††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:
deceased††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: 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 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 Institute of Particle Physics,
Canada††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 BMCC/CUNY, Science Department, New York, New
York, U.S.A.††thanks: affiliated member at Kavli IPMU (WPI), the University of
Tokyo, Japan††thanks: also at J-PARC, Tokai, Japan

The T2K Collaboration

# Measurement of the single $\pi^{0}$ production rate in neutral current
neutrino interactions on water

K. Abe  University of Tokyo, Institute for Cosmic Ray Research, Kamioka
Observatory, Kamioka, Japan  J. Amey  Imperial College London, Department of
Physics, London, United Kingdom  C. Andreopoulos  STFC, Rutherford Appleton
Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United
Kingdom  University of Liverpool, Department of Physics, Liverpool, United
Kingdom  M. Antonova  Institute for Nuclear Research of the Russian Academy of
Sciences, Moscow, Russia  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  S. Assylbekov  Colorado State
University, Department of Physics, Fort Collins, Colorado, U.S.A.  D. Autiero
Université de Lyon, Université Claude Bernard Lyon 1, IPN Lyon (IN2P3),
Villeurbanne, France  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  P. Bartet-Friburg  UPMC, Université
Paris Diderot, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes
Energies (LPNHE), Paris, France  M. Batkiewicz  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  S. Berkman  University of British Columbia, Department of Physics
and Astronomy, Vancouver, British Columbia, Canada  TRIUMF, Vancouver, British
Columbia, Canada  S. Bhadra  York University, Department of Physics and
Astronomy, Toronto, Ontario, Canada  S. Bienstock  UPMC, 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  S. Bordoni  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  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. Buizza Avanzini
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau,
France  R.G. Calland  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. Campbell  Colorado State
University, Department of Physics, Fort Collins, 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  R. Castillo  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
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  Colorado State University,
Department of Physics, Fort Collins, Colorado, U.S.A.  N. Chikuma  University
of Tokyo, Department of Physics, Tokyo, Japan  G. Christodoulou  University of
Liverpool, Department of Physics, Liverpool, United Kingdom  A. Clifton
Colorado State University, Department of Physics, Fort Collins, Colorado,
U.S.A.  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  L. Cremonesi  Queen Mary
University of London, School of Physics and Astronomy, London, 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  D. Dewhurst  Oxford
University, Department of Physics, Oxford, United Kingdom  F. Di Lodovico
Queen Mary University of London, School of Physics and Astronomy, London,
United Kingdom  S. Di Luise  ETH Zurich, Institute for Particle Physics,
Zurich, Switzerland  S. Dolan  Oxford University, Department of Physics,
Oxford, United Kingdom  O. Drapier  Ecole Polytechnique, IN2P3-CNRS,
Laboratoire Leprince-Ringuet, Palaiseau, France  K.E. Duffy  Oxford
University, Department of Physics, Oxford, United Kingdom  J. Dumarchez  UPMC,
Université Paris Diderot, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de
Hautes Energies (LPNHE), Paris, France  M. Dunkman  Michigan State University,
Department of Physics and Astronomy, East Lansing, Michigan, U.S.A.  P. Dunne
Imperial College London, Department of Physics, London, United Kingdom  M.
Dziewiecki  Warsaw University of Technology, Institute of Radioelectronics,
Warsaw, Poland  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  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  M. Friend  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki, Japan  Y. Fujii  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  D. Fukuda
Okayama University, Department of Physics, Okayama, Japan  Y. Fukuda  Miyagi
University of Education, Department of Physics, Sendai, Japan  A.P. Furmanski
University of Warwick, Department of Physics, Coventry, United Kingdom  V.
Galymov  Université de Lyon, Université Claude Bernard Lyon 1, IPN Lyon
(IN2P3), Villeurbanne, France  A. Garcia  Institut de Fisica d’Altes Energies
(IFAE), The Barcelona Institute of Science and Technology, Campus UAB,
Bellaterra (Barcelona) Spain  S.G. Giffin  University of Regina, Department of
Physics, Regina, Saskatchewan, Canada  C. Giganti  UPMC, Université Paris
Diderot, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies
(LPNHE), Paris, France  K. Gilje  State University of New York at Stony Brook,
Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  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  N.
Grant  University of Warwick, Department of Physics, Coventry, United Kingdom
D.R. Hadley  University of Warwick, Department of Physics, Coventry, United
Kingdom  L. Haegel  University of Geneva, Section de Physique, DPNC, Geneva,
Switzerland  J.T. Haigh  University of Warwick, Department of Physics,
Coventry, United Kingdom  P. Hamilton  Imperial College London, Department of
Physics, London, United Kingdom  D. Hansen  University of Pittsburgh,
Department of Physics and Astronomy, Pittsburgh, Pennsylvania, U.S.A.  J.
Harada  Osaka City University, Department of Physics, Osaka, Japan  T. Hara
Kobe University, Kobe, Japan  M. Hartz  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  TRIUMF, Vancouver,
British Columbia, Canada  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  R.L. Helmer  TRIUMF, Vancouver, British Columbia,
Canada  M. Hierholzer  University of Bern, Albert Einstein Center for
Fundamental Physics, Laboratory for High Energy Physics (LHEP), Bern,
Switzerland  A. Hillairet  University of Victoria, Department of Physics and
Astronomy, Victoria, British Columbia, Canada  A. Himmel  Duke University,
Department of Physics, Durham, North Carolina, U.S.A.  T. Hiraki  Kyoto
University, Department of Physics, Kyoto, Japan  A. Hiramoto  Kyoto
University, Department of Physics, Kyoto, Japan  S. Hirota  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  F. Hosomi  University of
Tokyo, Department of Physics, Tokyo, Japan  K. Huang  Kyoto University,
Department of Physics, Kyoto, Japan  A.K. Ichikawa  Kyoto University,
Department of Physics, Kyoto, Japan  K. Ieki  Kyoto University, Department of
Physics, Kyoto, Japan  M. Ikeda  University of Tokyo, Institute for Cosmic Ray
Research, Kamioka Observatory, Kamioka, Japan  J. Imber  Ecole Polytechnique,
IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France  J. Insler
Louisiana State University, Department of Physics and Astronomy, Baton Rouge,
Louisiana, U.S.A.  R.A. Intonti  INFN Sezione di Bari and Università e
Politecnico di Bari, Dipartimento Interuniversitario di Fisica, Bari, Italy
T.J. Irvine  University of Tokyo, Institute for Cosmic Ray Research, Research
Center for Cosmic Neutrinos, Kashiwa, Japan  T. Ishida  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  T. Ishii
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
E. Iwai  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki, 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  A. Jacob  Oxford University, Department of Physics, Oxford, United
Kingdom  B. Jamieson  University of Winnipeg, Department of Physics, Winnipeg,
Manitoba, Canada  M. Jiang  Kyoto University, Department of Physics, Kyoto,
Japan  S. Johnson  University of Colorado at Boulder, Department of Physics,
Boulder, Colorado, U.S.A.  J.H. Jo  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  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  National
Centre for Nuclear Research, Warsaw, Poland  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  I. Karpikov  Institute
for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia  T.
Katori  Queen Mary University of London, School of Physics and Astronomy,
London, United Kingdom  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  D. Kielczewska  University of Warsaw, Faculty of
Physics, Warsaw, Poland  T. Kikawa  Kyoto University, Department of Physics,
Kyoto, Japan  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  RWTH Aachen University, III. Physikalisches Institut, Aachen, Germany
T. Koga  University of Tokyo, Department of Physics, Tokyo, Japan  P.P. Koller
University of Bern, Albert Einstein Center for Fundamental Physics, Laboratory
for High Energy Physics (LHEP), Bern, Switzerland  A. Konaka  TRIUMF,
Vancouver, British Columbia, Canada  K. Kondo  Kyoto University, Department of
Physics, Kyoto, Japan  A. Kopylov  Institute for Nuclear Research of the
Russian Academy of Sciences, Moscow, Russia  L.L. Kormos  Lancaster
University, Physics Department, Lancaster, United Kingdom  A. Korzenev
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland  Y.
Koshio  Okayama University, Department of Physics, Okayama, Japan  K. Kowalik
National Centre for Nuclear Research, Warsaw, Poland  W. Kropp  University of
