
distance traversed in iron, and muon candidate tracks that travel through the
entire standard module and escape have a lower limit on their momentum. The
momentum threshold for a muon to escape the standard module is approximately 1
GeV/c. The selected events are binned using the reconstructed momentum and
angle with respect to the beam direction (list of bin edges available in
Appendix A). Stopping and escaping events are considered together as a single
CC-$0\pi$ sample in this analysis (Sample IX).

The kinematic distribution of the signal sample separated by true topology is
shown in Fig. 10 with data plus statistical errors overlaid. The INGRID sample
is notably less pure than the ND280 sample, with a much higher background
primarily coming from pions being misidentified as muons. For the cross-
section extraction, the kinematic regions of $p_{\mu}<0.35\;\mathrm{GeV}/c$
and $\cos(\theta_{\mu})<0.50$ are excluded from the analysis to remove regions
of no acceptance due to the detector geometry.

(a)

(b)

Figure 10: Event distribution for measured data and MC prediction in
reconstructed equivalent distance in iron and angle for the INGRID signal
sample stacked by true topology. Through-going events are all placed in the
final distance bin. The purity of each topology is listed in the legend.

###  III.4 Control regions

To provide a better constraint on the background contributions, a set of
control samples are included in the analysis. As with the signal selections,
the ND280 and INGRID control samples are designed to select similar types of
events, however the additional capabilities of ND280 allow for more
complicated event topologies.

####  III.4.1 ND280

The ND280 selection includes three control samples to select events with a
pion, constraining the primary background contribution to the signal
selection. These samples follow similar initial data quality cuts and criteria
for identifying a muon candidate, but also require the identification of a
pion candidate. A new addition for this analysis compared to previous ND280
analyses is the inclusion of a separate sample designed to identify low
momentum pion events by detecting the presence of a Michel decay electron in
FGD1. The control samples are categorized by the pion content as follows:

  * •

Sample VI (CC-$1\pi^{+}$): defined by a single muon candidate in the TPC and
one $\pi^{+}$ candidate in the TPC;

  * •

Sample VII (CC-Other): a muon candidate, one $\pi^{+}$ candidate, and at least
one additional track in the TPC;

  * •

Sample VIII (CC-Michel): a muon candidate in the TPC and a delayed Michel
electron in FGD1 indicating the presence of a low momentum $\pi^{+}$ below
tracking threshold.

The kinematic distributions of each sample separated by true topology are
shown in Fig. 11. The data clearly shows a deficit compared to the nominal MC
prediction for the CC-$1\pi^{+}$ sample while the opposite is seen in the CC-
Other sample, highlighting the need to include the control samples for a data
driven background constraint. This deficit of CC-$1\pi^{+}$ events has been
observed in previous ND280 analyses [69, 71]. However in the CC-Michel sample,
which contains mostly CC-$1\pi^{+}$ events, the data has a similar overall
normalization compared to the nominal MC prediction, and also shows an excess
at the peak of the distribution. This tension between the CC-$1\pi^{+}$ and
CC-Michel samples and the impact on the analysis is discussed further in Sec.
V.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 11: Event distribution for measured data and MC prediction in
reconstructed muon momentum and angle for the ND280 control samples stacked by
true topology. The purity of each topology is listed in the legend, and the
last bin for muon momentum contains all events with momentum greater than 5
GeV/c.

####  III.4.2 INGRID

The INGRID selection includes a single control sample to select events with a
single pion candidate track. Events must contain exactly two or three tracks
that share a common vertex, with the highest-momentum minimum-ionizing track
labelled as the muon candidate, the other minimum-ionizing track as the pion
candidate, and a third track that if present must be proton-like. The PID cuts
have been tuned for this sample to have a higher efficiency for selecting pion
tracks compared to selecting proton tracks for the signal sample. The
kinematic distribution of the control sample separated by true topology is
shown in Fig. 12. Stopping and escaping events are considered together as a
single CC-$1\pi$ (events with a muon and a single charged pion track) sample
in this analysis (Sample X). Similar to the ND280 control samples, the INGRID
data shows a deficit of interactions producing a pion compared to the nominal
MC prediction.

(a)

(b)

Figure 12: Event distribution for measured data and MC prediction in
reconstructed equivalent distance in iron and angle for the INGRID control
sample stacked by true topology. Through-going events are all placed in the
final distance bin. The purity of each topology is listed in the legend.

##  IV Analysis strategy

###  IV.1 Binned likelihood fit

This analysis uses an unregularized binned maximum likelihood fit similar to
the analyses in Refs. [67, 68, 69, 71, 72], to fit a set of signal and control
samples to provide a data-driven background constraint, to unfold the detector
effects, and to extract the number of selected signal events in the analysis
bins. The ND280 and INGRID samples are fit simultaneously to extract the
CC-$0\pi$ cross section for each detector and produce a correlated result. For
the purposes of the analysis, ND280 and INGRID events occupy different bins
but are otherwise treated similarly. The analysis framework has been
significantly improved compared to previous T2K CC-$0\pi$ results
(specifically Refs. [67, 68, 69, 71]), for example including an improved
treatment of the MC statistical uncertainty and principal component analysis
to reduce the dimensionality of the fit.

