††thanks: also at BMCC/CUNY, Science Department, New York, New York, U.S.A.

The Super-Kamiokande Collaboration

††thanks: also at Université Paris-Saclay††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
J-PARC, Tokai, Japan††thanks: also at JINR, Dubna, Russia††thanks: also at the
Graduate University of Science and Technology, Vietnam Academy of Science and
Technology††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 joint oscillation analysis of Super-Kamiokande atmospheric and T2K
accelerator neutrino data

K. Abe  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  S. Abe  University of Tokyo,
Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  C.
Bronner  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, 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  K.
Hiraide  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  K. Hosokawa  University of Tokyo,
Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  K.
Ieki  M. Ikeda  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  J. Kameda
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. Kanemura  R. Kaneshima  Y.
Kashiwagi  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  Y. Kataoka  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  S.
Miki  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  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  S. Moriyama  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  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. 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  Y. Noguchi  K. Sato  University of
Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, 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  H. Shiba  K. Shimizu  University
of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka,
Japan  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  Y. Sonoda  Y.
Suzuki  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  A. Takeda  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.
Takemoto  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  H. Tanaka  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. Yano  University of Tokyo, Institute for Cosmic Ray
Research, Kamioka Observatory, Kamioka, Japan  S. Han  University of Tokyo,
Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos,
Kashiwa, Japan  T. Kajita  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  ILANCE, CNRS – University of Tokyo International
Research Laboratory, Kashiwa, Chiba, 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. Tashiro  T. Tomiya  X. Wang  S.
Yoshida  University of Tokyo, Institute for Cosmic Ray Research, Research
Center for Cosmic Neutrinos, Kashiwa, Japan  P. Fernandez  L. Labarga  N.
Ospina  B. Zaldivar  University Autonoma Madrid, Department of Theoretical
Physics, Madrid, Spain  B. W. Pointon  British Columbia Institute of
Technology, Department of Physics, Burnaby, British Columbia, Canada  TRIUMF,
Vancouver, British Columbia, Canada  E. Kearns  Boston University, Department
of Physics, Boston, Massachusetts, 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  J. Mirabito
Boston University, Department of Physics, Boston, Massachusetts, U.S.A.  J. L.
Raaf  Boston University, Department of Physics, Boston, Massachusetts, U.S.A.
L. Wan  Boston University, Department of Physics, Boston, Massachusetts,
U.S.A.  T. Wester  Boston University, Department of Physics, Boston,
Massachusetts, U.S.A.  J. Bian  N. J. Griskevich  University of California,
Irvine, Department of Physics and Astronomy, Irvine, California, U.S.A.  M. B.
Smy  H. W. 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  V. Takhistov
University of California, Irvine, Department of Physics and Astronomy, Irvine,
California, U.S.A.  High Energy Accelerator Research Organization (KEK),
Tsukuba, Ibaraki, Japan  A. Yankelevich  University of California, Irvine,
Department of Physics and Astronomy, Irvine, California, U.S.A.  J. Hill
California State University, Department of Physics, Dominguez Hills, Carson,
California, U.S.A  M. C. Jang  S. H. Lee  D. H. Moon  R. G. Park  Chonnam
National University, Institute for Universe and Elementary Particles, Gwangju,
Korea  B. Bodur  Duke University, Department of Physics, Durham, North
Carolina, U.S.A.  K. Scholberg  C. W. Walter  Duke University, Department of
Physics, Durham, North Carolina, 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  A. Beauchêne  O.
Drapier  A. Giampaolo  Th. A. Mueller  A. D. Santos  P. Paganini  B. Quilain
R. Rogly  Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet,
Palaiseau, France  T. Nakamura  Gifu University, Department of Physics, Gifu,
Japan  J. S. Jang  Gwangju Institute of Science and Technology, GIST College,
Gwangju, Korea  L. N. Machado  University of Glasgow, School of Physics and
Astronomy, Glasgow, United Kingdom  J. G. Learned  University of Hawaii,
Department of Physics and Astronomy, Honolulu, Hawaii, U.S.A.  K. Choi  N.
Iovine  Institute for Basic Science (IBS), Center for Underground Physics,
Daejeon, Korea  S. Cao  Institute For Interdisciplinary Research in Science
and Education (IFIRSE), ICISE, Quy Nhon, Vietnam  L. H. V. Anthony  D. Martin
N. W. Prouse  M. Scott  Y. Uchida  Imperial College London, Department of
Physics, London, United Kingdom  V. Berardi  N. F. Calabria  M. G. Catanesi
E. Radicioni  INFN Sezione di Bari and Università e Politecnico di Bari,
Dipartimento Interuniversitario di Fisica, Bari, Italy  A. Langella  G. De
Rosa  INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica,
Napoli, Italy  G. Collazuol  M. Feltre  F. Iacob  M. Mattiazzi  INFN Sezione
di Padova and Università di Padova, Dipartimento di Fisica, Padova, Italy  L.
Ludovici  INFN Sezione di Roma and Università di Roma “La Sapienza”, Roma,
Italy  M. Gonin  L. Périssé  G. Pronost  ILANCE, CNRS – University of Tokyo
International Research Laboratory, Kashiwa, Chiba, Japan  C. Fujisawa  S.
Horiuchi  M. Kobayashi  Y.M. Liu  Y. Maekawa  Y. Nishimura  R. Okazaki  Keio
University, Department of Physics, Kanagawa, Japan  R. Akutsu  M. Friend  T.
Hasegawa  T. Ishida  T. Kobayashi  M. Jakkapu  T. Matsubara  T. Nakadaira
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
K. Nakamura  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki, 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. Oyama  A. Portocarrero Yrey  K.
Sakashita  T. Sekiguchi  T. Tsukamoto  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki, Japan  N. Bhuiyan  G. T. Burton  F. Di
Lodovico  J. Gao  A. Goldsack  T. Katori  J. Migenda  R. M. Ramsden  Z. Xie
King’s College London, Department of Physics, Strand, London, United Kingdom
S. Zsoldos  King’s College London, Department of Physics, Strand, London,
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. T. Suzuki  Y. Takagi  Kobe
University, Kobe, 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  H. Zhong  Kobe University, Kobe, Japan  J. Feng  L.
Feng  J. R. Hu  Z. Hu  M. Kawaue  T. Kikawa  M. Mori  Kyoto University,
Department of Physics, Kyoto, 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  R. A. Wendell  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. Yasutome  Kyoto
University, Department of Physics, Kyoto, Japan  S. J. Jenkins  N. McCauley
P. Mehta  A. Tarrant  University of Liverpool, Department of Physics,
Liverpool, United Kingdom  M. J. Wilking  University of Minnesota, School of
Physics and Astronomy, Minneapolis, Minnesota, U.S.A.  Y. Fukuda  Miyagi
University of Education, Department of Physics, Sendai, Japan  Y. Itow  Nagoya
University, Institute for Space-Earth Environmental Research, Nagoya, Aichi,
Japan  Nagoya University, Kobayashi-Maskawa Institute for the Origin of
Particles and the Universe, Nagoya, Aichi, Japan  H. Menjo  K. Ninomiya  Y.
Yoshioka  Nagoya University, Institute for Space-Earth Environmental Research,
Nagoya, Aichi, Japan  J. Lagoda  M. Mandal  P. Mijakowski  Y. S. Prabhu  J.
Zalipska  National Centre for Nuclear Research, Warsaw, Poland  M. Jia  J.
Jiang  W. Shi  C. Yanagisawa  State University of New York at Stony Brook,
Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  M. Harada