California, Irvine, Department of Physics and Astronomy, Irvine, California,
U.S.A.  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.  J. Lagoda  National Centre for Nuclear Research, Warsaw, Poland  I.
Lamont  Lancaster University, Physics Department, Lancaster, United Kingdom
M. Lamoureux  IRFU, CEA Saclay, Gif-sur-Yvette, France  E. Larkin  University
of Warwick, Department of Physics, Coventry, United Kingdom  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. Lazos  University of Liverpool,
Department of Physics, Liverpool, United Kingdom  M. Licciardi  Ecole
Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France  T.
Lindner  TRIUMF, Vancouver, British Columbia, Canada  Z.J. Liptak  University
of Colorado at Boulder, Department of Physics, Boulder, Colorado, U.S.A.  R.P.
Litchfield  Imperial College London, Department of Physics, London, 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  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. Marteau  Université de Lyon, Université Claude Bernard
Lyon 1, IPN Lyon (IN2P3), Villeurbanne, France  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  S. Martynenko  State University of New York at Stony Brook,
Department of Physics and Astronomy, Stony Brook, New York, U.S.A.  T.
Maruyama  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  P. Mijakowski  National
Centre for Nuclear Research, Warsaw, Poland  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.  A. Missert  University of Colorado at Boulder, Department
of Physics, Boulder, Colorado, U.S.A.  M. Miura  University of Tokyo,
Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  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  J. Myslik  University of Victoria, Department of Physics
and Astronomy, Victoria, British Columbia, Canada  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  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  C. Nielsen
University of British Columbia, Department of Physics and Astronomy,
Vancouver, British Columbia, Canada  TRIUMF, Vancouver, British Columbia,
Canada  M. Nirkko  University of Bern, Albert Einstein Center for Fundamental
Physics, Laboratory for High Energy Physics (LHEP), Bern, Switzerland  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  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  R. Ohta
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, 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
City University, Department of Physics, Osaka, Japan  W. Oryszczak  University
of Warsaw, Faculty of Physics, Warsaw, Poland  S.M. Oser  University of
British Columbia, Department of Physics and Astronomy, Vancouver, British
Columbia, Canada  TRIUMF, Vancouver, British Columbia, Canada  T. Ovsyannikova
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia  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.  N.D. Patel  Kyoto University, Department of Physics, Kyoto, Japan  P.
Paudyal  University of Liverpool, Department of Physics, Liverpool, United
Kingdom  M. Pavin  UPMC, Université Paris Diderot, CNRS/IN2P3, Laboratoire de
Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France  D. Payne
University of Liverpool, Department of Physics, Liverpool, United Kingdom
J.D. Perkin  University of Sheffield, Department of Physics and Astronomy,
Sheffield, United Kingdom  Y. Petrov  University of British Columbia,
Department of Physics and Astronomy, Vancouver, British Columbia, Canada
TRIUMF, Vancouver, British Columbia, Canada  L. Pickard  University of
Sheffield, Department of Physics and Astronomy, Sheffield, United Kingdom  L.
Pickering  Imperial College London, Department of Physics, London, 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  UPMC, Université Paris Diderot,
CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE),
Paris, France  M. Posiadala-Zezula  University of Warsaw, Faculty of Physics,
Warsaw, Poland  J.-M. Poutissou  TRIUMF, Vancouver, British Columbia, Canada
R. Poutissou  TRIUMF, Vancouver, British Columbia, Canada  A. Pritchard
University of Liverpool, Department of Physics, Liverpool, United Kingdom  P.
Przewlocki  National Centre for Nuclear Research, Warsaw, Poland  B. Quilain
Kyoto University, Department of Physics, Kyoto, 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  P.N. Ratoff  Lancaster University,
Physics Department, Lancaster, United Kingdom  M. Ravonel  University of
Geneva, Section de Physique, DPNC, Geneva, Switzerland  M.A. Rayner
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland  A. Redij
University of Bern, Albert Einstein Center for Fundamental Physics, Laboratory
for High Energy Physics (LHEP), Bern, Switzerland  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  P. Rojas  Colorado State University,
Department of Physics, Fort Collins, Colorado, U.S.A.  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  R. Sacco  Queen Mary University of London,
School of Physics and Astronomy, London, United Kingdom  K. Sakashita  High
Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan  F.
Sánchez  Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute
of Science and Technology, Campus UAB, Bellaterra (Barcelona) Spain  F. Sato
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
E. Scantamburlo  University of Geneva, Section de Physique, DPNC, Geneva,
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  TRIUMF, Vancouver, British
Columbia, Canada  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  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  T. Shirahige  Okayama University,
Department of Physics, Okayama, Japan  S. Short  Queen Mary University of
London, School of Physics and Astronomy, London, United Kingdom  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  M. Sorel  IFIC (CSIC & University of Valencia),
Valencia, Spain  L. Southwell  Lancaster University, Physics Department,
Lancaster, United Kingdom  P. Stamoulis  IFIC (CSIC & University of Valencia),
Valencia, Spain  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  Y. Suda  University of Tokyo, Department of
Physics, Tokyo, Japan  S. Suvorov  Institute for Nuclear Research of the
Russian Academy of Sciences, Moscow, Russia  A. Suzuki  Kobe University, Kobe,
Japan  K. Suzuki  Kyoto University, Department of Physics, Kyoto, 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  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  S. Takahashi  Kyoto University,
Department of Physics, Kyoto, 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  University of Toronto, Department of Physics, Toronto, Ontario, Canada
TRIUMF, Vancouver, British Columbia, Canada  D. Terhorst  RWTH Aachen
University, III. Physikalisches Institut, Aachen, Germany  R. Terri  Queen
Mary University of London, School of Physics and Astronomy, London, United
Kingdom  T. Thakore  Louisiana State University, Department of Physics and
Astronomy, Baton Rouge, Louisiana, U.S.A.  L.F. Thompson  University of
Sheffield, Department of Physics and Astronomy, Sheffield, United Kingdom  S.
Tobayama  University of British Columbia, Department of Physics and Astronomy,
Vancouver, British Columbia, Canada  TRIUMF, Vancouver, British Columbia,
Canada  W. Toki  Colorado State University, Department of Physics, Fort
Collins, Colorado, U.S.A.  T. Tomura  University of Tokyo, Institute for
Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan  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  A. Vacheret  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.  Z. Vallari  State University of New
York at Stony Brook, Department of Physics and Astronomy, Stony Brook, New
York, U.S.A.  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  T.
Wachala  H. Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland
K. Wakamatsu  Osaka City University, Department of Physics, Osaka, Japan  C.W.
Walter  Duke University, Department of Physics, Durham, North Carolina, 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  W. Warzycha  University of Warsaw, Faculty of
Physics, Warsaw, Poland  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  R.J. Wilkes
University of Washington, Department of Physics, Seattle, Washington, U.S.A.
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  Imperial College London, Department of Physics,
London, United Kingdom  Y. Yamada  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki, Japan  K. Yamamoto  Osaka City
University, Department of Physics, Osaka, Japan  M. Yamamoto  Kyoto
University, Department of Physics, Kyoto, Japan  C. Yanagisawa  State
University of New York at Stony Brook, Department of Physics and Astronomy,
Stony Brook, New York, U.S.A.  T. Yano  Kobe University, Kobe, 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  J. Yoo  Louisiana
State University, Department of Physics and Astronomy, Baton Rouge, Louisiana,
U.S.A.  K. Yoshida  Kyoto University, Department of Physics, Kyoto, Japan  T.
Yuan  University of Colorado at Boulder, Department of Physics, Boulder,
Colorado, U.S.A.  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  L. Zambelli  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki, Japan  K. Zaremba  Warsaw University of
Technology, Institute of Radioelectronics, 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
J. Żmuda  Wroclaw University, Faculty of Physics and Astronomy, Wroclaw,
Poland