This method varies the input MC using a set of fit parameters for both signal
and background events to find the best agreement to the data, and the values
and corresponding errors of these parameters at the best-fit point are then
used for the cross-section extraction. The primary parameters of interest in
the fit are the “template parameters” $c_{i}$ which scale the total number of
signal events in each kinematic truth bin $i$ (seventy in total for this
analysis), and are completely free parameters with no prior constraint. The
rest of the parameters are the systematic (or nuisance) parameters that
describe variations to the flux, detector, and neutrino interaction model
(described in Sec. IV.2). Separate flux and detector parameters (including
correlations when available) are included for ND280 and INGRID, while both
detectors use the same neutrino interaction model parameters.

The best-fit parameters are found by minimizing the negative log-likelihood
ratio (also approximated as the chi-square), and is split into a statistical
and systematic contribution as follows:

$\chi^{2}\approx-2\log\mathcal{L}=-2\log\mathcal{L}_{\text{stat}}-2\log\mathcal{L}_{\text{syst}},$
(2)

where

$\begin{split}&-2\log\mathcal{L}_{\text{stat}}=\\\ &2\sum_{j}^{\text{reco
bins}}\left(\beta_{j}N^{\text{MC}}_{j}-N^{\text{obs}}_{j}+N^{\text{obs}}_{j}\log\frac{N^{\text{obs}_{j}}}{\beta_{j}N^{\text{MC}}_{j}}+\frac{\beta^{2}_{j}-1}{2\sigma^{2}_{j}}\right)\end{split}$
(3)

and

$-2\log\mathcal{L}_{\text{syst}}=(\vec{p}-\vec{p}_{\text{prior}})\mathbf{V}_{\text{syst}}^{-1}(\vec{p}-\vec{p}_{\text{prior}}).$
(4)

Equation 3 is the modified statistical log-likelihood ratio following the
Barlow–Beeston method [73, 74] for including the uncertainty of finite MC
simulation. $N^{\text{MC}}_{j}$ and $N^{\text{obs}}_{j}$ are the number of
simulated and observed events for each reconstructed bin $j$. The
Barlow–Beeston scaling parameter for each bin $\beta_{j}$ is given by the
following:

$\beta_{j}=\frac{1}{2}\left(-(N^{\text{MC}}_{j}\sigma^{2}_{j}-1)+\sqrt{(N^{\text{MC}}_{j}\sigma^{2}_{j}-1)^{2}+4N^{\text{MC}}_{j}\sigma^{2}_{j}}\right)$
(5)

where $\sigma^{2}_{j}$ is the relative variance of the number of MC events
$N^{\text{MC}}_{j}$ in the bin. In the limit of infinite MC simulation,
$\sigma^{2}_{j}\rightarrow 0$ and $\beta_{j}\rightarrow 1$ giving the standard
Poisson log-likelihood ratio. Equation 4 is a Gaussian penalty term to account
for the contribution from varying the systematic parameters $\vec{p}$ during
the fit compared to their fixed prior values $\vec{p}_{\text{prior}}$ and
uncertainty. A covariance matrix $\mathbf{V}_{\text{syst}}$ is used to
describe the prior uncertainty and correlations between the parameters.

The input MC simulation for a reconstructed bin $j$ is the sum of weighted
signal and background events, and can be expressed as:

$N^{\text{MC}}_{j}=\sum^{\text{true
bins}}_{i}\left(c_{i}w^{\text{sig}}_{ij}(\vec{p})N^{\text{sig}}_{ij}+w^{\text{bkg}}_{ij}(\vec{p})N^{\text{bkg}}_{ij}\right)$
(6)

where $N^{\text{sig}}_{ij}$ and $N^{\text{bkg}}_{ij}$ are the signal and
background events for truth kinematic bin $i$ and reconstructed bin $j$ as
predicted by the MC simulation, $c_{i}$ are the signal template parameters,
and $w_{ij}$ are the weights as a function of the systematic parameters
$\vec{p}$, and depend on the truth and reconstructed bins $i$ and $j$.

###  IV.2 Systematic uncertainties

There are three types of systematic uncertainties considered for this analysis
and included in the fit as parameters: flux, detector, and neutrino
interaction model uncertainties.

The neutrino flux uncertainty is parameterized as scale factors in forty total
bins of true neutrino energy with separate flux parameters (or bins) for ND280
and INGRID. Only the $\nu_{\mu}$ flavor is considered for this analysis due to
the small contribution of the $\bar{\nu}_{\mu}$, $\nu_{e}$, and
$\bar{\nu}_{e}$ flavors. These parameters use the same energy binning scheme
and can only affect events for their respective detector (the flux bin edges
can be found in Appendix B). They have a prior constraint described by a
covariance matrix, which includes the correlations between energy bins and
between the fluxes at each detector. As shown in Fig. 13, the fluxes at ND280
and INGRID are highly correlated a priori. The high energy bin (10 to 30 GeV)
for ND280 is less correlated than the lower energy bins due to an increase in
the hadron uncertainties for that bin (mostly from kaon decay). Since the
number of events in the analysis corresponding to this energy range is small,
it has little effect on the analysis. For a given true neutrino energy bin,
identical weights are given to signal and background events. The flux
uncertainty is dominated by the hadronic multiplicity and decay modeling,
along with other contributions, such as uncertainties in the horn current and
alignment.

Figure 13: Input flux correlation matrix binned in neutrino energy for both
ND280 and INGRID. The flux is highly correlated both across the energy
spectrum and between the detectors.