Y. Hino  H. Ishino  Okayama University, Department of Physics, Okayama, Japan
Y. Koshio  Okayama University, Department of Physics, Okayama, 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  F. Nakanishi  S. Sakai  T. Tada  T. Tano  Okayama
University, Department of Physics, Okayama, Japan  T. Ishizuka  Osaka Electro-
Communication University, Media Communication Center, Neyagawa, Osaka, Japan
G. Barr  D. Barrow  Oxford University, Department of Physics, Oxford, United
Kingdom  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  S. Samani  Oxford University, Department of
Physics, Oxford, United Kingdom  D. Wark  Oxford University, Department of
Physics, Oxford, United Kingdom  STFC, Rutherford Appleton Laboratory, Harwell
Oxford, and Daresbury Laboratory, Warrington, United Kingdom  A. Holin  F.
Nova  Rutherford Appleton Laboratory, Harwell, Oxford, United Kingdom  S. Jung
B. S. Yang  J. Y. Yang  J. Yoo  Seoul National University, Department of
Physics, Seoul, Korea  J. E. P. Fannon  L. Kneale  M. Malek  J. M. McElwee  M.
D. Thiesse  L. F. Thompson  S. T. Wilson  University of Sheffield, Department
of Physics and Astronomy, Sheffield, United Kingdom  H. Okazawa  Shizuoka
University of Welfare, Department of Informatics in Social Welfare, Yaizu,
Shizuoka, Japan  S. M. Lakshmi  University of Silesia, Institute of Physics,
Katowice, Poland  S. B. Kim  E. Kwon  J. W. Seo  I. Yu  Sungkyunkwan
University, Department of Physics, Suwon, Korea  A. K. Ichikawa  K. D.
Nakamura  S. Tairafune  Tohoku University, Faculty of Science, Department of
Physics, Miyagi, Japan  K. Nishijima  Tokai University, Department of Physics,
Hiratsuka, Kanagawa, Japan  A. Eguchi  K. Nakagiri  University of Tokyo,
Department of Physics, Tokyo, Japan  Y. Nakajima  University of Tokyo,
Department of Physics, Tokyo, 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  S. Shima  N.
Taniuchi  E. Watanabe  University of Tokyo, Department of Physics, Tokyo,
Japan  M. Yokoyama  University of Tokyo, Department of Physics, Tokyo, 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  P. de Perio  S. Fujita  C. Jesús-Valls  K. Martens  K.
M. Tsui  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  M. R. 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.  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  S. Izumiyama  M. Kuze  R.
Matsumoto  K. Terada  Tokyo Institute of Technology, Department of Physics,
Tokyo, Japan  R. Asaka  M. Ishitsuka  H. Ito  Y. Ommura  N. Shigeta  M.
Shinoki  K. Yamauchi  T. Yoshida  Tokyo University of Science, Faculty of
Science and Technology, Department of Physics, Noda, Chiba, Japan  R. Gaur
TRIUMF, Vancouver, British Columbia, Canada  V. Gousy-Leblanc  also at
University of Victoria, Department of Physics and Astronomy, PO Box 1700 STN
CSC, Victoria, BC V8W 2Y2, Canada.  TRIUMF, Vancouver, British Columbia,
Canada  M. Hartz  A. Konaka  X. Li  TRIUMF, Vancouver, British Columbia,
Canada  S. Chen  B. D. Xu  Y. Wu  A.Q. Zhang  B. Zhang  Tsinghua University,
Department of Engineering Physics, Beijing, China  M. Posiadala-Zezula
University of Warsaw, Faculty of Physics, Warsaw, Poland  S. B. Boyd  R.
Edwards  D. Hadley  M. Nicholson  M. O’Flaherty  B. Richards  University of
Warwick, Department of Physics, Coventry, United Kingdom  A. Ali  University
of Winnipeg, Department of Physics, Winnipeg, Manitoba, Canada  TRIUMF,
Vancouver, British Columbia, Canada  B. Jamieson  University of Winnipeg,
Department of Physics, Winnipeg, Manitoba, Canada  S. Amanai  Ll. Marti  A.
Minamino  R. Shibayama  R. Shimamura  S. Suzuki  Yokohama National University,
Department of Physics, Yokohama, Japan  University Autonoma Madrid, Department
of Theoretical Physics, Madrid, Spain  University of Bern, Albert Einstein
Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP),
Bern, Switzerland  Boston University, Department of Physics, Boston,
Massachusetts, U.S.A.  University of British Columbia, Department of Physics
and Astronomy, Vancouver, British Columbia, Canada  University of California,
Irvine, Department of Physics and Astronomy, Irvine, California, U.S.A.  IRFU,
CEA, Université Paris-Saclay, Gif-sur-Yvette, France  University of Colorado
at Boulder, Department of Physics, Boulder, Colorado, U.S.A.  Colorado State
University, Department of Physics, Fort Collins, Colorado, U.S.A.  Duke
University, Department of Physics, Durham, North Carolina, U.S.A.  Eötvös
Loránd University, Department of Atomic Physics, Budapest, Hungary  ETH
Zurich, Institute for Particle Physics and Astrophysics, Zurich, Switzerland
Hanoi University of Science, Vietnam National University, Hanoi, Vietnam  CERN
European Organization for Nuclear Research, Genéve, Switzerland  University of
Geneva, Section de Physique, DPNC, Geneva, Switzerland  University of Glasgow,
School of Physics and Astronomy, Glasgow, United Kingdom  Ghent University,
Department of Physics and Astronomy, Gent, Belgium  H. Niewodniczanski
Institute of Nuclear Physics PAN, Cracow, Poland  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  University of Houston,
Department of Physics, Houston, Texas, U.S.A.  Institut de Fisica d’Altes
Energies (IFAE) - The Barcelona Institute of Science and Technology, Campus
UAB, Bellaterra (Barcelona) Spain  Institut für Physik, Johannes Gutenberg-
Universität Mainz, Staudingerweg 7, Mainz, Germany  IFIC (CSIC & University of
Valencia), Valencia, Spain  Institute For Interdisciplinary Research in
Science and Education (IFIRSE), ICISE, Quy Nhon, Vietnam  Imperial College
London, Department of Physics, London, United Kingdom  INFN Sezione di Bari
and Università e Politecnico di Bari, Dipartimento Interuniversitario di
Fisica, Bari, Italy  INFN Sezione di Napoli and Università di Napoli,
Dipartimento di Fisica, Napoli, Italy  INFN Sezione di Padova and Università
di Padova, Dipartimento di Fisica, Padova, Italy  INFN Sezione di Roma and
Università di Roma “La Sapienza”, Roma, Italy  Institute for Nuclear Research
of the Russian Academy of Sciences, Moscow, Russia  International Centre of
Physics, Institute of Physics (IOP), Vietnam Academy of Science and Technology
(VAST), 10 Dao Tan, Ba Dinh, Hanoi, Vietnam  ILANCE, CNRS – University of
Tokyo International Research Laboratory, Kashiwa, Chiba, 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  Keio University, Department of Physics, Kanagawa, Japan
King’s College London, Department of Physics, Strand, London, United Kingdom
Kobe University, Kobe, Japan  Kyoto University, Department of Physics, Kyoto,
Japan  Lancaster University, Physics Department, Lancaster, United Kingdom
Lawrence Berkeley National Laboratory, Berkeley, California, U.S.A.  Ecole
Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France
University of Liverpool, Department of Physics, Liverpool, United Kingdom
Louisiana State University, Department of Physics and Astronomy, Baton Rouge,
Louisiana, U.S.A.  Joint Institute for Nuclear Research, Dubna, Moscow Region,
Russia  Michigan State University, Department of Physics and Astronomy, East
Lansing, Michigan, U.S.A.  Miyagi University of Education, Department of
Physics, Sendai, Japan  National Centre for Nuclear Research, Warsaw, Poland
State University of New York at Stony Brook, Department of Physics and
Astronomy, Stony Brook, New York, U.S.A.  STFC, Rutherford Appleton
Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United
Kingdom  Okayama University, Department of Physics, Okayama, Japan  Osaka
Metropolitan University, Department of Physics, Osaka, Japan  Oxford
University, Department of Physics, Oxford, United Kingdom  University of
Pennsylvania, Department of Physics and Astronomy, Philadelphia, Pennsylvania
U.S.A.  University of Pittsburgh, Department of Physics and Astronomy,
Pittsburgh, Pennsylvania, U.S.A.  Queen Mary University of London, School of
Physics and Astronomy, London, United Kingdom  University of Regina,
Department of Physics, Regina, Saskatchewan, Canada  University of Rochester,
Department of Physics and Astronomy, Rochester, New York, U.S.A.  Royal
Holloway University of London, Department of Physics, Egham, Surrey, United