###### Abstract

The single $\pi^{0}$ production rate in neutral current neutrino interactions
on water in a neutrino beam with a peak neutrino energy of $0.6$ GeV has been
measured using the PØD, one of the subdetectors of the T2K near detector. The
production rate was measured for data taking periods when the PØD contained
water ($2.64\times 10^{20}$ protons-on-target) and also periods without water
($3.49\times 10^{20}$ protons-on-target). A measurement of the neutral current
single $\pi^{0}$ production rate on water is made using appropriate
subtraction of the production rate with water in from the rate with water out
of the target region. The subtraction analysis yields
$106{}\pm{}41{}\textrm{\,(stat.)}{}\pm{}69\textrm{\,(sys.)}{}$ signal events,
which is consistent with the prediction of $157$ events from the nominal
simulation. The measured to expected ratio is
$0.68{}\pm{}0.26{}\textrm{\,(stat.)}{}\pm{}0.44{}\textrm{\,(sys.)}{}\pm{}0.12{}\textrm{\,(flux)}{}$.
The nominal simulation uses a flux integrated cross section of $7.63\times
10^{-39}~{}\textrm{cm}^{2}$ per nucleon with an average neutrino interaction
energy of $1.3$ GeV.

###### pacs:

12.15.Mm, 13.15.+g

##  I Introduction

The Tokai to Kamioka (T2K) long-baseline neutrino experiment is designed to
make precision measurements of the neutrino oscillation parameters
$\theta_{23}$ and $\Delta m^{2}_{32}$ via $\nu_{\mu}$ disappearance and to
search for the mixing angle $\theta_{13}$ via $\nu_{e}$ appearance in a
$\nu_{\mu}$ beam. An intense, almost pure beam of $\nu_{\mu}$ is produced by
colliding 30 GeV protons with a graphite target at the J-PARC facility in
Tokai-mura, IbarakiAbe  _et al._ (2011). The resultant neutrino beam is
directed $2.5^{\circ}$ away from the axis between the target and the far
detector, resulting in a narrow band beam with peak energy near 0.6 GeV. The
direction, stability and flux of the beam are measured using a suite of near
detectors (ND280) located 280 m downstream of the target. At this distance,
the neutrino beam is not expected to have been affected by oscillations. The
far detector, Super-Kamiokande, is located 295 km downstream of the target, a
distance consistent with the oscillation maximum. Super-Kamiokande uses water
as both a detection medium and target to measure the amount of $\nu_{e}$ and
$\nu_{\mu}$ present after oscillation has occurred. As neutral current
$\pi^{0}$ events can cause an irreducible background to the $\nu_{e}$
appearance signal, it is important to provide a constraint using measurements
of the production rate on water using the near detector.

