††thanks: now at CERN††thanks: now at CERN††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 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 National
Research Nuclear University ”MEPhI” and Moscow Institute of Physics and
Technology, Moscow, Russia††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:
affiliated member at Kavli IPMU (WPI), the University of Tokyo, Japan††thanks:
also at J-PARC, Tokai, Japan††thanks: deceased††thanks: also at J-PARC, Tokai,
Japan††thanks: also at JINR, Dubna, Russia††thanks: also at J-PARC, Tokai,
Japan††thanks: affiliated member at Kavli IPMU (WPI), the University of Tokyo,
Japan††thanks: also at 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: affiliated member at Kavli IPMU (WPI), the University of
Tokyo, Japan††thanks: deceased††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

# Search for light sterile neutrinos with the T2K far detector Super-
Kamiokande
at a baseline of 295 km

K. Abe  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  R. Akutsu  University of Tokyo, Institute for
Cosmic Ray Research, Research Center for Cosmic Neutrinos, Kashiwa, Japan  A.
Ali  INFN Sezione di Padova and Università di Padova, Dipartimento di Fisica,
Padova, Italy  C. Andreopoulos  STFC, Rutherford Appleton Laboratory, Harwell
Oxford, and Daresbury Laboratory, Warrington, United Kingdom  University of
Liverpool, Department of Physics, Liverpool, United Kingdom  L. Anthony
University of Liverpool, Department of Physics, Liverpool, United Kingdom  M.
Antonova  IFIC (CSIC & University of Valencia), Valencia, Spain  S. Aoki  Kobe
University, Kobe, Japan  A. Ariga  University of Bern, Albert Einstein Center
for Fundamental Physics, Laboratory for High Energy Physics (LHEP), Bern,
Switzerland  Y. Ashida  Kyoto University, Department of Physics, Kyoto, Japan
Y. Awataguchi  Tokyo Metropolitan University, Department of Physics, Tokyo,
Japan  Y. Azuma  Osaka City University, Department of Physics, Osaka, Japan
S. Ban  Kyoto University, Department of Physics, Kyoto, Japan  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  C. Barry  University of Liverpool, Department of Physics, Liverpool,
United Kingdom  M. Batkiewicz-Kwasniak  H. Niewodniczanski Institute of
Nuclear Physics PAN, Cracow, Poland  F. Bench  University of Liverpool,
Department of Physics, Liverpool, United Kingdom  V. Berardi  INFN Sezione di
Bari and Università e Politecnico di Bari, Dipartimento Interuniversitario di
Fisica, Bari, Italy  S. Berkman  University of British Columbia, Department of
Physics and Astronomy, Vancouver, British Columbia, Canada  TRIUMF, Vancouver,
British Columbia, Canada  R.M. Berner  University of Bern, Albert Einstein
Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP),
Bern, Switzerland  L. Berns  Tokyo Institute of Technology, Department of
Physics, Tokyo, Japan  S. Bhadra  York University, Department of Physics and
Astronomy, Toronto, Ontario, Canada  S. Bienstock  Sorbonne Université,
Université Paris Diderot, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de
Hautes Energies (LPNHE), Paris, France  A. Blondel  University of Geneva,
Section de Physique, DPNC, Geneva, Switzerland  S. Bolognesi  IRFU, CEA
Saclay, Gif-sur-Yvette, France  B. Bourguille  Institut de Fisica d’Altes
Energies (IFAE), The Barcelona Institute of Science and Technology, Campus
UAB, Bellaterra (Barcelona) Spain  S.B. Boyd  University of Warwick,
Department of Physics, Coventry, United Kingdom  D. Brailsford  Lancaster
University, Physics Department, Lancaster, 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  M. Buizza Avanzini  Ecole Polytechnique,
IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France  J. Calcutt
Michigan State University, Department of Physics and Astronomy, East Lansing,
Michigan, U.S.A.  T. Campbell  University of Colorado at Boulder, Department
of Physics, Boulder, Colorado, U.S.A.  S. Cao  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  S.L. Cartwright
University of Sheffield, Department of Physics and Astronomy, Sheffield,
United Kingdom  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  A. Chappell
University of Warwick, Department of Physics, Coventry, United Kingdom  C.
Checchia  INFN Sezione di Padova and Università di Padova, Dipartimento di
Fisica, Padova, Italy  D. Cherdack  University of Houston, Department of
Physics, Houston, Texas, U.S.A.  N. Chikuma  University of Tokyo, Department
of Physics, Tokyo, Japan  G. Christodoulou  University of Liverpool,
Department of Physics, Liverpool, United Kingdom  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  D. Coplowe  Oxford University, Department of Physics, Oxford,
United Kingdom  A. Cudd  Michigan State University, Department of Physics and
Astronomy, East Lansing, Michigan, U.S.A.  A. Dabrowska  H. Niewodniczanski
Institute of Nuclear Physics PAN, Cracow, Poland  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
P.F. Denner  University of Warwick, Department of Physics, Coventry, United
Kingdom  S.R. Dennis  University of Liverpool, Department of Physics,
Liverpool, United Kingdom  C. Densham  STFC, Rutherford Appleton Laboratory,
Harwell Oxford, and Daresbury Laboratory, Warrington, United Kingdom  F. Di
Lodovico  Queen Mary University of London, School of Physics and Astronomy,
London, United Kingdom  N. Dokania  State University of New York at Stony
Brook, Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  S.
Dolan  Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet,
Palaiseau, France  IRFU, CEA Saclay, Gif-sur-Yvette, France  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, Université Paris Diderot, CNRS/IN2P3,
Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France
P. Dunne  Imperial College London, Department of Physics, London, United
Kingdom  S. Emery-Schrenk  IRFU, CEA Saclay, Gif-sur-Yvette, France  A.
Ereditato  University of Bern, Albert Einstein Center for Fundamental Physics,
Laboratory for High Energy Physics (LHEP), Bern, Switzerland  P. Fernandez
IFIC (CSIC & University of Valencia), Valencia, Spain  T. Feusels  University
of British Columbia, Department of Physics and Astronomy, Vancouver, British
Columbia, Canada  TRIUMF, Vancouver, British Columbia, Canada  A.J. Finch
Lancaster University, Physics Department, Lancaster, United Kingdom  G.A.
Fiorentini  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  C. Francois  University of Bern, Albert
Einstein Center for Fundamental Physics, Laboratory for High Energy Physics
(LHEP), Bern, Switzerland  M. Friend  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki, Japan  Y. Fujii  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  R. Fujita  University of
Tokyo, Department of Physics, Tokyo, Japan  D. Fukuda  Okayama University,
Department of Physics, Okayama, Japan  Y. Fukuda  Miyagi University of
Education, Department of Physics, Sendai, Japan  K. Gameil  University of
British Columbia, Department of Physics and Astronomy, Vancouver, British
Columbia, Canada  TRIUMF, Vancouver, British Columbia, Canada  C. Giganti
Sorbonne Université, Université Paris Diderot, CNRS/IN2P3, Laboratoire de
Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France  F. Gizzarelli
IRFU, CEA Saclay, Gif-sur-Yvette, France  T. Golan  Wroclaw University,
Faculty of Physics and Astronomy, Wroclaw, Poland  M. Gonin  Ecole
Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France
D.R. Hadley  University of Warwick, Department of Physics, Coventry, United
Kingdom  J.T. Haigh  University of Warwick, Department of Physics, Coventry,
United Kingdom  P. Hamacher-Baumann  RWTH Aachen University, III.
Physikalisches Institut, Aachen, Germany  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  N.C.
Hastings  University of Regina, Department of Physics, Regina, Saskatchewan,
Canada  T. Hayashino  Kyoto University, Department of Physics, Kyoto, 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  A. Hiramoto  Kyoto University,
Department of Physics, Kyoto, Japan  M. Hogan  Colorado State University,
Department of Physics, Fort Collins, Colorado, U.S.A.  J. Holeczek  University
of Silesia, Institute of Physics, Katowice, Poland  N.T. Hong Van  Institute
For Interdisciplinary Research in Science and Education (IFIRSE), ICISE, Quy
Nhon, Vietnam  Institute of Physics (IOP), Vietnam Academy of Science and
Technology (VAST), Hanoi, Vietnam  F. Hosomi  University of Tokyo, Department
of Physics, Tokyo, Japan  F. Iacob  INFN Sezione di Padova and Università di
Padova, Dipartimento di Fisica, Padova, Italy  A.K. Ichikawa  Kyoto
University, Department of Physics, Kyoto, Japan  M. Ikeda  University of
Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