Kingdom  RWTH Aachen University, III. Physikalisches Institut, Aachen, Germany
University of Minnesota, School of Physics and Astronomy, Minneapolis,
Minnesota, U.S.A.  Universidad de Sevilla, Departamento de Física Atómica,
Molecular y Nuclear, Sevilla, Spain  University of Sheffield, Department of
Physics and Astronomy, Sheffield, United Kingdom  University of Silesia,
Institute of Physics, Katowice, Poland  Sorbonne Université, CNRS/IN2P3,
Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France
South Dakota School of Mines and Technology, Rapid City, South Dakota, U.S.A.
University of Tokyo, Department of Physics, Tokyo, Japan  University of Tokyo,
Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
University of Tokyo, Institute for Cosmic Ray Research, Research Center for
Cosmic Neutrinos, Kashiwa, Japan  Tokyo Institute of Technology, Department of
Physics, Tokyo, Japan  Tokyo Metropolitan University, Department of Physics,
Tokyo, Japan  Tokyo University of Science, Faculty of Science and Technology,
Department of Physics, Noda, Chiba, Japan  University of Toronto, Department
of Physics, Toronto, Ontario, Canada  TRIUMF, Vancouver, British Columbia,
Canada  University of Warsaw, Faculty of Physics, Warsaw, Poland  Warsaw
University of Technology, Institute of Radioelectronics and Multimedia
Technology, Warsaw, Poland  Tohoku University, Faculty of Science, Department
of Physics, Miyagi, Japan  University of Warwick, Department of Physics,
Coventry, United Kingdom  University of Winnipeg, Department of Physics,
Winnipeg, Manitoba, Canada  Wroclaw University, Faculty of Physics and
Astronomy, Wroclaw, Poland  Yokohama National University, Department of
Physics, Yokohama, Japan  York University, Department of Physics and
Astronomy, Toronto, Ontario, Canada  K. Abe  University of Tokyo, Institute
for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  S. 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. Andreopoulos  University of Liverpool, Department of Physics, Liverpool,
United Kingdom  L. Anthony  Imperial College London, Department of Physics,
London, United Kingdom  M. Antonova  IFIC (CSIC & University of Valencia),
Valencia, Spain  S. Aoki  Kobe University, Kobe, Japan  K.A. Apte  Imperial
College London, Department of Physics, London, United Kingdom  T. Arai
University of Tokyo, Department of Physics, Tokyo, Japan  T. Arihara  Tokyo
Metropolitan University, Department of Physics, Tokyo, Japan  S. Arimoto
Kyoto University, Department of Physics, Kyoto, 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  N. Babu  Louisiana
State University, Department of Physics and Astronomy, Baton Rouge, Louisiana,
U.S.A.  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  P. Bates  University of Liverpool, Department
of Physics, Liverpool, United Kingdom  M. Batkiewicz-Kwasniak  H.
Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland  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, Gif-sur-Yvette, France  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  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
Universidad de Sevilla, Departamento de Física Atómica, Molecular y Nuclear,
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  Lawrence Berkeley National
Laboratory, Berkeley, California, U.S.A.  A. Chalumeau  Sorbonne Université,
CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE),
Paris, 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, Pennsylvania U.S.A.  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  F. Cormier  TRIUMF, Vancouver, British Columbia, Canada
A. Cudd  University of Colorado at Boulder, Department of Physics, Boulder,
Colorado, U.S.A.  D. D’ago  INFN Sezione di Padova and Università di Padova,
Dipartimento di Fisica, Padova, Italy  C. Dalmazzone  Sorbonne Université,
CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE),
Paris, France  T. Daret  IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette,
France  P. Dasgupta  Eötvös Loránd University, Department of Atomic Physics,
Budapest, Hungary  C. Davis  University of Pennsylvania, Department of Physics
and Astronomy, Philadelphia, Pennsylvania U.S.A.  Yu.I. Davydov  Joint
Institute for Nuclear Research, Dubna, Moscow Region, Russia  A. De Roeck
CERN European Organization for Nuclear Research, Genéve, 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  R. Dharmapal  Wroclaw University, Faculty
of Physics and Astronomy, Wroclaw, Poland  F. Di Lodovico  King’s College
London, Department of Physics, Strand, London, United Kingdom  G. Diaz Lopez
Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de
Hautes Energies (LPNHE), Paris, France  S. Dolan  CERN European Organization
for Nuclear Research, Genéve, 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  K.E. Duffy  Oxford University, Department
of Physics, Oxford, United Kingdom  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  J. Elias
University of Rochester, Department of Physics and Astronomy, Rochester, New
York, U.S.A.  S. Emery-Schrenk  IRFU, CEA, Université Paris-Saclay, Gif-sur-
Yvette, France  G. Erofeev  Institute for Nuclear Research of the Russian
Academy of Sciences, Moscow, Russia  A. Ershova  Ecole Polytechnique,
IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France  G. Eurin  IRFU,
CEA, Université Paris-Saclay, 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  L. Feng  Kyoto University, Department
of Physics, Kyoto, Japan  D. Ferlewicz  University of Tokyo, Department of
Physics, Tokyo, Japan  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  Universidad de Sevilla, Departamento de Física Atómica, Molecular y
Nuclear, 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  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, Japan
J. González Rosa  Universidad de Sevilla, Departamento de Física Atómica,
Molecular y Nuclear, 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  K.
Gorshanov  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  S. Han  University of Tokyo, Institute for
Cosmic Ray Research, Research Center for Cosmic Neutrinos, Kashiwa, Japan
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, 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  I. Heitkamp  Tohoku University, Faculty of Science,
Department of Physics, Miyagi, Japan  D. Henaff  INFN Sezione di Padova and
Università di Padova, Dipartimento di Fisica, Padova, Italy  Y. Hino  Okayama
University, Department of Physics, Okayama, 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  K. Hosokawa  University of
Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
J. Hu  Kyoto University, Department of Physics, Kyoto, Japan  A.K. Ichikawa
Tohoku University, Faculty of Science, Department of Physics, Miyagi, Japan
K. Ieki  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, 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  A. Izmaylov  Institute for Nuclear
Research of the Russian Academy of Sciences, Moscow, Russia  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  M. Jia  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  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, 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.  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. Karpova  University of
Geneva, Section de Physique, DPNC, Geneva, Switzerland  S.P. Kasetti
Louisiana State University, Department of Physics and Astronomy, Baton Rouge,
Louisiana, U.S.A.  V.S. Kasturi  University of Geneva, Section de Physique,
DPNC, Geneva, Switzerland  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, United Kingdom  Y.
Kawamura  Osaka Metropolitan University, Department of Physics, Osaka, Japan
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, United Kingdom  V. Kiseeva  Joint
Institute for Nuclear Research, Dubna, Moscow Region, Russia  J. Kisiel
University of Silesia, Institute of Physics, Katowice, Poland  L. Kneale
University of Sheffield, Department of Physics and Astronomy, Sheffield,
United Kingdom  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, Mainz, Germany  S. Kodama
University of Tokyo, Department of Physics, Tokyo, Japan  M. Kolupanova