This paper details the first measurement of neutral current single $\pi^{0}$
production (NC1$\pi^{0}$) on water, using a neutrino beam with peak energy of
$0.6$ GeVAbe  _et al._ (2013a). The mean neutrino energy for the NC1$\pi^{0}$
interactions selected in this analysis is $1.3$ GeV.

Two processes dominate neutral current single $\pi^{0}$ production by
neutrinos: resonant production and coherent scattering. In resonant
production, a neutrino interacts with a nucleon to produce a baryonic
resonance, usually $\Delta(1232)$, which subsequently decays to a nucleon and
a $\pi^{0}$. Coherent scattering occurs when a neutrino interacts with the
entire nucleus, exchanging little energy and leaving the nucleus in its ground
state. The dominant decay mode for a $\pi^{0}$ is to two photons Olive  _et
al._ (2014) and if one decay photon is not detected, an NC1$\pi^{0}$ event can
be indistinguishable from a charged current $\nu_{e}$ interaction, leading to
an irreducible background in $\nu_{\mu}\to\nu_{e}$ oscillation measurements.
Whilst previous measurements performed using the T2K near detector have
improved our knowledge of sub-GeV neutrino interactions, the rate of
NC1$\pi^{0}$ production on water is still relatively unknown at the neutrino
energies of the T2K beam. Measurements of NC1$\pi^{0}$ production on a variety
of targets and different neutrino energy distributions have been made at other
experimentsPohl  _et al._ (1979); Nakayama  _et al._ (2005); Aguilar-Arevalo
_et al._ (2010); Kurimoto  _et al._ (2010a, b).

In this analysis, the signal is defined by the final state particles, with an
NC1$\pi^{0}$ interaction defined by a single $\pi^{0}$ particle exiting the
nucleus along with any number of protons and neutrons but no charged leptons
or other mesons. The rate of signal events on water is determined using event
samples with a two photon signature from exposures with water in and out of
the target region. Using the presence of a muon decay tag, two photon
candidate events are divided into signal-enriched and background-enriched
samples. The number of signal events, number of background events, energy
scale, and shape of the background are then determined for each sample using a
simultaneous maximum likelihood fit to the invariant mass distribution of the
signal-enriched and background-enriched samples. Finally, the number of
interactions on water is determined using a weighted subtraction of the rate
of signal events determined during the exposure with water in the target
region and the exposure with the water removed.

The major sections of this paper are as follows. Section II describes the T2K
ND280 $\pi^{0}$ detector, as well as the simulation of the expected neutrino
interactions and detector response. Section III describes the event selection
efficiencies and reconstruction resolutions for signal-enriched and
background-enriched event samples and the selected event samples are described
in Section IV. The extraction of the number of signal events is described in
Section V followed by a discussion of the systematic uncertainty in Section
VI. Section VII describes the calculation of the event rate on water and
compares it with the expectation.

##  II  T2K ND280 PØD Description and Simulation

The T2K ND280 $\pi^{0}$ Detector (PØD) is a scintillator-based tracking
calorimeter optimized to measure NC1$\pi^{0}$ production in the momentum range
that contributes backgrounds to $\nu_{e}$ appearance measurements Assylbekov
_et al._ (2012). The PØD is composed of layers of plastic scintillator
alternating with water bags and brass or lead and is one of the first large
scale detectors to use Multi-Pixel Photon Counters (MPPCs). Relative to the
neutrino beam, it sits upstream of a tracking detector made up of two fine
grain scintillator modules placed between three time projection chambers. Both
the PØD and tracking detector are in a 0.2 T magnetic field and surrounded by
electromagnetic calorimeters and muon range detectors Abgrall  _et al._
(2011); Allan  _et al._ (2013); Aoki  _et al._ (2013); Amaudruz  _et al._
(2012).

The PØD comprises 40 scintillator modules, each 38 mm thick, formed from two
layers of scintillating bars with the long axis oriented either horizontally,
or vertically, and instrumented using wavelength shifting fibers with an MPPC
on one end and mirrored on the other Assylbekov  _et al._ (2012). The
triangular scintillating bars used to produce each of the two layers in each
module have a height of 17 mm and a base of 32 mm and are interlocked to form
a layer that is 17 mm thick. Two views are formed of an event, commonly
labeled the X-Z, and the Y-Z view, where the $z$ axis is horizontal and points
downstream, the $y$ axis points in the vertical direction, and the $x$ axis is
perpendicular to the Y-Z plane. A minimum ionizing particle will typically
generate a charge in the MPPC equivalent to approximately
$38~{}\mathrm{photoelectrons}/\mathrm{cm}$, or an average of about
$30~{}\mathrm{photoelectrons}$ in a single bar. The scintillator modules are
arranged in three regions. The most upstream and downstream regions are made
of seven modules interleaved with 4.5 mm thick sheets of stainless steel-clad
lead that function as 4.9 radiation length electromagnetic calorimeters to
improve the containment of photons and electrons. The central region serves as
a target containing water. It has 25 water target layers that are 28 mm thick
interleaved with 26 scintillator modules and 1.3 mm brass sheets. When water
is in the detector, the target fiducial region contains approximately 1900 kg
of water and 3570 kg of other materials. Data collected with and without water
in the PØD are analyzed separately.

Table 1:  Summary of T2K runs, including the configuration of the PØD, and the number of protons on target (POT) used in this analysis. T2K Run | PØD Configuration | POT
---|---|---
Run I | Water-In | $2.96\times 10^{19}$
Run II | Water-In | $6.96\times 10^{19}$
Run II | Water-Out | $3.59\times 10^{19}$
Run III | Water-Out | $1.35\times 10^{20}$
Run IV | Water-In | $1.65\times 10^{20}$
Run IV | Water-Out | $1.78\times 10^{20}$
Total | Water-Out | $3.49\times 10^{20}$
Total | Water-In | $2.64\times 10^{20}$

This analysis utilizes data collected with a predominantly $\nu_{\mu}$ beam
generated between January 2010 and May 2013, see Abe  _et al._ (2013a) for a
detailed description. The neutrinos are generated using a fast extracted
$30~{}\mathrm{GeV}$ proton beam with a spill of 6–8 bunches that are separated
by 582 ns. The proton beam strikes a graphite target producing pions and kaons
which, after magnetically focusing the positive mesons, decay in flight to
neutrinos. The magnetic focusing can be altered to focus negative mesons. The
T2K runs, the configuration of the PØD, and the corresponding protons on
target (POT) are summarized in Table 1.