The detector uncertainty is parameterized as scale factors on the event rate
for each reconstructed bin with separate detector parameters for ND280 and
INGRID. They have a prior constraint described by a covariance matrix
including the correlations between the reconstructed bins for a given
detector, however ND280 and INGRID use separate matrices and are completely
uncorrelated in the fit. In principle, several detector uncertainties could be
considered correlated between them, for example using the same pion secondary
interaction modeling in geant4 for the detector simulation, but this was out
of scope for this analysis. Independent and dedicated control samples for each
detector are used to evaluate the detector uncertainties based on data-MC
agreement. The largest contribution to the detector uncertainty is the pion
secondary interaction modeling. Since the fit includes a detector parameter
for each reconstructed bin, this adds up to many hundreds of parameters.
Principal component analysis is used to reduce the total number of detector
parameters by more than half by transforming the parameters to their
eigenspace and removing the parameters that contribute less information
according to their eigenvalues such that 99% of the total information in the
covariance matrix is retained.

The neutrino interaction uncertainty is included in the fit using a set of
twenty-one parameters that are designed to weight events based on aspects of
the neutrino interaction model for both signal and background samples,
including final state interactions (similar to Ref. [69]). A table listing the
neutrino interaction parameter names and their priors can be found in Appendix
C, and are described as follows. Variations to the signal model are included
through changing the shape of the CCQE cross section by varying the axial mass
$M^{QE}_{A}$, and with two parameters to alter the overall normalization of
and shape of the 2p2h model. The resonant pion model has two shape parameters,
the axial mass $M^{RES}_{A}$ and the axial form factor at zero momentum
transfer $C^{A}_{5}$, and a normalization for the non-resonant background
$I_{1/2}$. Additionally, two normalization parameters for CC-$1\pi$ events are
included to give the fit additional freedom to adjust the pion background and
prevent over-fitting of the flux parameters. For deep inelastic scattering
events, a custom shape parameter (DIS multi-pi shape) is used to give greater
freedom at lower neutrino energy along with two normalization parameters for
DIS and multi-pi events. The other major event topologies (coherent and
neutral current) are each given a normalization parameter. Finally a set of
six parameters are included to allow the pion FSI model to vary within the
fit, separated by different reaction channels (absorption, production, charge
exchange, and scattering) and pion momentum range. The prior uncertainty and
correlations between parameters are encoded in a single covariance matrix.
ND280 and INGRID share the same neutrino interaction parameters but the event
weights are calculated for each detector separately.

###  IV.3 Cross-section extraction

The flux-integrated differential cross section as a function of true muon
kinematics $x=p_{\mu}\,\cos(\theta_{\mu})$ for each detector is calculated
using the following:

$\frac{\mathrm{d}\sigma}{\mathrm{d}x_{i}}=\frac{\hat{N}^{\text{sig}}_{i}}{\epsilon_{i}\Phi
N_{\text{nucleons}}\Delta x_{i}}$ (7)

where $\hat{N}^{\text{sig}}_{i}$ is the best-fit number of selected signal
events in truth bin $i$ summed across all samples, $\epsilon_{i}$ is the bin-
by-bin efficiency correction, $\Phi$ is the integral of the neutrino flux
evaluated at the best-fit parameters, $N_{\text{nucleons}}$ is the number of
target nucleons in the fiducial volume, and $\Delta x_{i}$ is the bin width.
The bin edges for the extracted cross section can be found in Appendix A.

The cross-section uncertainty is calculated by numerically propagating the
post-fit uncertainty for the fit parameters assuming they follow a
multivariate Gaussian distribution. The post-fit covariance matrix is Cholesky
decomposed and used to create correlated random variations (or “throws”) of
the fit parameters that follow the same multivariate distribution as the
covariance matrix. This procedure is repeated $10^{4}$ times to sample the
likelihood space encoded in the post-fit covariance matrix. For each thrown
variation of the fit parameters, all the events are reweighted using the
thrown parameter values and the cross section is recalculated as in Eq. 7.
Additionally for each variation, the integrated flux is recalculated, the
selection efficiency is allowed to vary based on the thrown parameters, and
the number of targets is varied independently for each detector. The
efficiency for each cross-section bin and its uncertainty for ND280 and INGRID
are shown in Figs. 14 and 15 respectively. In general for both ND280 and
INGRID the efficiency increases at forward angle and higher momentum as muons
leave longer tracks. The number of target nucleons and its uncertainty for
ND280 are $5.53\times 10^{29}\pm 0.67\%$, and INGRID are $1.76\times
10^{29}\pm 0.38\%$, and includes other elements in addition to carbon and
hydrogen present in the fiducial volumes of each detector. The post-fit
$\nu_{\mu}$ flux integral and uncertainty is $\mathrm{2.29}\times
10^{13}\;\mathrm{cm}^{-2}$ and 6.0% for ND280 and $\mathrm{3.14}\times
10^{13}\;\mathrm{cm}^{-2}$ and 6.1% for INGRID. The resulting distribution of
cross-section values represent the plausible variations of the fit according
to the post-fit uncertainties and correlations. Finally, the cross-section
($\mathrm{d}\sigma/\mathrm{d}x$) uncertainties are calculated using the
ensemble of random throws and are parameterized using a covariance matrix,
assuming the uncertainties are Gaussian distributed.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Figure 14: Selection efficiency with post-fit uncertainty for the ND280 cross-
section bins as function of true muon momentum in muon angle bins. Note that
the final bin extending to 30 GeV/c has been omitted for clarity.