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  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  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  V. Kurochka  Institute for Nuclear Research of the
Russian Academy of Sciences, Moscow, Russia  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, Madrid, Spain  M. Lachat  University of
Rochester, Department of Physics and Astronomy, Rochester, New York, U.S.A.
K. Lachner  University of Warwick, Department of Physics, Coventry, United
Kingdom  J. Lagoda  National Centre for Nuclear Research, Warsaw, Poland  S.M.
Lakshmi  University of Silesia, Institute of Physics, Katowice, Poland  M.
Lamers James  Lancaster University, Physics Department, Lancaster, United
Kingdom  STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury
Laboratory, Warrington, United Kingdom  A. Langella  INFN Sezione di Napoli
and Università di Napoli, Dipartimento di Fisica, Napoli, Italy  J.-F. Laporte
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France  D. Last
University of Rochester, Department of Physics and Astronomy, Rochester, New
York, U.S.A.  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  D. Leon Silverio
South Dakota School of Mines and Technology, Rapid City, South Dakota, U.S.A.
S. Levorato  INFN Sezione di Padova and Università di Padova, Dipartimento di
Fisica, Padova, Italy  S. Lewis  King’s College London, Department of Physics,
Strand, London, United Kingdom  C. Lin  Imperial College London, Department of
Physics, London, United Kingdom  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, 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.  K.K. Mahtani  State University of New York at Stony Brook, Department
of Physics and Astronomy, Stony Brook, New York, 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
R. Matsumoto  Tokyo Institute of Technology, Department of Physics, Tokyo,
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, Pennsylvania U.S.A.  K. Mavrokoridis
University of Liverpool, Department of Physics, Liverpool, United Kingdom  E.
Mazzucato  IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France  N.
McCauley  University of Liverpool, Department of Physics, Liverpool, 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  Universidad de
Sevilla, Departamento de Física Atómica, Molecular y Nuclear, Sevilla, Spain
P. Mehta  University of Liverpool, Department of Physics, Liverpool, United
Kingdom  L. Mellet  Michigan State University, Department of Physics and
Astronomy, East Lansing, Michigan, U.S.A.  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  S. Miki  University of Tokyo, Institute for Cosmic Ray Research,
Kamioka Observatory, Kamioka, Japan  E. Miller  King’s College London,
Department of Physics, Strand, London, 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.  A. Muñoz  Ecole Polytechnique, IN2P3-CNRS, Laboratoire
Leprince-Ringuet, Palaiseau, France  ILANCE, CNRS – University of Tokyo
International Research Laboratory, Kashiwa, Chiba, Japan  L. Munteanu  CERN
European Organization for Nuclear Research, Genéve, 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  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  Kyoto University, Department of Physics, Kyoto, Japan
D.T. Nguyen  Hanoi University of Science, Vietnam National University, Hanoi,
Vietnam  V.Q. Nguyen  Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-
Ringuet, Palaiseau, France  K. Niewczas  Ghent University, Department of
Physics and Astronomy, Gent, Belgium  S. Nishimori  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  Y. Nishimura  Keio
University, Department of Physics, Kanagawa, Japan  Y. Noguchi  University of
Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, 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, Mainz, Germany
T. Odagawa  Kyoto University, Department of Physics, Kyoto, Japan  R. Okazaki
Keio University, Department of Physics, Kanagawa, 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. Onda  Kyoto
University, Department of Physics, Kyoto, Japan  N. Ospina  University
Autonoma Madrid, Department of Theoretical Physics, Madrid, Spain  L. Osu
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau,
France  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  J. Pasternak  Imperial College London,
Department of Physics, London, United Kingdom  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.  M. Pfaff  Imperial College London, Department of Physics, London,
United Kingdom  L. Pickering  STFC, Rutherford Appleton Laboratory, Harwell
Oxford, and Daresbury Laboratory, Warrington, 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  H. Prasad  Wroclaw
University, Faculty of Physics and Astronomy, Wroclaw, 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  P.T. Quyen  Institute For
Interdisciplinary Research in Science and Education (IFIRSE), ICISE, Quy Nhon,
Vietnam  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. Ramirez  University of Pennsylvania, Department of
Physics and Astronomy, Philadelphia, Pennsylvania U.S.A.  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
L. Russo  Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire
et de Hautes Energies (LPNHE), Paris, France  A. Rychter  Warsaw University of
Technology, Institute of Radioelectronics and Multimedia Technology, Warsaw,
Poland  W. Saenz  Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique
Nucléaire et de Hautes Energies (LPNHE), Paris, France  K. Sakashita  High
Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  F.
Sánchez  University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
Y. Sato  Tokyo University of Science, Faculty of Science and Technology,
Department of Physics, Noda, Chiba, Japan  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  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  Y. Shiraishi  Okayama University,
Department of Physics, Okayama, Japan  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  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
Y. Stroke  Institute for Nuclear Research of the Russian Academy of Sciences,
Moscow, Russia  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  M. Tada  High Energy Accelerator Research Organization
(KEK), Tsukuba, Ibaraki, Japan  S. Tairafune  Tohoku University, Faculty of
Science, Department of Physics, Miyagi, 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  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. 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. 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, Gif-sur-Yvette, France  E. Villa  CERN European Organization for
Nuclear Research, Genéve, 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  H.T. Wallace  University of Sheffield,
Department of Physics and Astronomy, Sheffield, United Kingdom  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  Oxford University, Department of
Physics, Oxford, United Kingdom  STFC, Rutherford Appleton Laboratory, Harwell
Oxford, and Daresbury Laboratory, Warrington, United Kingdom  A. Weber
Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7,
Mainz, Germany  R. Wendell  Kyoto University, Department of Physics, Kyoto,
Japan  M.J. Wilking  University of Minnesota, School of Physics and Astronomy,
Minneapolis, Minnesota, U.S.A.  C. Wilkinson  Lawrence Berkeley National
Laboratory, Berkeley, California, U.S.A.  J.R. Wilson  King’s College London,
Department of Physics, Strand, London, United Kingdom  K. Wood  Lawrence
Berkeley National Laboratory, Berkeley, California, U.S.A.  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  State University
of New York at Stony Brook, Department of Physics and Astronomy, Stony Brook,
New York, U.S.A.  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
J. Zhang  TRIUMF, Vancouver, British Columbia, Canada  University of British
Columbia, Department of Physics and Astronomy, Vancouver, British Columbia,
Canada  X.Y. Zhao  ETH Zurich, Institute for Particle Physics and
Astrophysics, Zurich, Switzerland  H. Zhong  Kobe University, Kobe, Japan  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, United Kingdom