The simulated data set used in this analysis corresponds to $4.01\times
10^{21}$ POT (water-out configuration), and $7.18\times 10^{21}$ POT (water-in
configuration). Neutrino interactions are simulated using the NEUT Hayato
(2009) event generator, version 5.1.4.2, with the interactions distributed
within the full ND280 volume, as well as the surrounding hall. Interactions on
all nuclear targets present in ND280 are simulated. Details of the neutrino
interaction simulation process are described in Hayato (2009), Abe  _et al._
(2013b) and Abe  _et al._ (2014). The T2K run periods are simulated using the
nominal detector and beam configurations, and then combined using the
appropriate POT normalization to form the final expectation. External, non-
beam associated, backgrounds are not simulated, but are limited in the data
sample by the duty cycle of the neutrino beam. Particles produced in neutrino
interactions are simulated using GEANT 4.9.4 Agostinelli  _et al._ (2003). The
standard GEANT physics list for electromagnetic interactions is used in the
simulation.

Neutral current single $\pi^{0}$ production in the T2K neutrino beam is
dominated by resonant $\Delta(1232)$ production, which is simulated using the
Rein-Sehgal Rein and Sehgal (1981) model for neutrino-induced resonant pion
production. The simulated NC1$\pi^{0}$ cross section on water integrated over
the T2K neutrino beam flux is $7.63\times 10^{-39}~{}\textrm{cm}^{2}$ or
$4.24\times 10^{-40}~{}\textrm{cm}^{2}~{}\textrm{nucleon}^{-1}$ while the
NC1$\pi^{0}$ cross section for the fiducial region in the water-out
configuration is $4.20\times 10^{-40}~{}\textrm{cm}^{2}~{}\textrm{amu}^{-1}$
Abe  _et al._ (2013a); Hayato (2009). There is an additional $12\%$
uncertainty in the neutrino flux integrated over the energy of neutrinos
generating an NC1$\pi^{0}$ interactionAbe  _et al._ (2013a). This uncertainty
is larger than presented in other T2K analyses because of the higher average
neutrino energy, and, for this analysis, is unconstrained by other near
detector measurements to allow direct comparison between the data and
simulation.

##  III Event Reconstruction and Selection

Events are reconstructed in the PØD using scintillation light signals that
occur in time windows containing the neutrino bunch arrival. A hit is
constructed from the integrated charge during each time window, and the time
relative to the start of the window at which the integrated light signal
crosses a threshold equivalent to approximately 2.5 photoelectrons. Activity
in different time windows is independently reconstructed as separate events.
The reconstruction proceeds by selecting groups of hits consistent with a
track-like signature that is classified as a light-ionizing track, such as a
muon or charged pion, a heavy-ionizing track, such as a proton, or a non-track
object such as a portion of an electromagnetic shower. Hits from non-track
objects, as well as any hits not gathered into a track-like object are then
used to form groups that are consistent with shower-like particles such as
photons or electrons coming from a single vertex. In events without a track-
like signature, the vertex is estimated by assuming that the particle
signatures in the event emanate from a single point, with the particle
directions going away from the vertex. While events with track-like objects
will generally be rejected in the later analysis, if a track-like object is
found, then the vertex is fixed at the upstream end of the longest track.
After vertex reconstruction, all reconstructed non-track like objects, are
classified as either EM-like, or shower-like. The shower-like objects
primarily comprise interacting pions, interacting protons, or misidentified
light-ionizing tracks. The result of the reconstruction is a single vertex
with an associated collection of objects corresponding to light-ionizing
tracks, heavy-ionizing tracks, EM-like, and other shower-like objects. A muon
decay tag is associated with the reconstructed vertex when energy deposition
consistent with a Michel electron is found.

A signal-enriched sample of exactly two photon candidates with invariant mass
less than 500 $\textrm{MeV}/\textrm{c}^{2}$ is selected using eight selection
criteria: event quality, vertex in the fiducial volume, energy containment in
the PØD, lack of a muon decay signature, fraction of energy in the two most
energetic photon candidates, particle identification, reconstructed direction
and object separation. In comparison to the signal, a distinguishing
characteristic of the background is that it contains either a $\mu$, or a
charged pion, both of which can generate a muon decay signature, so a separate
background-enriched sample is selected by applying all criteria with the
exception of the muon decay criterion which is reversed.

To be considered in this analysis, an event must occur during a neutrino beam
spill and have a single reconstructed vertex as well as good data quality. The
vertex must be in the fiducial volume defined as at least $25$ cm from the
edge of the active volume and inside the water target region of the PØD Gilje
(2014). The containment criteria requires that all reconstructed objects are
contained inside the PØD by requiring that no reconstructed objects have hits
in the last layer of the PØD or in the outer two bars of any layer. This
limits external background and improves the photon energy reconstruction.

The signature of interest is two reconstructed photons from the $\pi^{0}$
decay with no evidence of a muon-like object. To ensure that selected events
have two reconstructed photon candidates containing most of the recorded
energy deposition, a “charge-in-shower” requirement is placed on the fraction
of energy in the two most energetic EM-like objects. The required fractions of
92% (water-in), and 80% (water-out) were chosen to optimize the statistical
significance of the selected number of signal events using simulated samples.
Due to the planar nature of the PØD, and the shape of the scintillator bars,
the performance degrades for particles at an angle of more than approximately
$75^{\circ}$ from the $z$ axis. As such, the direction of the reconstructed
total event momentum must be less than $60^{\circ}$ from the $z$ axis,
limiting the phase space covered by this measurement.

Two well-separated decay photon candidates are required to limit the
background from particles with overlapping energy deposits. The object
separation in each projection is calculated by finding the distance between
the two closest hits of the reconstructed objects. Due to the planar nature of
the PØD, it is possible for two objects to overlap in one projection, but not
in the other and separation is only required in one of the two projections.
The object separation is required to be greater than 9 cm (14 cm) in at least
one projection for the water-in (water-out) configuration.

Table 2:  Efficiencies and the purity of the selection. On-Water and Not-Water indicate the material that the neutrino interacted with. | Efficiency, $\epsilon$ | Purity
---|---|---
Water-In |  |
Total | $6.10\%$ | $48.7\%$
On-Water | $6.20\%$ | $56.2\%$
Not-Water | $6.04\%$ | $45.3\%$
Water-Out |  |
Total | $4.79\%$ | $46.1\%$

(a) Water-In configuration (b) Water-Out configuration

Figure 1:  The residual of the reconstructed vertex position relative to the
true vertex position along the beam direction for selected NC1$\pi^{0}$
events. The vertical lines correspond to the $16\%$ and $84\%$ quantiles.