(a)

(b)

(c)

Figure 15: Selection efficiency with post-fit uncertainty for the INGRID
cross-section bins as function of true muon momentum in muon angle bins. Note
that the final bin extending to 30 GeV/c has been omitted for clarity.

A set of fits were performed to estimate the total systematic uncertainty and
the contribution from each systematic parameter class (flux, neutrino
interaction, and detector) on the measured cross-section bins. A fit using
only the template parameters is used as a baseline for the uncertainty (and
corresponds approximately to the statistical uncertainty), and additional fits
were performed that include each systematic parameter class to estimate its
impact (in addition to the template parameters). Each fit used the nominal
Monte Carlo prediction as the “data” so that the best-fit point is at the
nominal value for every parameter; this guarantees each fit has the same best-
fit point and allows for a more accurate comparison. The results are shown for
the analysis cross-section bins for ND280 and INGRID in Figs. 16 and 17
respectively, and show roughly equal contributions from the flux, neutrino
interaction, and detector parameters to the total uncertainty. Additionally,
the uncertainty for the low momentum bins in general is higher than mid to
higher momentum bins for a given angle bin. This procedure cannot be applied
in the same way to data as each fit will have a different best-fit point
resulting in a different total uncertainty, preventing an equal comparison
between the fits.

Figure 16: Estimated total systematic uncertainty separated by parameter class
for the ND280 cross-section bins as function of true muon momentum in muon
angle bins. Note that the final bin extending to 30 GeV/c has been omitted for
clarity.

Figure 17: Estimated total systematic uncertainty separated by parameter class
for the INGRID cross-section bins as function of true muon momentum in muon
angle bins. Note that the final bin extending to 30 GeV/c has been omitted for
clarity.

###  IV.4 Validation

The cross-section extraction was validated using a series of mock data
studies, where a known simulated data set was used as input to the fit and the
performance of the extraction procedure was studied. These mock data sets
cover a wide range of alterations, for example using data-driven modifications
such as the deficit seen at low $Q^{2}$ by MINER$\nu$A [75], modifications to
the resonant pion production model, or changes to the flux model. For each of
these mock data sets, the cross-section extraction was able to recover the
expected true cross section to within the $1\sigma$ uncertainties (often
matching the true cross section nearly exactly), showing a robust procedure.
The overall $\chi^{2}$ agreement between the extracted and true cross section
is also calculated as follows:

$\chi^{2}=\sum^{N}_{ij}\left(\frac{\mathrm{d}\sigma^{\text{meas}}}{\mathrm{d}x_{i}}-\frac{\mathrm{d}\sigma^{\text{true}}}{\mathrm{d}x_{i}}\right)\mathbf{V}^{-1}_{ij}\left(\frac{\mathrm{d}\sigma^{\text{meas}}}{\mathrm{d}x_{j}}-\frac{\mathrm{d}\sigma^{\text{true}}}{\mathrm{d}x_{j}}\right)$
(8)

where $N$ is the number of cross-section bins, $x_{i}$ and $x_{j}$ are the
$i$th and $j$th kinematic bin respectively, and $\mathbf{V}$ is the cross-
section covariance matrix.

The post-fit p-value was calculated for the fit to data (or mock data) as
another metric to check the validity of the result. First, numerous
statistical and systematically varied samples of the MC prediction were
produced and then fit to build a post-fit log-likelihood distribution from Eq.
2. The p-value is the fraction of the simulated likelihood distribution that
is greater than the post-fit log-likelihood of the fit in question. A value of
0.05 for the p-value has been chosen as the threshold to require further
investigation of the result.

##  V Results

The distributions of the reconstructed events used to calculate the cross
section are shown in Figs. 19 and 20 for ND280 and Fig. 21 for INGRID as a
function of the muon kinematics compared to the nominal and post-fit MC
predictions with data plus statistical errors overlaid. In general the fit is
able to adjust the fit parameters as described in Sec. IV to match the
observed data in the signal samples for both detectors within expected
statistical fluctuations.

Nearly all systematic parameters had a post-fit value within their $1\sigma$
prior uncertainty, with the normalization parameters for DIS and multi-$\pi$
events pulled further than $1\sigma$ to accommodate the difference between the
nominal MC and the data in the control samples as discussed previously in Sec.
III. Additionally, the 2p2h shape parameter was pulled to the boundary
corresponding to pushing the distribution of 2p2h events toward smaller
momentum and energy transfer. The p-value for the fit to data compared to the
nominal input model was calculated to be approximately 0.01, and was
investigated further to verify the robustness of the result. The extracted
cross sections for ND280 and INGRID are shown in Figs. 22 and 23 respectively,
and includes an additional uncertainty to account for possible missing freedom
in the fit indicated by the poor p-value. A discussion of the poor p-value is
provided in the following section (Sec. V.1). Additional plots of the
extracted cross section including the last momentum bin extending to 30 GeV/c
are shown in Appendix D.