###### Abstract

The Super-Kamiokande and T2K collaborations present a joint measurement of
neutrino oscillation parameters from their atmospheric and beam neutrino data.
It uses a common interaction model for events overlapping in neutrino energy
and correlated detector systematic uncertainties between the two datasets,
which are found to be compatible. Using 3244.4 days of atmospheric data and a
beam exposure of $19.7(16.3)\times 10^{20}$ protons on target in
(anti)neutrino mode, the analysis finds a 1.9$\sigma$ exclusion of CP-
conservation (defined as $J_{\scriptscriptstyle\mathrm{CP}}=0$) and a
preference for the normal mass ordering.

Introduction—Following the observation of neutrino oscillations [1],
experiments now aim to fully characterize the three-flavor mixing paradigm
described by the Pontecorvo–Maki–Nakagawa–Sakata matrix. Here, neutrino mixing
is governed by three mixing angles ($\theta_{13}$, $\theta_{23}$, and
$\theta_{12}$), two mass splittings ($\Delta m^{2}_{32}$ and $\Delta
m^{2}_{21}$), and one Charge Parity (CP) violating phase
($\delta_{\scriptscriptstyle\mathrm{CP}}$). While some oscillation parameters
have been precisely measured [2], others remain relatively unconstrained. In
particular, the CP-violating phase, the ordering of the neutrino mass states
(MO), and the octant of $\theta_{23}$ have not been determined experimentally.
The Jarlskog invariant [3, 4],
$J_{\scriptscriptstyle\mathrm{CP}}=\sin\theta_{13}\cos^{2}\theta_{13}\sin\theta_{12}\cos\theta_{12}\sin\theta_{23}\cos\theta_{23}\sin\delta_{\scriptscriptstyle\mathrm{CP}}$,
gives the magnitude of a potential CP violation.

Experimental setup—The Super-Kamiokande (SK) experiment [5] measures
atmospheric neutrino oscillations using a large multi-purpose water Cherenkov
detector located in the Kamioka mine in Gifu, Japan. The detector has a 32
kiloton inner detector optically separated from a 2 meter thick outer
detector, which mainly serves as a veto region. Atmospheric neutrinos,
produced by the interaction of cosmic rays with nuclei in the Earth’s
atmosphere, include a mixture of neutrino flavor states, as well as a wide
range of propagation baselines (15$\sim$13000 km) and neutrino energies
(MeV$\sim$TeV).

The Tokai-to-Kamioka (T2K) long-baseline neutrino experiment [6] measures
neutrino oscillations over a baseline of 295 km using a primarily muon
(anti)neutrino beam produced by the neutrino facility at J-PARC, located in
Ibaraki, Japan. SK is T2K’s far detector and measures neutrinos after
oscillations 2.5∘ off of the beam axis. The beam neutrino flux and neutrino
interaction cross sections are constrained by a suite of near detectors (T2K
ND) situated 280 m downstream of the neutrino production target.

Motivation for a joint analysis—T2K’s off-axis neutrino beam provides a narrow
energy spectrum peaked at 600 MeV and a known direction for beam-induced
events at SK. This enables a precise determination of $\sin^{2}(2\theta_{23})$
and $|\Delta m^{2}_{32}|$ using the “disappearance” channels ($\hskip
1.42262pt\hbox
to0.0pt{\hss\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{(}}}\overline{\nu}\hbox
to0.0pt{\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{)}}\hss}_{\mu}\rightarrow\hskip
1.42262pt\hbox
to0.0pt{\hss\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{(}}}\overline{\nu}\hbox
to0.0pt{\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{)}}\hss}_{\mu}$), and some
constraint on the CP-violating phase and the MO via the lower statistics
“appearance” channels ($\hskip 1.42262pt\hbox
to0.0pt{\hss\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{(}}}\overline{\nu}\hbox
to0.0pt{\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{)}}\hss}_{\mu}\rightarrow\hskip
1.42262pt\hbox
to0.0pt{\hss\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{(}}}\overline{\nu}\hbox
to0.0pt{\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{)}}\hss}_{e}$). The beam
composition can be changed from primarily neutrinos to primarily antineutrinos
by switching the polarity of electromagnetic focusing horns, providing the
ability to compare neutrino and antineutrino oscillations. T2K’s baseline
probes the first oscillation maximum and matter effects have a limited impact.
Nonetheless, there are notable parameter degeneracies between the MO and
$\delta_{\scriptscriptstyle\mathrm{CP}}$ [7]. Degeneracies between the lower
and upper octants of $\theta_{23}$ also affect the measurements. SK’s
atmospheric neutrino sample, on the other hand, provides a comparatively weak
constraint on the atmospheric mixing parameters, due to limited information
about the incoming neutrino direction, and a broader range of neutrino
energies. However, upward-going neutrinos experience large matter effects,
producing asymmetric oscillations between neutrinos and antineutrinos and
providing sensitivity to both the octant of $\theta_{23}$ and the MO through
the appearance channel at 2$\sim$10 GeV. This provides a means of breaking the
MO–$\delta_{\scriptscriptstyle\mathrm{CP}}$ degeneracy, complementing the MO
sensitivity achieved at T2K through its lower energy $\hskip 1.42262pt\hbox
to0.0pt{\hss\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{(}}}\overline{\nu}\hbox
to0.0pt{\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{)}}\hss}_{e}$ appearance
events. Additionally, common systematic uncertainties at SK can be better
constrained in a joint fit than in the individual experiments, due to the
addition of the T2K ND constraints to the SK analysis and the large statistics
atmospheric sample to the T2K analysis.