T. Inoue  Osaka City University, Department of Physics, Osaka, Japan  R.A.
Intonti  INFN Sezione di Bari and Università e Politecnico di Bari,
Dipartimento Interuniversitario di Fisica, Bari, Italy  T. Ishida  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  T. Ishii
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  K. Iwamoto  University of Tokyo,
Department of Physics, Tokyo, Japan  A. Izmaylov  IFIC (CSIC & University of
Valencia), Valencia, Spain  Institute for Nuclear Research of the Russian
Academy of Sciences, Moscow, Russia  B. Jamieson  University of Winnipeg,
Department of Physics, Winnipeg, Manitoba, Canada  C. Jesus  Institut de
Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science and
Technology, Campus UAB, Bellaterra (Barcelona) Spain  M. Jiang  Kyoto
University, Department of Physics, Kyoto, Japan  S. Johnson  University of
Colorado at Boulder, Department of Physics, Boulder, Colorado, U.S.A.  P.
Jonsson  Imperial College London, Department of Physics, London, United
Kingdom  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  Oxford
University, Department of Physics, Oxford, 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  D. Karlen  University of
Victoria, Department of Physics and Astronomy, Victoria, British Columbia,
Canada  TRIUMF, Vancouver, British Columbia, Canada  T. Katori  Queen Mary
University of London, School of Physics and Astronomy, London, United Kingdom
Y. Kato  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  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  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  H. Kim  Osaka City University, Department of
Physics, Osaka, Japan  J. Kim  University of British Columbia, Department of
Physics and Astronomy, Vancouver, British Columbia, Canada  TRIUMF, Vancouver,
British Columbia, Canada  S. King  Queen Mary University of London, School of
Physics and Astronomy, London, United Kingdom  J. Kisiel  University of
Silesia, Institute of Physics, Katowice, Poland  A. Knight  University of
Warwick, Department of Physics, Coventry, United Kingdom  A. Knox  Lancaster
University, Physics Department, Lancaster, United Kingdom  T. Kobayashi  High
Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  L.
Koch  STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury
Laboratory, Warrington, United Kingdom  T. Koga  University of Tokyo,
Department of Physics, Tokyo, Japan  A. Konaka  TRIUMF, Vancouver, British
Columbia, Canada  L.L. Kormos  Lancaster University, Physics Department,
Lancaster, United Kingdom  Y. Koshio  Okayama University, Department of
Physics, Okayama, Japan  K. Kowalik  National Centre for Nuclear Research,
Warsaw, Poland  H. Kubo  Kyoto University, Department of Physics, Kyoto, Japan
Y. Kudenko  Institute for Nuclear Research of the Russian Academy of Sciences,
Moscow, Russia  R. Kurjata  Warsaw University of Technology, Institute of
Radioelectronics, Warsaw, Poland  T. Kutter  Louisiana State University,
Department of Physics and Astronomy, Baton Rouge, Louisiana, U.S.A.  M. Kuze
Tokyo Institute of Technology, Department of Physics, Tokyo, Japan  L. Labarga
University Autonoma Madrid, Department of Theoretical Physics, 28049 Madrid,
Spain  J. Lagoda  National Centre for Nuclear Research, Warsaw, Poland  M.
Lamoureux  IRFU, CEA Saclay, Gif-sur-Yvette, France  P. Lasorak  Queen Mary
University of London, School of Physics and Astronomy, London, United Kingdom
M. Laveder  INFN Sezione di Padova and Università di Padova, Dipartimento di
Fisica, Padova, Italy  M. Lawe  Lancaster University, Physics Department,
Lancaster, United Kingdom  M. Licciardi  Ecole Polytechnique, IN2P3-CNRS,
Laboratoire Leprince-Ringuet, Palaiseau, France  T. Lindner  TRIUMF,
Vancouver, British Columbia, Canada  R.P. Litchfield  University of Glasgow,
School of Physics and Astronomy, Glasgow, United Kingdom  X. Li  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  A. Longhin  INFN Sezione di Padova and
Università di Padova, Dipartimento di Fisica, Padova, Italy  J.P. Lopez
University of Colorado at Boulder, Department of Physics, Boulder, Colorado,
U.S.A.  T. Lou  University of Tokyo, Department of Physics, Tokyo, Japan  L.
Ludovici  INFN Sezione di Roma and Università di Roma “La Sapienza”, Roma,
Italy  X. Lu  Oxford University, Department of Physics, Oxford, United Kingdom
T. Lux  Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of
Science and Technology, Campus UAB, Bellaterra (Barcelona) Spain  L. Magaletti
INFN Sezione di Bari and Università e Politecnico di Bari, Dipartimento
Interuniversitario di Fisica, Bari, Italy  K. Mahn  Michigan State University,
Department of Physics and Astronomy, East Lansing, Michigan, U.S.A.  M. Malek
University of Sheffield, Department of Physics and Astronomy, Sheffield,
United Kingdom  S. Manly  University of Rochester, Department of Physics and
Astronomy, Rochester, New York, U.S.A.  L. Maret  University of Geneva,
Section de Physique, DPNC, Geneva, Switzerland  A.D. Marino  University of
Colorado at Boulder, Department of Physics, Boulder, Colorado, U.S.A.  J.F.
Martin  University of Toronto, Department of Physics, Toronto, Ontario, Canada
P. Martins  Queen Mary University of London, School of Physics and Astronomy,
London, United Kingdom  T. Maruyama  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki, Japan  T. Matsubara  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  V. Matveev
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  K. Mavrokoridis  University of Liverpool, Department of Physics,
Liverpool, United Kingdom  W.Y. Ma  Imperial College London, Department of
Physics, London, United Kingdom  E. Mazzucato  IRFU, CEA Saclay, Gif-sur-
Yvette, France  M. McCarthy  York University, Department of Physics and
Astronomy, Toronto, Ontario, Canada  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.  A. Mefodiev  Institute for
Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  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  A. Minamino  Yokohama National
University, Faculty of Engineering, Yokohama, Japan  O. Mineev  Institute for
Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  S. Mine
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  ETH Zurich,
Institute for Particle Physics, Zurich, Switzerland  S. Moriyama  University
of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka,
Japan  J. Morrison  Michigan State University, Department of Physics and
Astronomy, East Lansing, Michigan, U.S.A.  Th.A. Mueller  Ecole Polytechnique,
IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France  S. Murphy  ETH
Zurich, Institute for Particle Physics, Zurich, Switzerland  Y. Nagai
University of Colorado at Boulder, Department of Physics, Boulder, Colorado,
U.S.A.  T. Nakadaira  High Energy Accelerator Research Organization (KEK),
Tsukuba, Ibaraki, 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, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  A. Nakamura  Okayama University, Department of
Physics, Okayama, Japan  K.G. Nakamura  Kyoto University, Department of
Physics, Kyoto, 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  Kyoto University, Department of Physics, Kyoto, Japan  Y. Nakanishi
Kyoto University, Department of Physics, Kyoto, Japan  S. Nakayama  University
of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka,
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. Nantais  University of
Toronto, Department of Physics, Toronto, Ontario, Canada  K. Niewczas  Wroclaw
University, Faculty of Physics and Astronomy, Wroclaw, Poland  K. Nishikawa
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
Y. Nishimura  University of Tokyo, Institute for Cosmic Ray Research, Research
Center for Cosmic Neutrinos, Kashiwa, Japan  T.S. Nonnenmacher  Imperial
College London, Department of Physics, London, United Kingdom  P. Novella
IFIC (CSIC & University of Valencia), Valencia, Spain  J. Nowak  Lancaster
University, Physics Department, Lancaster, United Kingdom  H.M. O’Keeffe
Lancaster University, Physics Department, Lancaster, United Kingdom  L.
O’Sullivan  University of Sheffield, Department of Physics and Astronomy,
Sheffield, United Kingdom  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 City University, Department of
Physics, Osaka, Japan  S.M. Oser  University of British Columbia, Department
of Physics and Astronomy, Vancouver, British Columbia, Canada  TRIUMF,
Vancouver, British Columbia, Canada  R.A. Owen  Queen Mary University of
London, School of Physics and Astronomy, London, United Kingdom  Y. Oyama
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
V. Palladino  INFN Sezione di Napoli and Università di Napoli, Dipartimento di