###  V.1 Discussion on the poor p-value

As part of the data fit validation a p-value was calculated for the post-fit
result as described in Sec. IV.4 to gauge the compatibility of the result with
the nominal input model. The overall p-value for the original fit to data was
calculated to be approximately 0.01, indicating that, relative to the input
model, the observed data was an unlikely fluctuation. Based on the post-fit
likelihood for each sample and the systematic contribution, the two main
hypotheses were the pion modelling for background events (including the
separation of samples for tracked versus Michel-tagged pions) and the high
momentum bins considered in the fit. Several tests and different
configurations of the fit were considered to see the impact on the result and
to evaluate the need for an additional uncertainty.

To test the freedom of the pion model, two additional interaction model
parameters were included to introduce more freedom at low pion and muon
momentum where the majority of tension is present. One parameter was allowed
to further alter the overall normalization of out-of-fiducial volume events
(which are more likely at lower muon momentum), and the other changes the
kinematics of the intermediate $\Delta$ decay in resonant pion interactions,
which modifies the outgoing pion spectrum. In the fit to data, the rate of
out-of-fiducial events was increased and the $\Delta$-decay parameter was
moved to increase the rate of low-momentum pions (which correlates with low-
momentum muons). However the total post-fit likelihood only improved by about
1% compared to the data fit without these extra parameters, showing little
sensitivity to the change in pion kinematics.

Next an alternative configuration of the fit combines the ND280 CC-$1\pi^{+}$
and CC-Michel control samples (Samples VI and VIII respectively) in an attempt
to quantify the role of the control samples on the background model, inspired
by how these samples were used in previous T2K analyses [69, 71]. Overall the
fit with the merged control samples gives similar results to the original fit,
but with slightly better post-fit likelihood for the systematic contribution
and a p-value of 0.024. The post-fit likelihood for the signal samples are
nearly identical to the original showing little impact from the merged versus
separated pion control samples. The merged sample performs slightly better
compared to being separated, highlighting the tension between these samples as
a driver of the poor p-value.

For the final test of the pion model, the fit was tested using only a single
pion control sample (ND280 CC-$1\pi^{+}$, ND280 CC-Michel, INGRID CC-$1\pi$)
at a time. The post-fit likelihood for the other samples largely were the same
and the systematic contribution to the likelihood was about 10% smaller (which
is expected as fewer bins should in general easier to describe using the same
systematic parameters) for each test case, indicating a robust result with
respect to the pion control samples. The little to no effect on the signal
samples across these tests is primarily due to the low contamination of pion
events and the relative fraction of events in the signal versus control
samples.

Another alternative configuration removes the high momentum bins extending to
30 GeV/c for each ND280 sample (except the backward bin) as these bins were
contributing a disproportional amount to the total $\chi^{2}$ relative to what
would be expected from only statistical fluctuations. This was performed as an
additional closure test to check that there was no pathological behavior
regarding these bins that could be driving the p-value result. The fit
performs moderately better as expected when removing problematic bins with a
p-value of 0.065. Given the modest increase of the p-value and since the
analysis is less sensitive to this kinematic region, these bins were
considered not to be a problem.

The goal of these tests was to see if a large difference in p-value or post-
fit likelihood was noticeable and if it required an additional uncertainty.
The consistency of the post-fit results for the original fit to data and the
variety of alternative fit configurations is evidence of a robust result for
the analysis, and based on these additional investigations the small p-value
is not an indication of a biased result and is driven by the measured data.
Furthermore the slight variation in extracted cross section from the different
tests were all well covered by the uncertainty on the original result.
However, to be conservative, an additional uncorrelated uncertainty is added
across all bins to cover the average difference between the original fit and
the fit with merged ND280 control samples and the fit where the highest ND280
momentum bins were removed as these showed the largest difference in the
extracted cross section. This additional uncertainty uses a similar method to
the PDG to calculate how much the errors needed to be scaled to cover the
different central values at 68% confidence level by construction [76]. The
percent error increase for each kinematic bin is shown in Fig. 18 where most
bins had a 2% or less increase in error and the large increases generally
correspond to the highest momentum bins.

Figure 18: Percent error increase for each cross-section bin (flattened as a
1D array) from the the additional studies for the small p-value.

Figure 19: Event distribution for measured data and the pre-/post-fit MC
prediction in reconstructed muon momentum and angle for the ND280 signal
samples.

Figure 20: Event distribution for measured data and the pre-/post-fit MC
prediction in reconstructed muon momentum and angle for the ND280 control
samples.

Figure 21: Event distribution for measured data and the pre-/post-fit MC
prediction in reconstructed muon distance and angle for the INGRID signal
sample (top) and control sample (bottom).

Figure 22: Extracted ND280 cross section as a function of muon momentum in
angle bins compared to the nominal NEUT MC prediction. Note that the final bin
extending to 30 GeV/c has been omitted for clarity.

Figure 23: Extracted INGRID cross section as a function of muon momentum in
angle bins compared to the nominal NEUT MC prediction. Note that the final bin
extending to 30 GeV/c has been omitted for clarity.

###  V.2 Model comparisons

In this section, the measured cross sections are compared to a small selection
of neutrino interaction models. The agreement between the measurement and
models is quantified via the $\chi^{2}$ (relative to the number of degrees of
freedom) as in Eq. 8 where $\sigma^{\text{true}}$ is replaced by the model
prediction $\sigma^{\text{model}}$. The model predictions were produced by
generating a sufficiently large number of neutrino interactions on hydrocarbon
using the T2K on- and off-axis flux for each model. Generated events that
satisfy the CC-$0\pi$ signal definition are selected to calculate the flux
integrated cross section for each detector. The comparisons between this
result and following models were facilitated by the nuisance software package
[77].