Analysis strategy—The analysis described here is based on previous analyses
from the two experiments [8, 9], modified to produce a coherent joint
analysis. Neutrino oscillation parameters are measured by comparing
predictions for the rates and spectra of the atmospheric and beam neutrinos to
observations performed at SK and making statistical inferences, following both
frequentist and Bayesian approaches. The predictions are made using a model of
the two experiments, covering neutrino fluxes, interactions, and detector
response, with associated uncertainties. This model is built by unifying
aspects of the two experiments’ analyses where appropriate, and using each
individual experiment’s approach otherwise.

Due to the similarities in neutrino energy spectra and event selections, T2K
and low energy atmospheric events are described by a common neutrino
interaction model. The remaining SK atmospheric events correspond to neutrinos
of higher energies, for which the constraint on interaction uncertainties
coming from the lower energy neutrino measurements at the T2K ND is not always
directly applicable. As a result, for these events, the same base interaction
model is used for the initial simulation, but largely independent parameters
are used for interaction systematic uncertainties. The neutrino flux models of
the two experiments [8, 10, 11] are mostly independent, with the only common
source of systematic uncertainty coming from hadron production in proton
collisions. Hadron production is tuned using different measurements in the two
models: the SK atmospheric flux model uses atmospheric muon measurements [12,
13], whereas T2K’s flux model uses measurements by the NA61/SHINE experiment
[14]. The resulting uncertainties on the flux prediction are therefore
considered to be independent between the two models. The neutrino events of
the two experiments are observed in the same detector, and the correlated
effects of detector systematic uncertainties on SK and T2K event samples were
evaluated for the joint analysis.

Event selection—This analysis uses a total of eighteen SK atmospheric and five
T2K event samples, constructed as described in Refs. [9] and [15]. The event
selections are based primarily on the number of reconstructed Cherenkov rings,
the type of those rings, and the number of delayed Michel electron candidates.
The ring types are either showering ($e$-like) or non-showering ($\mu$-like)
and are the basis of the separation between $\hskip 1.42262pt\hbox
to0.0pt{\hss\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{(}}}\overline{\nu}\hbox
to0.0pt{\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{)}}\hss}_{e}$ and $\hskip
1.42262pt\hbox
to0.0pt{\hss\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{(}}}\overline{\nu}\hbox
to0.0pt{\raisebox{4.30554pt}{\scalebox{0.5}[0.5]{)}}\hss}_{\mu}$ events. The
T2K selections target events with little activity in the SK outer detector,
so-called fully contained (FC) events, with a single Cherenkov ring. This
topology primarily selects charged current quasi-elastic (CCQE)-like events,
although in neutrino running mode an additional sample probes $\nu_{e}$ events
containing a below-Cherenkov-threshold $\pi^{+}$ by requiring exactly one
$e$-like ring and one Michel electron. Atmospheric neutrinos span a much wider
range of energies, and the atmospheric FC sample is divided into sub- and
multi-GeV categories based on the deposited visible energy in the detector.
The SK analysis additionally includes events with significant energy
deposition in the outer detector. The T2K beam samples and FC single-ring sub-
GeV atmospheric samples in SK have a large kinematic overlap, but differ
slightly in their respective event selections, which remain the same as in the
publications above. One additional selection criterion, however, is applied to
both the SK FC and T2K samples to remove neutron contamination from the Michel
candidates for each event, which changes the event rates by
$\mathcal{O}(1\%)$.

Interaction model—Neutrino interactions are simulated with the NEUT generator
v5.4.0 [16] using the same configuration as T2K’s analysis [8]. The common
“low-energy” uncertainty model used for the T2K and atmospheric SK FC sub-GeV
samples is based on T2K’s model, with additions to cover important
uncertainties for the SK atmospheric analysis. Additional normalization
uncertainties on the neutral current single $\pi^{0}$ model are introduced,
which scale the resonant and coherent contributions separately, motivated by
studies of MiniBooNE data [17, 18]. A supplementary uncertainty on the CCQE
cross-section ratio $\sigma_{\nu_{e}}/\sigma_{\nu_{\mu}}$ is added based on
the difference of this ratio between the spectral function model [19] used in
this analysis and new calculations using the Hartree-Fock model with Continuum
Random Phase Approximation [20, 21]. The ability of the low energy model to
describe the atmospheric sub-GeV data samples is evaluated by comparing its
predictions using T2K’s ND constraint to the observed data for the down-going
part of those samples. The down-going events are mostly unaffected by
oscillations, and can therefore be used to test the model without biasing the
oscillation measurement. Good agreement with data is found for the samples
targeting events without pions in the final state. For the samples targeting
charged current single charged pion (CC1$\pi^{+}$) events, a significant data
excess is seen: 225 events are observed for 160.0 $\pm$ 12.6(stat) $\pm$
14.3(syst) predicted in the $e$-like sample, and 84 are observed in the
$\mu$-like sample for 52.0 $\pm$ 7.2(stat) $\pm$ 5.3(syst) predicted. The
excess is localized at low lepton momentum in the $e$-like sample, and
uniformly distributed in the $\mu$-like sample. An excess is also seen at low
momentum in the corresponding $e$-like beam sample, but is not significant due
to the low statistics of this sample. As a result of the observed excesses, an
interaction model uncertainty is added to change the shape of the pion three-
momentum spectrum for charged-current resonant interactions by modifying the
Adler angle [22] distribution, based on theoretically motivated [23, 24] and
empirical modifications. A reconstruction uncertainty is also added, as
detailed in the next section.