(a) Water-In configuration (b) Water-Out configuration

Figure 2:  The distribution of the fractional difference between the
reconstructed NC1$\pi^{0}$ momentum and the true momentum for selected
NC1$\pi^{0}$ events. A Gaussian distribution is fit to the central region.

Figure 1 shows the position of the reconstructed vertex relative to the true
vertex position along the $z$ axis for the water-out configuration of the PØD
for simulated NC1$\pi^{0}$ events that have passed all selection criteria. For
the water-in (water-out) configuration, the biases are $-0.06{}$ cm ($0.08{}$
cm) along the $x$ axis, $0.06{}$ cm ($0.20{}$ cm) along the $y$ axis, and
$1.67{}$ cm ($1.72{}$ cm) along the $z$ axis. The expected vertex residual
distribution is asymmetric due it’s dependence on the reconstructed photon
position and direction, and is characterized by half the distance between the
$16\%$ and $84\%$ quantiles. For the water-in (water-out) configuration, the
resolutions are $5.5{}$ cm ($6.8{}$ cm) along the $x$ axis, $6.1{}$ cm
($8.0{}$ cm) along the $y$ axis, $8.6{}$ cm ($11.2{}$ cm) along the $z$ axis.

The momentum resolution of the $\pi^{0}$ is a combination of the energy and
angular resolution for two reconstructed photons. The total energy for the
reconstructed photons is determined calorimetrically, and the fraction of the
total energy carried by each reconstruct photons is calculated using the
projections where the photon objects are geometrically distinct. Figure 2
shows the fractional momentum residual (the difference of the reconstructed
and true momenta divided by the true momentum) for the water-out configuration
of the PØD for NC1$\pi^{0}$ events passing all selection criteria. A Gaussian
is fit to the central region to determine the shift and width of the momentum
distribution. The fractional momentum residual distribution has a mean of
$-3.2\%$ with a width of $18.7\%$ for the PØD water-in configuration. For the
water-out configuration, the mean is $-0.8\%$ with a width of $21.1\%$. The
reconstructed opening angle distribution for simulated NC1$\pi^{0}$ events
passing all selection criteria in both the water-in and water-out
configurations has a mean of $-0.01$ rad from the nominal value and an RMS of
$0.06$ rad.

(a) Water-In configuration (b) Water-Out configuration

Figure 3:  The efficiency to select an NC1$\pi^{0}$ event as a function of the
true momentum of the $\pi^{0}$.

The reconstruction efficiency, $\epsilon$, for an NC1$\pi^{0}$ event and
signal-enriched sample purity are summarized in Table 2. The efficiency is
defined as the number of true NC1$\pi^{0}$ events reconstructed in the
fiducial volume divided by the number of NC1$\pi^{0}$ interactions occurring
within the same volume, while the purity is defined as the fraction of the
selected events which result from a true NC1$\pi^{0}$ interaction. The average
efficiency is $6.10\%$ for the water-in configuration, and $4.79\%$ for the
water-out configuration. There is a small location dependence in the
efficiency for the water-in configuration, so the efficiency is tabulated
separately for interactions which occur in the water target, and for
interactions which occur on another material. The average purity for the
water-in (water-out) configuration is $48.7\%$ ($46.1\%$) for all events with
a two photon invariant mass less than 500 $\textrm{MeV}/\textrm{c}^{2}$
corresponding to a rejection of more than $99.5\%$ of the background events.
Figure 3 shows the efficiency of the NC1$\pi^{0}$ selection as a function of
the true $\pi^{0}$ momentum.

##  IV  Selected Event Samples

Table 3:  The breakdown of the sample of events that satisfy the selection criteria for the PØD water-in configuration. The sample of simulated events is broken down into signal and background and then the background sample is further subdivided by interaction type. The values have been rounded. | Signal-Enriched Sample | Background-Enriched Sample
---|---|---
Data | $775$ |  |  | $227$ |  |
Expectation | $893$ |  |  | $331$ |  |
Signal |  | $435$ |  |  | $33$ |
Background |  | $458$ |  |  | $297$ |
Neutral Current |  |  | $109$ |  |  | $74$
Charged Current w/ $\pi^{0}$ |  |  | $56$ |  |  | $39$
Charged Current w/o $\pi^{0}$ |  |  | $239$ |  |  | $167$
External |  |  | $39$ |  |  | $9$
Multiple |  |  | $15$ |  |  | $8$
Table 4:  The breakdown of the sample of events that satisfy the selection criteria for the PØD water-out configuration. The sample of simulated events is broken down into signal and background and then the background sample is further subdivided by interaction type. The values have been rounded. | Signal-Enriched Sample | Background-Enriched Sample
---|---|---
Data | $555$ |  |  | $123$ |  |
Expectation | $629$ |  |  | $210$ |  |
Signal |  | $290$ |  |  | $24$ |
Background |  | $339$ |  |  | $187$ |
Non-Signal Neutral Current |  |  | $68$ |  |  | $45$
Charged Current w/ $\pi^{0}$ |  |  | $40$ |  |  | $22$
Charged Current w/o $\pi^{0}$ |  |  | $150$ |  |  | $100$
External |  |  | $70$ |  |  | $13$
Multiple |  |  | $11$ |  |  | $7$

(a) Water-In configuration (b) Water-Out configuration

Figure 4:  The distribution of the true neutrino energy for the simulated
events in the signal-enriched sample.

Tables 3 and 4 show the number of observed and expected events found in the
signal-enriched and background-enriched samples. The expectation for each
sample is broken down into the number of expected signal and background
events, and the number of background events is further broken down by the
presence of charged leptons with and without a $\pi^{0}$ in the final state of
the neutrino interaction. Categories are also included for simulated events
containing multiple neutrino interactions, and background entering from
outside the PØD. Approximately $10\%$ of the events in the background-enriched
sample are due to signal interactions. In the data, $775$ events were selected
as an NC1$\pi^{0}$-enriched sample for the water-in configuration and $555$
events were selected for the water-out configuration of the PØD compared to an
expectation of $893$ ($629$) for the water-in (water-out) configuration. The
distribution of the true neutrino energy for the selected sample of simulated
events is shown in Figure 4 separated by event topology with the mean neutrino
energy for the NC1$\pi^{0}$ signal being $1.3$ GeV.