  1. (i)

neut 5.5.0 [53, 52] : several different NEUT configurations were used: two
using the Benhar et al. [54] spectral function approach for the nuclear ground
state with different values of the axial mass ($M_{A}^{QE}=1.03$ and
$M_{A}^{QE}=1.21$ $\mathrm{GeV}/c^{2}$), and one using the Nieves et al. model
[20] for the nuclear ground state and quasi-elastic interactions (which is
based on a local Fermi gas). All NEUT models use the same pion production
model, multi-nucleon model from Nieves et al. [20], and FSI interaction model
as described earlier in Sec. III.1. This is a newer version of NEUT compared
to the nominal MC production (NEUT 5.3.2) used in the analysis.

  2. (ii)

genie 3.0.6 [78, 79]: two different GENIE configurations were used: the
“G18_01a” tune, which includes the Bodek–Ritchie modified relativistic Fermi
gas (BRRFG) for the ground state nuclear model, the GENIE empirical multi-
nucleon model [80], the Rein–Sehgal model for pion production, and the hA
model for FSI; the “G18_10b” tune, which uses the local Fermi gas (LFG) for
the nuclear model, the Nieves et al. multi-nucleon model, the Berger–Sehgal
model for pion production, and the hN model for FSI. The cross-section models
for both of these configurations are tuned using a preliminary version of the
fit to bubble chamber data as described in Ref. [81].

  3. (iii)

nuwro 21.09 [82]: several NuWro configurations were used: one using a spectral
function approach for the nuclear ground state with the Nieves multi-nucleon
model, and multiple using a local Fermi gas (LFG) for the nuclear ground state
with a different available multi-nucleon model: SuSAv2 [83], Nieves et al., or
Martini et al. [16]. All configurations use the same models for pion
production and FSI interactions and set $M_{A}^{QE}=1.03$
$\mathrm{GeV}/c^{2}$.

Tab. 3 contains the $\chi^{2}$ for the joint result and the $\chi^{2}$
considering a single detector. The joint $\chi^{2}$ for a given model
comparison will be slightly different from the sum of the individual
$\chi^{2}$ values due to the correlations between the detectors. Overall the
generator predictions do not describe the data well according to $\chi^{2}/N$
values ranging from approximately 1.5 to 3.0 for $N=70$ degrees of freedom
(measured bins) with 58 ND280 bins and 12 INGRID bins. The larger $\chi^{2}$
values for ND280 compared to INGRID is primarily due to ND280 having a finer
binning than INGRID. A unique aspect of this measurement is the ability to
compare how a given model does for ND280 and INGRID individually and how the
full result with correlations between ND280 and INGRID is better or worse than
the naive sum. For example, the two GENIE models used in this paper show
opposite behavior: one model describes ND280 better than the other but does
worse describing INGRID and vice versa.

Figures 24 and 25 show the data compared to each generator’s implementation of
a LFG nuclear ground state plus the Nieves et al. multi-nucleon model. The
pion production models will be roughly similar, however the FSI treatment is
different between each prediction. The generators mostly differ in the
normalization for the ND280 bins at the middle momentum range around the T2K
flux peak energy of 0.6 GeV, however all show very similar INGRID predictions.
For this particular set of models and generator versions, NEUT performs
notably better than GENIE and NuWro.

Figures 26 and 27 show the data compared to several different multi-nucleon
predictions using NuWro with a LFG ground state and the same parameters for
all other aspects of the generation. The predictions are very similar between
the different multi-nucleon models as implemented in NuWro, with a slight
preference for SuSAv2.

Model | ND280 | INGRID | Joint
---|---|---|---
Nominal MC (NEUT) | 136.34 | 18.21 | 158.71
NEUT LFG+Nieves | 106.46 | 11.46 | 116.26
NEUT SF+Nieves $M_{A}=1.03$ | 194.88 | 14.36 | 209.18
NEUT SF+Nieves $M_{A}=1.21$ | 158.71 | 9.98 | 170.93
NuWro SF+Nieves | 122.74 | 15.68 | 137.02
NuWro LFG+Nieves | 125.88 | 12.75 | 141.04
NuWro LFG+SuSAv2 | 121.57 | 11.13 | 135.38
NuWro LFG+Martini | 138.86 | 12.46 | 155.68
GENIE BRRFG+EmpMEC | 141.40 | 12.80 | 156.05
GENIE LFG+Nieves | 125.50 | 14.45 | 135.69
Table 3: Agreement between this result and the various model comparisons as
measured by the $\chi^{2}$ for both the joint result and when compared to each
detector individually. ND280 has 58 cross-section bins and INGRID has 12
cross-section bins for a combined 70 total bins.

Figure 24: Extracted ND280 cross section as a function of muon momentum in
angle bins compared to NEUT, GENIE, and NuWro all using a similar model. Note
that the final bin extending to 30 GeV/c has been omitted for clarity.

Figure 25: Extracted INGRID cross section as a function of muon momentum in
angle bins compared to NEUT, GENIE, and NuWro all using a similar model. Note
that the final bin extending to 30 GeV/c has been omitted for clarity.