Fisica, Napoli, Italy  J.L. Palomino  State University of New York at Stony
Brook, Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  V.
Paolone  University of Pittsburgh, Department of Physics and Astronomy,
Pittsburgh, Pennsylvania, U.S.A.  W.C. Parker  Royal Holloway University of
London, Department of Physics, Egham, Surrey, United Kingdom  P. Paudyal
University of Liverpool, Department of Physics, Liverpool, United Kingdom  M.
Pavin  TRIUMF, Vancouver, British Columbia, Canada  D. Payne  University of
Liverpool, Department of Physics, Liverpool, United Kingdom  L. Pickering
Michigan State University, Department of Physics and Astronomy, East Lansing,
Michigan, U.S.A.  C. Pidcott  University of Sheffield, Department of Physics
and Astronomy, Sheffield, United Kingdom  E.S. Pinzon Guerra  York University,
Department of Physics and Astronomy, Toronto, Ontario, Canada  C. Pistillo
University of Bern, Albert Einstein Center for Fundamental Physics, Laboratory
for High Energy Physics (LHEP), Bern, Switzerland  B. Popov  Sorbonne
Université, Université Paris Diderot, CNRS/IN2P3, Laboratoire de Physique
Nucléaire et de Hautes Energies (LPNHE), Paris, France  K. Porwit  University
of Silesia, Institute of Physics, Katowice, Poland  M. Posiadala-Zezula
University of Warsaw, Faculty of Physics, Warsaw, Poland  A. Pritchard
University of Liverpool, Department of Physics, Liverpool, United Kingdom  B.
Quilain  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. 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  ETH Zurich, Institute for Particle Physics,
Zurich, Switzerland  P.N. Ratoff  Lancaster University, Physics Department,
Lancaster, United Kingdom  E. Reinherz-Aronis  Colorado State University,
Department of Physics, Fort Collins, Colorado, U.S.A.  C. Riccio  INFN Sezione
di Napoli and Università di Napoli, Dipartimento di Fisica, Napoli, Italy  E.
Rondio  National Centre for Nuclear Research, Warsaw, Poland  B. Rossi  INFN
Sezione di Napoli and Università di Napoli, Dipartimento di Fisica, Napoli,
Italy  S. Roth  RWTH Aachen University, III. Physikalisches Institut, Aachen,
Germany  A. Rubbia  ETH Zurich, Institute for Particle Physics, Zurich,
Switzerland  A.C. Ruggeri  INFN Sezione di Napoli and Università di Napoli,
Dipartimento di Fisica, Napoli, Italy  A. Rychter  Warsaw University of
Technology, Institute of Radioelectronics, Warsaw, Poland  K. Sakashita  High
Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  F.
Sánchez  University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
S. Sasaki  Tokyo Metropolitan University, Department of Physics, Tokyo, Japan
C.M. Schloesser  ETH Zurich, Institute for Particle Physics, Zurich,
Switzerland  K. Scholberg  Duke University, Department of Physics, Durham,
North Carolina, U.S.A.  J. Schwehr  Colorado State University, Department of
Physics, Fort Collins, Colorado, U.S.A.  M. Scott  Imperial College London,
Department of Physics, London, United Kingdom  Y. Seiya  Osaka City
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  University of
Geneva, Section de Physique, DPNC, Geneva, Switzerland  R. Shah  STFC,
Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory,
Warrington, United Kingdom  Oxford University, Department of Physics, Oxford,
United Kingdom  A. Shaikhiev  Institute for Nuclear Research of the Russian
Academy of Sciences, Moscow, Russia  F. Shaker  University of Winnipeg,
Department of Physics, Winnipeg, Manitoba, Canada  D. Shaw  Lancaster
University, Physics Department, Lancaster, United Kingdom  A. Shaykina
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  A. Smirnov
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  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  Y. Sonoda  University of Tokyo, Institute for Cosmic
Ray Research, Kamioka Observatory, Kamioka, Japan  J. Steinmann  RWTH Aachen
University, III. Physikalisches Institut, Aachen, Germany  T. Stewart  STFC,
Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory,
Warrington, United Kingdom  P. Stowell  University of Sheffield, Department of
Physics and Astronomy, Sheffield, United Kingdom  S. Suvorov  Institute for
Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  IRFU, CEA
Saclay, Gif-sur-Yvette, France  A. Suzuki  Kobe University, Kobe, Japan  S.Y.
Suzuki  High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki,
Japan  Y. Suzuki  Kavli Institute for the Physics and Mathematics of the
Universe (WPI), The University of Tokyo Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba, Japan  A.A. Sztuc  Imperial College
London, Department of Physics, London, United Kingdom  R. Tacik  University of
Regina, Department of Physics, Regina, Saskatchewan, Canada  TRIUMF,
Vancouver, British Columbia, Canada  M. Tada  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki, 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  R. Tamura
University of Tokyo, Department of Physics, Tokyo, Japan  H.K. Tanaka
University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory,
Kamioka, Japan  H.A. Tanaka  SLAC National Accelerator Laboratory, Stanford
University, Menlo Park, California, USA  University of Toronto, Department of
Physics, Toronto, Ontario, Canada  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  K.M. Tsui  University of Liverpool, Department of
Physics, Liverpool, United Kingdom  T. Tsukamoto  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  M. Tzanov  Louisiana
State University, Department of Physics and Astronomy, Baton Rouge, Louisiana,
U.S.A.  Y. Uchida  Imperial College London, Department of Physics, London,
United Kingdom  W. Uno  Kyoto University, Department of Physics, Kyoto, Japan
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.  Z. Vallari  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  D. Vargas  Institut de Fisica d’Altes Energies
(IFAE), The Barcelona Institute of Science and Technology, Campus UAB,
Bellaterra (Barcelona) Spain  G. Vasseur  IRFU, CEA Saclay, Gif-sur-Yvette,
France  C. Vilela  State University of New York at Stony Brook, Department of
Physics and Astronomy, Stony Brook, New York, U.S.A.  T. Vladisavljevic
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  V.V. Volkov  Institute for Nuclear Research of the
Russian Academy of Sciences, Moscow, Russia  T. Wachala  H. Niewodniczanski
Institute of Nuclear Physics PAN, Cracow, Poland  J. Walker  University of
Winnipeg, Department of Physics, Winnipeg, Manitoba, Canada  Y. Wang  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  D. Wark  STFC, Rutherford Appleton Laboratory,
Harwell Oxford, and Daresbury Laboratory, Warrington, United Kingdom  Oxford
University, Department of Physics, Oxford, United Kingdom  M.O. Wascko
Imperial College London, Department of Physics, London, United Kingdom  A.
Weber  STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury
Laboratory, Warrington, United Kingdom  Oxford University, Department of
Physics, Oxford, United Kingdom  R. Wendell  Kyoto University, Department of
Physics, Kyoto, Japan  M.J. Wilking  State University of New York at Stony
Brook, Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  C.
Wilkinson  University of Bern, Albert Einstein Center for Fundamental Physics,
Laboratory for High Energy Physics (LHEP), Bern, Switzerland  J.R. Wilson
Queen Mary University of London, School of Physics and Astronomy, London,
United Kingdom  R.J. Wilson  Colorado State University, Department of Physics,
Fort Collins, Colorado, U.S.A.  C. Wret  University of Rochester, Department
of Physics and Astronomy, Rochester, New York, U.S.A.  Y. Yamada  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  K. Yamamoto
Osaka City University, Department of Physics, Osaka, Japan  S. Yamasu  Okayama
University, Department of Physics, Okayama, 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  S. Yen  TRIUMF, Vancouver, British Columbia, Canada  N.
Yershov  Institute for Nuclear Research of the Russian Academy of Sciences,
Moscow, Russia  M. Yokoyama  University of Tokyo, Department of Physics,
Tokyo, Japan  T. Yoshida  Tokyo Institute of Technology, Department of
Physics, Tokyo, Japan  M. Yu  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, Warsaw, Poland  G. Zarnecki  National Centre
for Nuclear Research, Warsaw, Poland  M. Ziembicki  Warsaw University of
Technology, Institute of Radioelectronics, Warsaw, Poland  E.D. Zimmerman
University of Colorado at Boulder, Department of Physics, Boulder, Colorado,
U.S.A.  M. Zito  IRFU, CEA Saclay, Gif-sur-Yvette, France  S. Zsoldos  Queen
Mary University of London, School of Physics and Astronomy, London, United
Kingdom  A. Zykova  Institute for Nuclear Research of the Russian Academy of
Sciences, Moscow, Russia