(a) Water-In configuration

(b) Water-Out configuration

Figure 5:  The expected and observed reconstructed invariant mass for the
signal-enriched and background-enriched samples in both the water-in and
water-out configurations. The left (right) plots show the distributions for
the signal-enriched (background-enriched) samples. The expectation for each
sample is normalized to the observed number of events.

(a) Water-In configuration (b) Water-Out configuration

Figure 6:  The expected and observed reconstructed $\pi^{0}$ energy for the
signal-enriched sample. The expectation for each sample is normalized to the
observed number of events.

The event signature for this analysis is two reconstructed photons with an
invariant mass, $M$, close to that of the $\pi^{0}$. The reconstructed
invariant mass is $M=\sqrt{2E_{1}E_{2}(1-\cos{\theta})}$ where $E_{1}$ and
$E_{2}$ are the reconstructed energies of each photon candidate and $\theta$
is the angle between the photon candidates. Figure 5 shows the distribution of
the selected events in the signal-enriched and background-enriched samples
where the expectation for each distribution has been normalized to the
observed number of events. The reconstructed energy distribution of the
signal-enriched samples is shown in Figure 6. The expected composition for
each distribution is shown using the same breakdown as in Tables 3 and 4,
however, the contributions from external and multiple interactions have been
combined into a single category.

##  V  Extracting the Signal Event Rate

The number of NC1$\pi^{0}$ events is found using a six parameter unbinned
extended maximum likelihood fit to the invariant mass distribution of the
signal-enriched and background-enriched samples. Four of the parameters,
$N_{\textrm{Sig}}^{\textrm{SE}}$, $N_{\textrm{Bkg}}^{\textrm{SE}}$,
$N_{\textrm{Sig}}^{\textrm{BE}}$, and $N_{\textrm{Bkg}}^{\textrm{BE}}$, are
related to the number of signal and background events in the signal-enriched
(SE) and background-enriched (BE) samples. The remaining two parameters
control the energy scale of electromagnetic particles relative to minimum
ionizing tracks, and the shape of the expected background.

The likelihood is extended by assuming that the probability of the observed
numbers of signal-enriched ($N_{\gamma\gamma}^{\textrm{SE}}$) and background-
enriched ($N_{\gamma\gamma}^{\textrm{BE}}$) events is given by the product of
Poisson distributions and, in each case, the expected number of two photon
events is a sum of the signal events ($N_{\textrm{Sig}}$) and the background
events ($N_{\textrm{Bkg}}$). The expected invariant mass distribution for the
signal (background) events in the signal-enriched (background-enriched) sample
is generated using the simulation after event reconstruction. The
distributions are normalized such that the sum over the signal-enriched bins
is equal to the total number of events, $N_{\gamma\gamma}^{\textrm{SE}}$, and,
likewise, for the background-enriched sample,
$N_{\gamma\gamma}^{\textrm{BE}}$.

Table 5:  Best fit values for the number of events in the PØD water-in and PØD water-out configurations. Only statistical uncertainties are included. |  $N_{\textrm{Sig}}^{\textrm{SE}}$ (expected) |  $N_{\textrm{Bkg}}^{\textrm{SE}}$ (expected) |  $N_{\textrm{Sig}}^{\textrm{BE}}$ (expected) |  $N_{\textrm{Bkg}}^{\textrm{BE}}$ (expected)
---|---|---|---|---
Water-In |  $342{}\pm{}33{}$ ($433$) |  $338\pm{}26$ ($429$) |  $26.9\pm{}2.6$ ($33$) |  $245\pm{}15$ ($278$)
Water-Out |  $246{}\pm{}26{}$ ($290$) |  $271\pm{}22$ ($335$) |  $20.4\pm{}2.2$ ($24$) |  $141\pm{}11$ ($184$)

(a) Water-In configuration

(b) Water-Out configuration

Figure 7:  Comparison of the data to the best fit invariant mass distributions
for the water-in and water-out configurations, with the best fit energy scale
applied to the data. The left (right) plots show the distributions for the
signal-enriched (background-enriched) samples. The effect of the measured
energy scale on the 500 $\textrm{MeV}/\textrm{c}^{2}$ selection criterion has
not been applied to the expectation.

The ratio of the number of signal and background events in the signal-enriched
sample to the numbers in the background-enriched sample
($N_{\textrm{Sig}}^{\textrm{SE}}/N_{\textrm{Sig}}^{\textrm{BE}}$ and
$N_{\textrm{Bkg}}^{\textrm{SE}}/N_{\textrm{Bkg}}^{\textrm{BE}}$) are
determined by the efficiency of the muon decay tag and the probability of a
muon decay tag false positive. Both relations are estimated using a sample of
stopping muons from neutrino interactions occurring upstream of the PØD. This
sample is selected by requiring a single track-like object entering the
upstream face of the detector, and stopping in the water target region.

The number of background events in the signal-enriched sample is related to
the background events in the background-enriched sample by the muon decay
reconstruction efficiency and is allowed to vary within the uncertainty on the
muon decay tag efficiency. For the water-in (water-out) configuration, the
expected efficiency is $45.6\%$ ($43.9\%$) and the observed efficiency is
$44.1\pm{}0.5\%$ ($46.2\pm{}0.6\%$). The fractional difference between data
and expectation is combined with its statistical error and used as a Gaussian
constraint in the likelihood on the ratio between the number of background
events in the signal-enriched and background-enriched samples. The constraint
is $3.4\%$ for the water-in configuration and $5.2\%$ for the water-out
configuration.

The fitted number of signal events in the background-enriched sample relative
to the number in the signal-enriched sample is allowed to vary within the
uncertainty on the probability of a false positive muon decay tag. The
uncertainty in modeling the false muon decay tag rate has been estimated by
fitting the time distribution of muon decay tags occurring after a stopping
muon, but within the same trigger window, to an exponential plus a constant.
The fitted exponential lifetimes are consistent with the expectation for muon
decay, and the constant term estimates the probability of incorrectly finding
a muon decay tag. For the water-in (water-out) configuration there is a
$1.1\pm{}0.5\%$ ($1.3\pm{}0.7\%$) difference in the constant term between the
data and expectation which provides a $\pm{}1.6\%$ ($\pm{}2.0\%$) constraint
on the false tag probability.