Figure 26: Extracted ND280 cross section as a function of muon momentum in
angle bins compared to several different multi-nucleon predictions using NuWro
and the same LFG ground state. Note that the final bin extending to 30 GeV/c
has been omitted for clarity.

Figure 27: Extracted INGRID cross section as a function of muon momentum in
angle bins compared to several different different multi-nucleon predictions
using NuWro and the same LFG ground state. Note that the final bin extending
to 30 GeV/c has been omitted for clarity.

###  V.3 Comparison to previous result

This analysis uses the same binning for the ND280 samples as the CC-$0\pi$
analysis from Ref. [69], allowing for a direct comparison between the results.
The main differences are the inclusion of more data for this result (T2K Run
8), increasing the neutrino-mode sample statistics by approximately a factor
of two, and the configuration of the fits, where this analysis did a neutrino-
only joint fit of on- and off-axis data and Ref. [69] did a joint anti-
neutrino and neutrino fit with only off-axis data. Both results are shown in
Fig. 28 with the final bin extending to 30 GeV/c omitted for clarity. The
majority of the bins agree within their $1\sigma$ error bars, and show a trend
for this result to report a smaller cross section at medium to higher muon
momentum (above 0.8 GeV/c) that is more pronounced at more forward-going
angles. Additionally, the high fluctuation in the cross section seen in the
2.0 to 3.0 GeV/c momentum bin in the most forward angle bin
($0.98<\cos{\theta_{\mu}}<1.00$) is now smaller and closer in value to the
neighboring bins compared to previous T2K CC-$0\pi$ results.

Figure 28: Extracted ND280 cross section from this analysis compared to the
neutrino analysis in Ref. [69]. The final momentum bin extending to 30 GeV/c
has been omitted for clarity.

##  VI Conclusions

This paper presents the first measurement of neutrino interactions without
pions in the final state using multiple energy spectra at T2K with the on- and
off-axis near detectors. The analysis was performed using a joint maximum
likelihood fit with signal and control samples from both detectors to minimize
the background uncertainties and perform the unfolding from reconstructed to
truth variables. The results include the cross-section measurement at each
detector and the correlation between them, providing additional information
compared to the individual measurements. Generator models continue to struggle
to describe the data, and for the comparisons performed in this paper, the
NEUT implementation of a LFG ground state plus the Nieves et al. multi-nucleon
model has the smallest $\chi^{2}/N\sim 1.66$, which is still very poor
agreement.

This analysis is the next step in combined measurements at T2K and further
opens up the possibility for more complex combinations of analyses. Only
neutrino-mode data was considered for this first analysis using multiple
energy spectra, but future analyses will include the anti-neutrino data.
Additionally, future versions of this analysis will include the T2K replica
target measurements from NA61/SHINE [84] for the flux modeling, and updates of
the neutrino interaction model.

Since this analysis was finalized, the WAGASCI [85] and BabyMIND [86]
detectors were added to the T2K near detector hall at an off-axis angle of 1.5
degrees and have started taking data. WAGASCI/BabyMIND data could be used to
extend this analysis to use three different energy spectra, and provide
additional statistics for interactions on both hydrocarbon and water. The
upcoming J-PARC accelerator upgrade [87] will increase the beam power
providing a higher rate of data taking. Finally, the ND280 upgrade [88] will
increase the detector capabilities, providing increased angle coverage, better
low momentum tracking, and additional target mass.

The data release for this analysis is hosted at Ref. [89]. It contains the
best-fit cross-section results, the nominal MC prediction, the associated
covariance matrix, the analysis binning, and the flux histograms.

## Acknowledgements

We thank the J-PARC staff for superb accelerator performance. We thank the
CERN NA61/SHINE Collaboration for providing valuable particle production data.
We acknowledge the support of MEXT, JSPS KAKENHI and bilateral programs,
Japan; NSERC, the NRC, and CFI, Canada; the CEA and CNRS/IN2P3, France; the
DFG, Germany; the INFN, Italy; the Ministry of Science and Education and the
National Science Centre, Poland; the RSF, RFBR and the Ministry of Science and
Higher Education, Russia; MICINN and ERDF funds and CERCA program, Spain; the
SNSF and SERI, Switzerland; the STFC and UKRI, UK; and the DOE, USA. We also
thank CERN for the UA1/NOMAD magnet, DESY for the HERA-B magnet mover system,
the BC DRI Group, Prairie DRI Group, ACENET, SciNet, and CalculQuebec
consortia in the Digital Research Alliance of Canada, and GridPP in the United
Kingdom, and the CNRS/IN2P3 Computing Center in France. In addition, the
participation of individual researchers and institutions has been further
supported by funds from the ERC (FP7), “la Caixa” Foundation, the European
Union’s Horizon 2020 Research and Innovation Programme under the Marie
Sklodowska-Curie grant; the JSPS, Japan; the Royal Society, UK; French ANR;
and the DOE Early Career programme, USA. This work was supported in part
through computational resources and services provided by the Institute for
Cyber-Enabled Research at Michigan State University. For the purposes of open
access, the authors have applied a Creative Commons Attribution licence to any
Author Accepted Manuscript version arising.