###### Abstract

We perform a search for light sterile neutrinos using the data from the T2K
far detector at a baseline of 295 km, with an exposure of 14.7 (7.6)$\times
10^{20}$ protons on target in neutrino (antineutrino) mode. A selection of
neutral current interaction samples are also used to enhance the sensitivity
to sterile mixing. No evidence of sterile neutrino mixing in the 3+1 model was
found from a simultaneous fit to the charged-current muon, electron and
neutral current neutrino samples. We set the most stringent limit on the
sterile oscillation amplitude $\sin^{2}\theta_{24}$ for the sterile neutrino
mass splitting $\Delta m^{2}_{41}<3\times 10^{-3}$ eV${}^{2}/c^{4}$.

###### pacs:

##  I Introduction

Over the last few decades, the theory of neutrino oscillations has been well
established through a series of experiments with neutrinos produced by the Sun
Cleveland  _et al._ (1998); Abdurashitov  _et al._ (2009); Altmann  _et al._
(2005); Hampel  _et al._ (1999); Aharmim  _et al._ (2005); Abe  _et al._
(2011a), nuclear reactors Araki  _et al._ (2005); An  _et al._ (2012); Abe
_et al._ (2013a); Ahn  _et al._ (2012), accelerators Ahn  _et al._ (2006);
Adamson  _et al._ (2013); Abe  _et al._ (2014a); Agafonova  _et al._ (2014);
Adamson  _et al._ (2016a) and in the atmosphere Fukuda  _et al._ (1998);
Aartsen  _et al._ (2015). Most data from these studies are consistent with the
three flavor paradigm where the three weakly interacting neutrino flavors are
related to three neutrino mass states by the PMNS mixing matrix Pontecorvo
(1968); Gribov and Pontecorvo (1969); Maki  _et al._ (1962). However,
deviations from the three flavor scheme have been reported. At LSND Aguilar
_et al._ (2001) and MiniBooNE Aguilar-Arevalo  _et al._ (2013), there were
excesses of $\bar{\nu}_{e}$ found in short-baseline $\bar{\nu}_{\mu}$ beams;
MiniBooNE also reported an excess in $\nu_{e}$ appearance Aguilar-Arevalo  _et
al._ (2018); radioactive calibration sources in gallium experiments Bahcall
_et al._ (1995); Abdurashitov  _et al._ (2006) showed a deficit of $\nu_{e}$
flux; and reactor experiments Mention  _et al._ (2011) observed less
$\bar{\nu}_{e}$ than expected. These results could be explained by a fourth
neutrino state with a mass difference $\Delta m^{2}\sim 1$ eV${}^{2}/c^{4}$
with respect to the three PMNS states Bilenky  _et al._ (1999); Barger  _et
al._ (2000); Kopp  _et al._ (2013); Gariazzo  _et al._ (2016). From the
measurements of the invisible decay width of the Z0 boson at the LEP collider,
the number of weakly interacting neutrino species with mass below 45
GeV$/c^{2}$ is limited to three Schael  _et al._ (2006), so the new neutrino
state must not couple to the weak interaction and is often referred to as
$sterile$. We can incorporate this additional neutrino state in the simple
“3+1” model Barger  _et al._ (2000), which involves the three active neutrinos
and one sterile neutrino, and study its effect on the oscillation signatures.
Currently, the null results, especially in the $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$ disappearance
channels, from short-baseline accelerator experiments like CCFR Stockdale  _et
al._ (1984), MiniBooNE/SciBooNE Cheng  _et al._ (2012) and T2K Abe  _et al._
(2015a); long-baseline experiments like MINOS/MINOS+ Adamson  _et al._ (2019)
and NOvA Adamson  _et al._ (2017); or atmospheric experiments like Super-
Kamiokande Abe  _et al._ (2015b) and IceCube Aartsen  _et al._ (2016, 2017),
have limited the available parameter space in the “3+1” model.