The model for the remaining SK samples (“high-energy model”) is based on that
used in the SK analysis, but shares the CCQE part with the low-energy model
with the exception of the high $Q^{2}$ (four-momentum transfer) parameters,
due to similarities in the CCQE events’ phase space outside of the high
$Q^{2}$ region. SK and T2K’s uncertainty models for resonant production and
deep inelastic scattering events are very similar, the main difference being
the existence of additional parameters and different nominal values in SK’s
analysis. For consistency, the single pion production parameters are set to
the same values as in T2K, which come from studies of external data. This
increases uncertainties compared to SK’s analysis. The model for pion final-
state interactions is tuned to external data [25], as done by T2K.

Data from T2K’s ND are used to constrain uncertainties on the interaction
parameters from the low-energy model and the correlated part of the high-
energy model, but not on the new uncertainties added for this analysis, or any
other aspect of the high-energy model, due to the lack of overlapping phase
space between the near-detector and non-sub-GeV atmospheric samples.

Detector model—The same version of the SK event reconstruction algorithm [9]
is used for the two experiments, to be able to derive correlations between
their detector and reconstruction systematic uncertainties. Many of the
detector uncertainties in both SK and T2K’s analyses are estimated from
comparisons between atmospheric data and simulation. For these, correlated
uncertainties are constructed by evaluating the effects of variations of the
detector parameters of the SK model on the number of events in the different
samples of the two experiments simultaneously. Correlations between the
reconstructed momentum scale uncertainty of the two experiments are found to
have an impact on the constraint on $\Delta{}m^{2}_{32}$ obtained in the data
fit. Three of the four analyses described in the next section treat the
corresponding parameters as correlated, while the fourth considers them
uncorrelated. The remaining detector uncertainties from the reference SK and
T2K analyses that are relevant for only one of the experiments are applied to
the corresponding samples. An additional systematic uncertainty is introduced
for the sub-GeV samples targeting CC$1\pi^{+}$ events. It allows single ring
single Michel electron events with low lepton momentum to migrate between
$\nu_{e}$-like and $\nu_{\mu}$-like samples. The size of this uncertainty
covers the excess in data observed for the down-going CC$1\pi^{+}$
$\nu_{e}$-like events at low momentum.

Oscillation analysis—Two Bayesian and two frequentist analyses based on the
model described above but with differences in technical implementation,
binning, and statistical methodology are used to fit the data. To constrain
uncertainties using the T2K ND, one analysis performs simultaneous fits of the
T2K ND, T2K far detector and SK atmospheric data, while the others use a
covariance matrix to encode T2K’s ND constraint on systematic parameters when
fitting the events observed at SK. The Bayesian analyses use Markov Chain
Monte Carlo methods to evaluate marginal likelihoods for the parameters of
interest, while the frequentist analyses compute the profile likelihood on a
fixed grid of values of the oscillation parameters of interest. For
atmospheric oscillation probability calculations, path-dependent density
averaging of the matter effect based on a four layer approximation of the PREM
model [26] is used, and the fast atmospheric oscillations at low energy are
smeared using different techniques depending on the analysis. The path-
dependence yields more precise oscillation probabilities than the conventional
approximation assuming layers of constant density. All analyses utilize a
binned log-likelihood test statistic assuming Poisson-distributed bin contents
plus Gaussian penalties for the systematic parameters. Finally, reactor
experiment measurements of $\theta_{13}$ using $\overline{\nu}_{e}$
disappearance, $\sin^{2}2\theta_{13}$ $=0.0853\pm 0.0027$ [2, 27, 28, 29, 30],
are used as an external constraint.

Robustness studies—Simulated datasets [8] are used to test the robustness of
the analysis to effects not included in the base systematic uncertainty model.
They are generated using alternative models, and fitted using the nominal
model to measure how the obtained $p$-values and constraints on oscillation
parameters would be affected by having assumed the wrong model. Fourteen such
simulated datasets are considered, corresponding to alternative neutrino
interaction models and data-driven effects at both T2K ND and SK. These
studies are used to estimate, amongst other things, how much the data excess
observed in the atmospheric down-going CC$1\pi^{+}$ samples could bias the
results despite the newly added uncertainties if it was coming from an unknown
systematic effect. Some of the simulated datasets produce a visible shift in
the preferred values for $\Delta m_{32}^{2}$. The uncertainty on $\Delta
m_{32}^{2}$ is inflated by $3.6\times 10^{-5}\ \mathrm{eV^{2}}/c^{4}$ to
account for these effects.

Dataset— The atmospheric dataset is slightly increased compared to [9] to
include the full Super-Kamiokande IV period (2008–2018), corresponding to a
total live-time of 3244.4 days. The same T2K dataset as in [8] is used,
corresponding to exposures of $19.7\times 10^{20}$ and $16.3\times 10^{20}$
protons on target in neutrino and antineutrino running modes, respectively.

Bayesian results—The Bayesian analyses assume uniform priors on
$\delta_{\scriptscriptstyle\mathrm{CP}}$ or
$\sin\delta_{\scriptscriptstyle\mathrm{CP}}$, $\sin^{2}\theta_{23}$, $\Delta
m^{2}_{32}$, and the MO. They find a preference for the normal ordering, and a
weak preference for the upper octant (Table 1). SK and T2K data prefer
different octants which leads the joint analysis to have a weaker octant
constraint than the individual experiments and a higher probability for
maximal mixing, while for the CP-violating phase, both experiments favor
similar values (Figure 1). The exclusion of the CP conserving values of
$J_{\scriptscriptstyle\mathrm{CP}}$ (Figure 2) and
$\delta_{\scriptscriptstyle\mathrm{CP}}$ is quantified by determining the
largest fraction of the posterior density for which the value considered is
not included in either of the corresponding highest posterior density credible
intervals obtained by the two Bayesian analyses (Table 2).

Table 1:  Octant and MO posterior probabilities using either the full dataset or samples from only one experiment and assuming equal prior probabilities. Values obtained by the second analysis are shown in parentheses.  | SK only | T2K only | SK+T2K
---|---|---|---
Upper octant | 0.318 (0.337) | 0.785 (0.761) | 0.611 (0.639)
Normal ordering | 0.654 (0.633) | 0.832 (0.822) | 0.900 (0.887)
Figure 1: The ($\sin^{2}\theta_{23}$, $\delta_{\scriptscriptstyle\mathrm{CP}}$) credible regions obtained with the SK, T2K, and combined datasets. The MO is marginalized over and a prior uniform in $\delta_{\scriptscriptstyle\mathrm{CP}}$ is used. Table 2:  Largest credible interval from the Bayesian analyses not containing different CP conserving values of $J_{\scriptscriptstyle\mathrm{CP}}$ and $\delta_{\scriptscriptstyle\mathrm{CP}}$. Values in parentheses indicate how these could change due to possible biases seen in robustness studies.  Value tested | Prior uniform in
---|---
| $\delta_{\scriptscriptstyle\mathrm{CP}}$ | $\sin(\delta_{\scriptscriptstyle\mathrm{CP}})$
$J_{\scriptscriptstyle\mathrm{CP}}=0$ |  $2.3\sigma$ ($2.2\sigma$) |  $2.0\sigma$ ($1.9\sigma$)
$\delta_{\scriptscriptstyle\mathrm{CP}}=0$ |  $2.6\sigma$ ($2.5\sigma$) |  $2.3\sigma$ ($2.2\sigma$)
$\delta_{\scriptscriptstyle\mathrm{CP}}=\pi$ |  $2.1\sigma$ ($1.9\sigma$) |  $1.6\sigma$ ($1.4\sigma$)
Figure 2: The posterior density for the Jarlskog invariant with credible
intervals overlaid, marginalized over both MOs, and assuming a uniform prior
in either $\delta_{\scriptscriptstyle\mathrm{CP}}$ or
$\sin\delta_{\scriptscriptstyle\mathrm{CP}}$.