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##  Appendix A Analysis binning

# bins |  $\cos(\theta_{\mu})$ bin |  $p_{\mu}$ bin edges (GeV/c)
---|---|---
1 | -1.00, 0.20 | 0, 30
5 | 0.20, 0.60 | 0, 0.3, 0.4, 0.5, 0.6, 30
6 | 0.60, 0.70 | 0, 0.3, 0.4, 0.5, 0.6, 0.8, 30
6 | 0.70, 0.80 | 0, 0.3, 0.4, 0.5, 0.6, 0.8, 30
7 | 0.80, 0.85 | 0, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 30
8 | 0.85, 0.90 | 0, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.5, 30
7 | 0.90, 0.94 | 0, 0.4, 0.5, 0.6, 0.8, 0.8, 1.25, 2.0, 30
10 | 0.94, 0.98 | 0, 0.4, 0.5, 0.6, 0.8, 0.8, 1.25, 1.5, 2.0,
|  | 3.0, 30
8 | 0.98, 1.00 | 0, 0.5, 0.7, 0.9, 1.25, 2.0, 3.0, 5.0, 30
Table 4: ND280 analysis binning for extracted cross section. # bins |  $\cos(\theta_{\mu})$ bin |  $p_{\mu}$ bin edges (GeV/c)
---|---|---
4 | 0.50, 0.82 | 0.35, 0.50, 0.70, 1.0, 30
4 | 0.82, 0.94 | 0.35, 0.50, 0.70, 1.0, 30
4 | 0.94, 1.00 | 0.35, 0.50, 0.70, 1.0, 30
Table 5: INGRID analysis binning for extracted cross section.

##  Appendix B Flux energy binning

ND280 | INGRID | Energy bin (GeV)
---|---|---
$f_{0}$ | $f_{20}$ | 0.0 - 0.1
$f_{1}$ | $f_{21}$ | 0.1 - 0.2
$f_{2}$ | $f_{22}$ | 0.2 - 0.3
$f_{3}$ | $f_{23}$ | 0.3 - 0.4
$f_{4}$ | $f_{24}$ | 0.4 - 0.5
$f_{5}$ | $f_{25}$ | 0.5 - 0.6
$f_{6}$ | $f_{26}$ | 0.6 - 0.7
$f_{7}$ | $f_{27}$ | 0.7 - 0.8
$f_{8}$ | $f_{28}$ | 0.8 - 1.0
$f_{9}$ | $f_{29}$ | 1.0 - 1.2
$f_{10}$ | $f_{30}$ | 1.2 - 1.5
$f_{11}$ | $f_{31}$ | 1.5 - 2.0
$f_{12}$ | $f_{32}$ | 2.0 - 2.5
$f_{13}$ | $f_{33}$ | 2.5 - 3.0
$f_{14}$ | $f_{34}$ | 3.0 - 3.5
$f_{15}$ | $f_{35}$ | 3.5 - 4.0
$f_{16}$ | $f_{36}$ | 4.0 - 5.0
$f_{17}$ | $f_{37}$ | 5.0 - 7.0
$f_{18}$ | $f_{38}$ | 7.0 - 10.0
$f_{19}$ | $f_{39}$ | 10.0 - 30.0
Table 6: The neutrino energy binning used for the flux systematic parameters.
Both the ND280 and INGRID flux parameters use the same energy binning, but are
treated as separate parameters in the fit.

##  Appendix C Neutrino interaction parameters

Parameter | Type | Prior | Error
---|---|---|---
$M_{A}^{QE}$ | Signal shape | 1.21 | 0.3
2p2h $\nu$ norm. | Signal normalization | 1.0 | 1.0
2p2h $\nu$ shape | Signal shape | 1.0 | 1.0
$M_{A}^{Res}$ | Bkg shape | 0.95 | 0.15
$C_{A}^{5}$ | Bkg shape | 1.01 | 0.12
Bkg Resonant ($I_{1/2}$) | Bkg normalization | 1.3 | 0.2
DIS Multiple pion | Bkg shape | 1.0 | 0.4
CC-1$\pi$ $E_{\nu}<$ 2.5 GeV | Bkg normalization | 1.0 | 0.5
CC-1$\pi$ $E_{\nu}>$ 2.5 GeV | Bkg normalization | 1.0 | 0.5
CC DIS | Bkg normalization | 1.0 | 0.5
CC Multi-$\pi$ | Bkg normalization | 1.0 | 0.5
CC Coherent on C | Bkg normalization | 1.0 | 1.0
NC Coherent | Bkg normalization | 1.0 | 0.3
NC Other | Bkg normalization | 1.0 | 0.3
CC $\nu_{e}$ | Bkg normalization | 1.0 | 0.03
FSI Inelastic, LE | Bkg shape | 1.0 | 0.41
FSI $\pi$ absorbtion | Bkg shape | 1.1 | 0.41
FSI Charge exchange, LE | Bkg shape | 1.0 | 0.57
FSI Inelastic, HE | Bkg shape | 1.8 | 0.34
FSI $\pi$ production | Bkg shape | 1.0 | 0.50
FSI Charge exchange, HE | Bkg shape | 1.8 | 0.28
Table 7: Cross-section modeling parameters used in this analysis along with
their type, prior, and prior fractional uncertainty.

##  Appendix D Additional data plots

Figure 29: Extracted ND280 cross section as a function of muon momentum in
angle bins compared to the nominal NEUT MC prediction including the final
momentum bin.

Figure 30: Extracted INGRID cross section as a function of muon momentum in
angle bins compared to the nominal NEUT MC prediction including the final
momentum bin.