The Tokai to Kamioka (T2K) experiment is a long-baseline accelerator neutrino
experiment in Japan which primarily measures muon neutrino disappearance and
electron neutrino appearance. While T2K is designed for studying standard
three flavor oscillation at ${\Delta m^{2}\sim 10^{-3}}$ eV${}^{2}/c^{4}$, it
also has the potential to search for oscillation signatures due to sterile
neutrinos around this ${\Delta m^{2}}$ range. Neutral current (NC) neutrino
interactions are also collected in the far detector, Super-Kamiokande (SK),
which can be used to enhance the sensitivity to sterile mixing as the sterile
neutrinos, unlike other active neutrinos, do not interact through CC or NC
scattering. We present a long-baseline search for sterile neutrinos in the
“3+1” framework, using both the charged-current (CC)
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$ and $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ samples and NC
samples at the far detector.

Sec. II briefly describes the sterile neutrino mixing model and its effect on
the oscillation probability (or oscillation signatures). The T2K experimental
setup is outlined in Sec. III, followed by event selection criteria in Sec.
IV. Sec. V explains the analysis strategy and Sec. VI presents our search
results. Finally, Sec. VII gives a summary and outlook of our sterile neutrino
study.

##  II “3+1” sterile neutrino mixing

In this study, we focus on a “3+1” like model where a single sterile neutrino
is added and mixed with the three active states, which is the simplest model
with sterile neutrino frequently used in neutrino oscillation analysis. In
this model, there is a new flavor state $\nu_{s}$ and a new mass state
$\nu_{4}$ with mass $m_{4}$ added to the three flavor framework. The relation
between the flavor and mass states is given by

$\ket{\nu_{\alpha}}=\sum U^{*}_{\alpha k}\ket{\nu_{k}},$ (1)

where $\ket{\nu_{\alpha}}$ are the flavor states and $\ket{\nu_{k}}$ are the
mass states. The original $3\times 3$ PMNS mixing matrix is expanded to a
$4\times 4$ matrix as:

$\textbf{U}=\begin{pmatrix}U_{e1}&U_{e2}&U_{e3}&U_{e4}\\\ U_{\mu 1}&U_{\mu
2}&U_{\mu 3}&U_{\mu 4}\\\ U_{\tau 1}&U_{\tau 2}&U_{\tau 3}&U_{\tau 4}\\\
U_{s1}&U_{s2}&U_{s3}&U_{s4}\\\ \end{pmatrix}.$ (2)

We choose the parameterization as in Harari and Leurer (1986):

$\textbf{U}=\textbf{U}_{34}\textbf{U}_{24}\textbf{U}_{14}\textbf{U}_{23}\textbf{U}_{13}\textbf{U}_{12},$
(3)

where $\textbf{U}_{ij}$ is a unitary rotation matrix of an angle $\theta_{ij}$
in the $ij$-plane. There are therefore three new mixing angles $\theta_{14}$,
$\theta_{24}$, $\theta_{34}$ and two new CP-violating phases $\delta_{14}$,
$\delta_{24}$. Note that $\sin^{2}\theta_{14}$ has been constrained to small
values by reactor experiments Adamson  _et al._ (2016b), and T2K has limited
sensitivity to $\theta_{14}$ and the new CP phases. Since there is no
significant correlation between them and the other oscillation parameters in
this study, we set $\theta_{14}=\delta_{14}=\delta_{24}=0$ to simplify the
mixing matrix.

At the far detector, the $\nu_{\mu}$ survival probability can be approximated
(omitting $\delta_{CP}$ terms) as:

$\begin{split}P(\nu_{\mu}\rightarrow\nu_{\mu})\approx
1&-\sin^{2}2\theta_{23}\cos^{4}\theta_{24}\sin^{2}\frac{\Delta
m^{2}_{31}L}{4E}\\\
&-\cos^{2}\theta_{23}\sin^{2}2\theta_{24}\sin^{2}\frac{\Delta
m^{2}_{41}L}{4E},\\\
&-\sin^{2}\theta_{23}\sin^{2}2\theta_{24}\sin^{2}\frac{\Delta
m^{2}_{43}L}{4E},\end{split}$ (4)

and the $\nu_{e}$ appearance probability as:

$P(\nu_{\mu}\rightarrow\nu_{e})\approx\sin^{2}2\theta_{13}\cos^{2}\theta_{24}\sin^{2}\theta_{23}\sin^{2}\frac{\Delta
m^{2}_{31}L}{4E}.$ (5)

Thus the CC channels are sensitive to $\theta_{24}$ and $\Delta m^{2}_{41}$.
Similarly, the active neutrino survival probability, which is manifested in
the NC channel, is sensitive to $\theta_{24}$, $\Delta m^{2}_{41}$, and
$\theta_{34}$:

$\begin{split}P_{NC}=1&-P(\nu_{\mu}\rightarrow\nu_{s})\\\ \approx
1&-\sin^{2}2\theta_{23}(A^{2}-\frac{1}{4}B^{2})\sin^{2}\frac{\Delta
m^{2}_{31}L}{4E}\\\ &-B(B\cos^{2}\theta_{23}-A\sin
2\theta_{23})\sin^{2}\frac{\Delta m^{2}_{41}L}{4E}\\\
&-B(B\sin^{2}\theta_{23}+A\sin 2\theta_{23})\sin^{2}\frac{\Delta
m^{2}_{43}L}{4E},\end{split}$ (6)

where ${A=\cos\theta_{24}\sin\theta_{34}}$ and ${B=\sin
2\theta_{24}\cos\theta_{34}}$. The antineutrino oscillation probabilities
follow similarly, but there are small differences due to the $\delta_{CP}$
terms which are not explicitly written here. Figure 1 shows schematically how
the oscillation probabilities are modified with the mixing of sterile
neutrinos.

Figure 1: The muon neutrino survival probability (top), electron neutrino
appearance probability (middle) and active neutrino survival probability
(bottom) as a function of neutrino energy, with and without sterile neutrino,
assuming $\Delta m^{2}_{31}>0$.

The addition of a sterile neutrino state which experiences no matter potential
(both CC and NC) complicates the calculation of oscillation in matter. We
estimated the possible impacts due to matter effects at T2K baseline and
energy with numerical calculation of oscillation probabilities using nuCraft
Wallraff and Wiebusch (2015), and found at most a few percent changes on the
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ and NC samples. This is negligible at
current precision, so we simply use the vacuum oscillation probabilities
(without approximation) in this study.

##  III The T2K experiment

The T2K experiment Abe  _et al._ (2011b) consists of a neutrino beam, a near
detector complex, and the water Cherenkov detector Super-Kamiokande Fukuda
_et al._ (2003) as the far detector at a baseline of 295 km. T2K is sensitive
to $\theta_{13}$ and $\delta_{CP}$ through the $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ appearance
searches, and can also make precision measurements on $\theta_{23}$ and mass
difference $\Delta m^{2}_{32}$ with the $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$ disappearance
samples.