Frequentist results—Ensembles of pseudo-experiments are constructed to
evaluate the frequentist significance of the CP and MO results, taking into
account statistical fluctuations and randomizing the values of nuisance
oscillation and systematic parameters according to their posterior [31] and
prior probability distributions respectively. Estimating the significance of
CP conservation (CPC) based on the presence or not of both $0$ and $\pi$ in
the $\delta_{\scriptscriptstyle\mathrm{CP}}$ confidence intervals was found to
have significant over-coverage. Instead, the log-likelihood ratio between
assuming CPC ($\sin\delta_{\scriptscriptstyle\mathrm{CP}}=0$, here equivalent
to $J_{\scriptscriptstyle\mathrm{CP}}=0$) and without any assumption is used
as a test statistic. For the neutrino MO, the log-likelihood ratio between
normal and inverted ordering is used (Figure 3).

The obtained $p$-values are summarized in Table 3. CPC is disfavored with a
lower $p$-value ($p=0.037$) than when using only the T2K data ($p=0.047$).
Good agreement ($p=0.75$) is found with an ensemble that allows for CP-
violation by assuming posterior-distributed
$\delta_{\scriptscriptstyle\mathrm{CP}}$ values. The inverted ordering is
disfavored while good agreement with the normal ordering hypothesis is found,
resulting in a $\mathrm{CL}_{s}$ parameter [32] for the inverted ordering of
0.18. The distribution of the MO test statistic depends on the assumed values
of $\sin^{2}\theta_{23}$ (from SK samples) and
$\delta_{\scriptscriptstyle\mathrm{CP}}$ (from T2K samples). The $p$-value for
the inverted ordering varies between 0.05 and 0.08 when assuming different
fixed true values for $\sin^{2}\theta_{23}$ and
$\delta_{\scriptscriptstyle\mathrm{CP}}$ over the range of their 90%
confidence intervals. The best-fit values and 68.3% confidence intervals
obtained using the Feldman–Cousins method [33] where necessary, are
$\delta_{\scriptscriptstyle\mathrm{CP}}=-1.76^{+0.73}_{-0.95}$,
$\sin^{2}\theta_{23}=0.468^{+0.106}_{-0.025}$, where MO was treated as a
nuisance parameter, and $\Delta m^{2}_{32}$ ($|\Delta
m^{2}_{31}|$)${}=2.520^{+0.048}_{-0.058}$ ($2.480^{+0.052}_{-0.048}$)${}\times
10^{-3}\,\mathrm{eV^{2}}$ for normal (inverted) ordering.

Table 3:  Frequentist $p$-values for the different CP and MO hypotheses. The most conservative of the two values obtained by the frequentist analyses is given. “$p$-studies” corresponds to the value up to which each $p$-value could increase due to biases seen in robustness studies.  Hypothesis |  $p$-value |  $p$-studies
---|---|---
CP conservation | 0.037 | 0.050
Inverted ordering | 0.079 | 0.080
Normal ordering | 0.58 | —
Figure 3: Distribution of the MO test statistic under true normal and inverted
ordering hypotheses. The filled areas to the left (right) of the data result
indicate the $p$-values for the inverted (normal) hypotheses.

Goodness of fit—The Bayesian analyses find good posterior predictive
$p$-values [34] using both the event spectra ($p=0.24$) and total event counts
($p=0.19$). The $p$-values for the individual T2K samples agree with the
reference T2K analysis [8] up to small differences coming predominantly from
model changes. The frequentist $p$-values [35] additionally show good
consistency between the values of the systematic parameters favored by the T2K
ND and atmospheric data ($p=0.19$), as well as between the atmospheric and
beam samples ($p=0.24$).

Discussion—The SK and T2K datasets favor similar values for the CP phase,
close to maximal CP violation, and both show a preference for the normal MO.
As a result, the combined analysis finds increased preferences for non-
conservation of CP symmetry and the normal ordering. When looking directly at
the exclusion of CPC through the presence of
$J_{\scriptscriptstyle\mathrm{CP}}=0$ in credible intervals or frequentist
$p$-values, an exclusion at the 2$\sigma$ level is found. However, the
significance can fall below 2$\sigma$ due to the potential weaknesses of the
uncertainty model tested using simulated datasets. The alternative models
having the most impact are the one assuming that the excess seen for down-
going CC1$\pi^{+}$-like events is fully due to an unknown systematic effect,
and an alternative nuclear model for CCQE interactions [36]. This indicates
areas where the robustness of the model should be improved for future
analyses.

Conclusion—The SK and T2K collaborations have produced a first joint analysis
of their data. A common neutrino interaction and detector model has been
developed for the events of the two experiments which overlap in energy, and
is found to be able to properly describe the two datasets. The results show an
exclusion of the CP-conserving value of the Jarlskog invariant with a
significance between 1.9$\sigma$ and 2.0$\sigma$, a limited preference for the
normal ordering, and no strong preference for the $\theta_{23}$ octant. This
first joint analysis is also an important step towards the combined beam and
atmospheric data analyses planned by next generation neutrino oscillation
experiments.

## Acknowledgements

The Super-Kamiokande collaboration gratefully acknowledges cooperation of the
Kamioka Mining and Smelting Company. The Super-Kamiokande experiment was built
and has been operated with funding from the Japanese Ministry of Education,
Science, Sports and Culture, and the U.S. Department of Energy.

The T2K collaboration would like to 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 NKFIH, Hungary;
the INFN, Italy; the Ministry of Science and Higher Education (2023/WK/04) and
the National Science Centre (UMO-2018/30/E/ST2/00441, UMO-2022/46/E/ST2/00336
and UMO-2021/43/D/ST2/01504), Poland; the RSF (RSF 24-12-00271) 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;
the DOE, USA; and NAFOSTED (103.99-2023.144), Vietnam. 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, GridPP and the Emerald High Performance
Computing facility 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 Sorbonne Université Emergences programmes; the
VAST-JSPS (No. QTJP01.02/20-22); and the DOE Early Career programme, USA. For
the purposes of open access, the authors have applied a Creative Commons
Attribution license to any Author Accepted Manuscript version arising.

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