The main ring accelerator in the Japan Proton Accelerator Research Complex
(J-PARC) produces a 30 GeV proton beam with spills every 2.48 s that contain
eight beam bunches which are 580 ns apart. The proton beam is extracted to the
neutrino beamline and collides with a graphite target to produce charged pions
and kaons. In the neutrino (antineutrino) beam mode, magnetic horns are used
to focus the positively (negatively)-charged pions and kaons into a 96 m long
decay volume filled with helium gas. These mesons typically decay into muon
neutrinos (antineutrinos). The neutrino beamline is directed at an angle of
2.5${}^{\text{o}}$ away from the far detector, so that the off-axis beam at SK
has a narrower peak at 0.6 GeV with much less $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ content than an
on-axis beam.

The near detector complex located at 280 m from the neutrino production target
contains two detectors. The on-axis detector, INGRID, is an array of 16
iron/scintillator detectors which precisely measure the beam direction and
intensity Abe  _et al._ (2012). The off-axis detector, ND280, is a magnetized
tracking detector which constrains the neutrino flux and cross-section model
parameters in the oscillation analysis.

The far detector, Super-Kamiokande, is located in Gifu prefecture, at a
distance of 295 km from the J-PARC neutrino beam. It is a water Cherenkov
detector consisting of 50 kt of ultra-pure water. The tank is optically
separated into two regions. The inner detector (ID) is a cylinder containing
32 kt of water and is instrumented with 11,129 inward-facing 20 inch
photomultiplier tubes (PMTs). The outer detector (OD) extends 2 m outward from
the ID and is instrumented with 1885 outward-facing 8 inch PMTs. The OD serves
as an active veto against cosmic-ray muons, and provides passive shielding
from radioactivity in the surrounding rock. The expected event rates at far
detector are calculated by multiplying the unoscillated neutrino spectra
(predicted by near detectors) with the corresponding oscillation
probabilities.

##  IV Event selection at far detector

The T2K Runs 1–8 data set used in this analysis was collected from Jan. 2010
to May 2017, corresponding to a beam exposure of $14.7\times 10^{20}$ protons
on target (POT) in neutrino mode and $7.6\times 10^{20}$ POT in antineutrino
mode. Events at the far detector are required to occur within 1 ms of the beam
spill time window, and be fully contained in the fiducial volume of the SK ID.
For the CC $\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$ and $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ samples, a new
Cherenkov-ring reconstruction algorithm Abe  _et al._ (2015c) is used to
select neutrino events, which improves signal/background discrimination and
expands the fiducial volume to increase statistics.

Table 1: Number of events expected and observed in the eight oscillation samples used in this analysis. Three flavor oscillation is assumed in expected rate.  Sample | Expected | Observed
---|---|---
$\nu_{\mu}$ CC-0$\pi$ | 268.4 | 240
$\bar{\nu}_{\mu}$ CC-0$\pi$ | 64.3 | 68
$\nu_{e}$ CC-0$\pi$ | 73.5 | 74
$\bar{\nu}_{e}$ CC-0$\pi$ | 7.9 | 7
$\nu_{e}$ CC-1$\pi^{+}$ | 6.9 | 15
$\nu$ NC$\pi^{0}$ | 49.5 | 53
$\bar{\nu}$ NC$\pi^{0}$ | 11.3 | 9
NC $\gamma$-deexcit. | 107.7 | 102
(Runs 1–4)

There are five CC analysis samples that are commonly used in the standard
three flavor oscillation analysis Abe  _et al._ (2018):
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$ CC-0$\pi$ and
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ CC-0$\pi$ samples which are enriched in CC
quasi-elastic (CCQE) events, and $\nu_{e}$ CC-1$\pi^{+}$ sample where a
$\pi^{+}$ below Cherenkov threshold is produced. The
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$ samples are binned in reconstructed
neutrino energy, and the $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ samples in
reconstructed lepton momentum and angle $\theta$ relative to the beam. Details
can be found in Abe  _et al._ (2018). Table 1 summarizes the event rates,
where the Monte Carlo (MC) expectation is calculated with
$\sin^{2}\theta_{23}=0.528$, $\Delta m^{2}_{32}=2.509\times 10^{-3}$
eV${}^{2}/c^{4}$, $\delta_{CP}=-1.601$ (the most probable values obtained by
the Bayesian analysis in Abe  _et al._ (2015c)), and
$\sin^{2}\theta_{13}=0.0219$ (taken from Patrignani  _et al._ (2016)). All
sterile mixing angles are set to zero.

In addition to the CC samples, beam-induced NC events are also collected in
SK. These events have previously only been used in publications for systematic
uncertainties Abe  _et al._ (2018) and cross-section Abe  _et al._ (2014b)
studies. In this analysis, NC$\pi^{0}$ and NC $\gamma$-deexcitation samples
are used in the oscillation fit to enhance the sensitivity to sterile mixing
parameters.

The NC$\pi^{0}$ samples select neutrino events with single $\pi^{0}$
production, where $\pi^{0}\rightarrow 2\gamma$ decay produces two visible
Cherenkov rings in the detector. Events with two electron-like Cherenkov rings
are selected as candidates for NC$\pi^{0}$ samples, and those with decay
electron candidates (from muons) are rejected. The invariant mass from the two
rings is required to be between 85 MeV$/c^{2}$ and 135 MeV$/c^{2}$ to be
consistent with the $\pi^{0}$ mass. From simulations, 68.5% (53.6%) of events
originate from a $\Delta$ resonance and 19.1% (34.9%) from coherent pion
production for (anti)neutrino mode. The NC single pion resonant (NC1$\pi$)
production is described by the Rein-Sehgal model Rein and Sehgal (1981), while
the coherent production is described by a tuned model of Rein-Sehgal Rein and
Sehgal (1983). In MC, NC events constitute 97.1% (98.5%) of the sample.

The NC $\gamma$-deexcitation sample was first reported in the measurement of
neutrino-oxygen NC quasi-elastic (NCQE) cross-section Abe  _et al._ (2014b).
The NCQE cross-section is calculated by a spectral function model Benhar  _et
al._ (2005, 1994) with the BBBA05 form factor parameterization Bradford  _et
al._ (2006), reweighting as a function of neutrino energy to match the
theoretical calculations Ankowski  _et al._ (2012). The NCQE interaction can
knockout a nucleon,

$\begin{split}\nu+^{16}\text{O}&\rightarrow\nu+p+^{15}\text{N}^{*},\text{
or}\\\ \nu+^{16}\text{O}&\rightarrow\nu+n+^{15}\text{O}^{*},\end{split}$

which produces primary $\gamma$ rays from residual nucleus deexcitation and
secondary $\gamma$ rays when knocked-out nucleons interact with other nuclei
in water. The emitted $\gamma$ rays are 10 MeV per event on average, which is
much less energetic than other samples. Momenta and vertex positions are
reconstructed using the low-energy tools developed for SK solar neutrino
analyses Abe  _et al._ (2011c). Cuts on reconstructed energy, fiducial volume,
event timing, vertex and reconstruction quality, detector pre-activity, and
Cherenkov opening angle are applied sequentially to remove beam-unrelated
(e.g. radioactivity) and beam-related CC backgrounds. The sample is estimated
to contain 76.9% NCQE and 17.6% NC non-QE events. The NC $\gamma$-deexcitation
sample is currently available only for T2K Runs 1–4 (from Jan. 2010 to May
2013), corresponding to $6.56\times 10^{20}$ POT. Rest of the data is under
reduction and validation with an improved event selection process.

Figure 2 shows the reconstructed $\pi^{0}$ momentum and $\gamma$ energy
distributions of the NC$\pi^{0}$ and NC $\gamma$-deexcitation samples
respectively, with event rates summarized in Table 1. Since the event spectra
have little information about true neutrino energy, the sensitivity to $\Delta
m^{2}_{41}$ is limited in the NC channel.

(a) NC$\pi^{0}$ sample

(b) NC $\gamma$-deexcitation sample (Runs 1–4)

Figure 2:  Reconstructed $\pi^{0}$ momentum spectra of NC$\pi^{0}$ samples
(top), and reconstructed gamma energy spectrum of NC $\gamma$-deexcitation
sample (bottom). The numbers of events in data and MC prediction are shown in
the legend.

##  V Analysis strategy

The overall analysis method is similar to that used in the standard T2K three
flavor analysis Abe  _et al._ (2018), including the incorporation of off-axis
near detector data and treatment of systematic uncertainties. However, this
analysis performs a simultaneous fit to the five CC and three newly added NC
samples to constrain the sterile mixing parameters in the “3+1” model.
Systematic parameters are added to accommodate the possible uncertainties in
the NC samples.

The neutrino flux is calculated by a data-driven simulation Abe  _et al._
(2017, 2013b), which incorporates the conditions of the proton beam, magnetic
horn current and neutrino beam-axis direction. Hadronic interactions are tuned
with the thin target measurements in the NA61/SHINE experiment Abgrall  _et
al._ (2016). Stability of the neutrino flux has been monitored by INGRID
throughout the whole data taking period. At the peak energy 0.6 GeV, the
(anti)neutrino mode beam contains 97.2% (96.2%) $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$, with only
0.42% (0.46%) $\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ contamination, and the flux uncertainty is
approximately 9%.

Neutrino events at the near and far detectors are generated by the NEUT 5.3.2
neutrino interaction generator Hayato (2009), which accounts for general
interaction and cross-section effects. Most of the cross-section and neutrino
flux parameters are constrained by ND280. The unoscillated CC candidate events
at ND280 are classified into different samples according to the event
topology, and is fit with a binned Poisson likelihood to extract the best-fit
parameters and correlated uncertainties. The central values and their
covariances are then propagated to estimate the far detector flux and cross-
section parameters and uncertainty covariance matrix. The fit to ND data was
done assuming no oscillation at ND280. This approximation is valid for small
$\Delta m^{2}_{41}$, below around 0.3 eV2/c4. However, NC and $\nu_{e}$
interaction parameters are not constrained by the ND280 fit. As a result, an
additional uncorrelated 30% normalization uncertainty is used in this analysis
for the NC1$\pi$ and NCQE channels. The values of these uncertainties are
conservative estimates determined from a previous cross-section analysis Abe
_et al._ (2015d) and NCQE theoretical model comparisons Ankowski  _et al._
(2015); Ankowski (2015). They therefore dominate the overall cross-section
uncertainty in the NC oscillation samples.

At the far detector, there are NEUT parameters (present in ND280 fit but not
constrained) that control the final state interactions inside nuclei and
secondary interactions with water molecules, altering the event topologies of
outgoing particles. For each event topology, the SK selection efficiency and
mis-identification rate is separately parameterized. The NC
$\gamma$-deexcitation sample has separate uncertainties related to primary and
secondary $\gamma$ production Abe  _et al._ (2014b). The uncertainties in
these parameters constitute the SK detector uncertainties.

The effects of systematic uncertainties on the predicted event rates are
summarized in Table 2. The NC cross-section errors are dominant in the NC
samples.

Table 2: Percentage systematic uncertainty on far detector event yields.  Sample | Flux | Cross-sec. | SK Detector | Total
---|---|---|---|---
$\nu_{\mu}$ CC-0$\pi$ | 4.1 | 4.7 | 3.3 | 4.8
$\bar{\nu}_{\mu}$ CC-0$\pi$ | 3.8 | 4.0 | 2.9 | 4.1
$\nu_{e}$ CC-0$\pi$ | 4.3 | 5.5 | 3.8 | 6.4
$\bar{\nu}_{e}$ CC-0$\pi$ | 3.9 | 5.2 | 4.3 | 6.4
$\nu_{e}$ CC-1$\pi^{+}$ | 4.3 | 5.0 | 17.1 | 17.7
$\nu$ NC$\pi^{0}$ | 4.2 | 20.1 | 8.8 | 21.3
$\bar{\nu}$ NC$\pi^{0}$ | 3.8 | 19.1 | 8.6 | 20.4
NC $\gamma$-deexcit. | 4.1 | 21.1 | 13.2 | 23.3

Using the flux and cross-section inputs from ND280, the unoscillated event
sample spectra at the far detector are calculated. Oscillation parameters are
varied to obtain the best agreement between data and predicted event rates. A
joint maximum-likelihood fit to eight far detector samples constrains the
sterile mixing parameters $\sin^{2}\theta_{24}$, $\sin^{2}\theta_{34}$ and
$\Delta m^{2}_{41}$. The log-likelihood is defined as

$-\ln\mathcal{L}=\sum_{i}[\mu_{i}-n_{i}+n_{i}\ln(n_{i}/\mu_{i})]+\frac{1}{2}\Delta\vec{f}^{T}V^{-1}\Delta\vec{f},$
(7)

where $n_{i}$ is the number of events in the $i$-th data bin, and
$\mu_{i}=\mu_{i}(\vec{\theta},\vec{f})$ is the expected event rate with
oscillation parameters $\vec{\theta}$ and systematic parameters $\vec{f}$. The
last term in Eq. 7 accounts for the systematic penalty with $\Delta\vec{f}$
being the difference between the systematic parameters and their prior values,
related by the covariance matrix V. The oscillation parameters
$\sin^{2}\theta_{23}$, $|\Delta m^{2}_{32}|$ and $\delta_{CP}$ are allowed to
vary without constraint; $\theta_{12}$ and $\Delta m^{2}_{21}$ are fixed to
their PDG values Patrignani  _et al._ (2016); and a penalty term is used to
constrain $\sin^{2}2\theta_{13}=0.0857\pm 0.0046$.

During the fitting process, at a grid point of
$(\sin^{2}\theta_{24},\sin^{2}\theta_{34},\Delta m^{2}_{41})$, the function in
Eq. 7 is minimized with respect to the other oscillation parameters and
systematic parameters. We use Wilks’s theorem to estimate the confidence
levels (C.L.) Wilks (1938). The results are cross-checked with Gaussian
CL${}_{\text{s}}$ contours Qian  _et al._ (2016) to ensure no significant bias
due to the physical limit of $\sin^{2}\theta_{24}\geq 0$ and
$\sin^{2}\theta_{34}\geq 0$.

##  VI Results

We consider the parameter space of $\Delta m^{2}_{41}>\Delta m^{2}_{21}$ which
is most sensitive in T2K. Two categories of fits are done for normal (NH,
$\Delta m^{2}_{31}>0$) and inverted (IH, $\Delta m^{2}_{31}<0$) neutrino mass
hierarchies respectively. The case of $\Delta m^{2}_{41}<0$ is very similar
and can be obtained by flipping the hierarchy. The “3+1” best-fit differs from
the standard three flavor best-fit by $\Delta\chi^{2}=1.0$ (4.7) for NH (IH).
From 2500 sets of MC studies with statistical fluctuations, this level of
disagreement is expected with the standard three flavor hypothesis in 50%
(30%) of the studies.

In the $(\sin^{2}\theta_{24},\Delta m^{2}_{41})$ parameter plane,
$\sin^{2}\theta_{24}$ is scanned from $10^{-3}$ to 1, and $\Delta m^{2}_{41}$
from $10^{-4}$ to 0.3 eV${}^{2}/c^{4}$. For larger values of $\Delta
m^{2}_{41}$, oscillations would be also seen at the near detectors, which is
beyond the scope of this analysis. Figure 3 shows the T2K 90% exclusion limits
together with results from other experiments. We have set the most stringent
limit on $\sin^{2}\theta_{24}$ for $\Delta m^{2}_{41}<3\times 10^{-3}$
eV${}^{2}/c^{4}$. In particular, the NC samples improve the limit by around
20% for ${\Delta m^{2}_{41}<10^{-3}}$ eV${}^{2}/c^{4}$. The limit is weaker at
larger $\Delta m^{2}_{41}$ due to the lack of high energy events, resulting
from the sharply peaked off-axis neutrino flux. The difference between NH and
IH comes from the $\Delta m^{2}_{43}$ oscillation term. It becomes
particularly important when $\Delta m^{2}_{41}\sim\Delta m^{2}_{31}$, as this
results in very different values of $\Delta m^{2}_{43}$ in NH and IH. In
partly-degenerate cases where $\Delta m^{2}_{41}$ and $\Delta m^{2}_{31}$ are
in integer multiples, the $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ and NC samples
are important in resolving ambiguities. In cases where one of the $\Delta
m^{2}$ values is very small, matter effects can significantly alter which mass
states are involved in the oscillation, but the overall
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ appearance probability is not affected by
more than few percent so this does not significantly modify the exclusion
limits.

The NC samples allow us to constrain $\theta_{34}$ in conjunction with
$\theta_{24}$. Because these samples have low statistics and large cross
section uncertainties, we have limited sensitivity, but our results are
consistent with other measurements. Figure 4 shows that we constrain
$\sin^{2}\theta_{24}<0.1$ and $|U_{\tau
4}|^{2}=\cos^{2}\theta_{24}\sin^{2}\theta_{34}<0.5$ at 90% C.L. if ${\Delta
m^{2}_{41}=0.1}$ eV${}^{2}/c^{4}$ is assumed. At smaller $\Delta m^{2}_{41}$
values, the limits are different between NH and IH.

Figure 3: The T2K 90% exclusion limits on $\sin^{2}\theta_{24}$ as a function
of $\Delta m^{2}_{41}$, with results from other experiments Adamson  _et al._
(2019); Abe  _et al._ (2015b); Aartsen  _et al._ (2016). The areas on the
right are excluded.

Figure 4: The T2K 90% and 99% exclusion limits on $\sin^{2}\theta_{24}$ and
$|U_{\tau 4}|^{2}=\cos^{2}\theta_{24}\sin^{2}\theta_{34}$ at $\Delta
m^{2}_{41}=0.1$ eV2 (top), with results from other experiments Aartsen  _et
al._ (2017); Abe  _et al._ (2015b), and exclusion limits at $\Delta
m^{2}_{41}=3\times 10^{-3}$ eV2 (bottom). The areas on the right are excluded.

##  VII Conclusions

Data collected by the T2K experiment between 2010 and 2017 (T2K Runs 1–8) have
been used to search for oscillation signatures due to light sterile neutrinos
in the “3+1” model. The sterile mixing parameters
$(\sin^{2}\theta_{24},\sin^{2}\theta_{34},\Delta m^{2}_{41})$ are constrained
by performing a joint fit of the five CC samples:
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}_{\mu}$ CC-0$\pi$, $\nu^{\hbox{\kern-8.0pt\raise
1.0pt\hbox{{\tiny(}{\lower 1.4pt\hbox{\bf--}}{\tiny)}}}}_{e}$ CC-0$\pi$,
$\nu_{e}$ CC-1$\pi^{+}$, and the three new NC samples:
$\nu^{\hbox{\kern-8.0pt\raise 1.0pt\hbox{{\tiny(}{\lower
1.4pt\hbox{\bf--}}{\tiny)}}}}$ NC$\pi^{0}$, NC $\gamma$-deexcitation, selected
at the far detector. Systematic uncertainties on the neutrino flux and CC
interaction cross-section are constrained by the ND280 data, while NC cross-
section uncertainties are determined from a comparison of theoretical models
and external data. The data are consistent with the standard three flavor
oscillation hypothesis. Limits have been set on the sterile mixing parameters,
with the world’s best constraint on $\sin^{2}\theta_{24}$ for $10^{-4}$
eV${{}^{2}/c^{4}<\Delta m^{2}_{41}<3\times 10^{-3}}$ eV${}^{2}/c^{4}$. The
data related to the measurement and results presented in this paper can be
found in Abe  _et al._ .

Our current precision is restricted by statistics and the uncertainty on the
NC interaction cross-section. Apart from future updates of the analysis as we
take more data, dedicated systematic studies are required for further
improvements to the precision. Another possible extension is to perform a
joint analysis of near and far detector data that would expand the range of
constraint to ${\Delta m^{2}_{41}\gtrsim 1}$ eV${}^{2}/c^{4}$ with additional
data at smaller $L/E$.

###### Acknowledgements.

We thank the J-PARC staff for superb accelerator performance. We thank the
CERN NA61/SHINE Collaboration for providing valuable particle production data.
We acknowledge the support of MEXT, Japan; NSERC (Grant No. SAPPJ-2014-00031),
NRC and CFI, Canada; CEA and CNRS/IN2P3, France; DFG, Germany; INFN, Italy;
National Science Centre (NCN) and Ministry of Science and Higher Education,
Poland; RSF, RFBR, and MES, Russia; MINECO and ERDF funds, Spain; SNSF and
SERI, Switzerland; STFC, UK; and DOE, USA. We also thank CERN for the
UA1/NOMAD magnet, DESY for the HERA-B magnet mover system, NII for SINET4, the
WestGrid and SciNet consortia in Compute Canada, and GridPP in the United
Kingdom. In addition, participation of individual researchers and institutions
has been further supported by funds from ERC (FP7), ”la Caixa” Foundation (ID
100010434, fellowship code LCF/BQ/IN17/11620050), the European Union’s Horizon
2020 Research and Innovation programme under the Marie Sklodowska-Curie grant
agreement no. 713673 and H2020 Grant No. RISE-GA644294-JENNIFER 2020; JSPS,
Japan; Royal Society, UK; the Alfred P. Sloan Foundation and the DOE Early
Career program, USA.

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