Since there is an uncertainty in the shape of the background underneath the
$\pi^{0}$ invariant mass peak, an extra shape parameter has been added to the
fit. The deviation from the expected background shape is assumed to have the
same shape as the signal probability distribution, while the normalization is
constrained by the background-enriched sample. The shape factor is allowed to
be positive or negative meaning that the amount of background in the region of
the $\pi^{0}$ invariant mass can be either increased or decreased. Two cases
are considered in the fit. In the first instance, the number of signal and
background events are determined by using the nominal shape for the background
which is equivalent to fixing the shape parameter to a value of zero. In the
second case, no prior constraint is placed on the shape parameter, and the
uncertainty in the rate is estimated by constraining it with both the signal-
enhanced and background-enhanced samples. See Section VI where this case is
used to estimate the systematic uncertainty due to the unknown background
shape.

The overall energy scale in the PØD is set using penetrating muon tracks, and
must be translated to an energy scale for electromagnetic particles with
uncertainty introduced due to the relative response of the detector to
different particle types. The final electromagnetic energy scale is determined
using the position of $\pi^{0}$ invariant mass peak. The mean difference
between the reconstructed and true photon opening angle in the simulation is
small ($0.01$ rad) and has negligible effect on the invariant mass
distribution so the difference between the measured and simulated invariant
mass scales is assigned to the energy scale uncertainty. No prior constraint
is placed on the energy scale parameter, however, based on a survey of the
detector material distribution and the uncertainties in the particle
propagation model, the prior uncertainty is approximately $10\%$ relative to
the energy scale determined using penetrating muons. In the water-in (water-
out) configuration, the fitted value for the electromagnetic energy scale
parameter is $89.5\pm{}3.4\%$ ($96.7\pm{}0.6\%$).

The best fit values for the number of signal and background events with the
energy scale parameter unconstrained, while using the nominal shape for the
background, are shown in Table 5. Figure 7 compares the invariant mass
expectation to the data, where the energy scale correction determined during
the fit has been applied to the data. Because the criteria requiring events
have a reconstructed invariant mass less than
$500~{}\textrm{MeV}/\textrm{c}^{2}{}$ is applied prior to determining the best
fit energy scale, the mass bins above $440~{}\textrm{MeV}/\textrm{c}^{2}{}$
are not fully populated with data. The goodness of fit is calculated as a
binned $\chi^{2}$ of the invariant mass distributions between
$0$–$440~{}\textrm{MeV}/\textrm{c}^{2}{}$ where the range has been limited to
the region that the data populates. Considering only statistical uncertainty,
the $\chi^{2}$ value for the PØD water-in configuration is $40.4$ for 39
degrees of freedom, leading to a p-value of $0.41$. The $\chi^{2}$ value for
the PØD water-out configuration is $53.5$ for 39 degrees of freedom, leading
to a p-value of $0.06$.

##  VI Systematics

The systematic uncertainties are summarized in Table 6, and are described
below. The detector systematics are separately estimated for the water-in and
water-out configurations. Since the detector performance is different, and run
periods do not overlap in time, the systematic uncertainty related to detector
performance is assumed to be uncorrelated between the water-in and water-out
configurations.

Table 6:  Summary of event rate systematic errors. The uncorrelated systematic errors are tabulated and summed, followed by the systematic error that is correlated between the water-in and water-out configurations. Parameter | Uncertainty
---|---
| Water-In | Water-Out
Geometry Differences | $2.8\%$ | $2.8\%$
PE Peak Discrepancy | $0.6\%$ | $0.4\%$
Energy Scale | $5.8\%$ | $0.9\%$
Channel to Channel Variations | $<0.1\%$ | $<0.1\%$
Time Variation of Energy Scale | $1.8\%$ | $1.8\%$
Mass Uncertainty | $0.4\%$ | $0.6\%$
Alignment | $<0.1\%$ | $<0.1\%$
Fiducial Volume Scaling | $1.5\%$ | $2.0\%$
Fiducial Volume Shift | $1.1\%$ | $1.7\%$
Flux Shape and Event Generator | $2.5\%$ | $3.3\%$
Track PID Efficiency | $5.4\%$ | $5.1\%$
Shower PID Efficiency | $6.6\%$ | $2.6\%$
Object Separation | $9.1\%$ | $11.6\%$
Charge-In-Shower | $6.6\%$ | $3.0\%$
Background Shape (statistical) | $3.8\%$ | $4.2\%$
Total Uncorrelated Systematic | $16.4\%$ | $15.0\%$
Total Correlated Systematic | $19.8\%$
Total Systematic | $25.7\%$ | $24.8\%$

Because the event reconstruction proceeds in two stages, first reconstructing
track-like signatures in each event, and then reconstructing the remaining
activity assuming showering signatures, reconstruction efficiencies primarily
affect the result in two ways. First, an inefficiency is introduced when an
electromagnetic object is reconstructed as track-like, because the object will
then not be considered by the shower reconstruction. Other efficiencies are
more closely related to the shower reconstruction, including efficiencies
related to the particle identification of showering signatures, the
reconstructed distance between showering objects, and the fraction of the
visible energy assigned to each showering object.

The track particle identification efficiency uncertainty is estimated using
the sample of stopping muons described in Section V. The uncertainty for each
input parameter to the particle identification procedure is estimated and
propagated through the particle identification likelihood to determine the
effect on the identification efficiency. For simulated muons, there is a
$5.40\pm{}0.05\%$ ($5.06\pm{}0.03\%$) uncertainty in the misidentification
rates for the water-in (water-out) configuration. Combining the difference in
quadrature with the statistical uncertainty leads to a total track object
particle identification systematic of $5.4\%$ ($5.1\%$) for the water-in
(water-out) configuration.

The efficiencies of the charge-in-shower, object separation and shower
particle identification criteria are related to the properties of a showering
particle and are studied using control samples selected by reversing these
cuts to create double “side-band” distributions. For example, to estimate the
uncertainty in the efficiency of the charge-in-shower criterion, events that
fail the object separation and shower particle identification criteria, but
which pass all other criteria, are selected to create a control sample with
low signal purity. The estimated uncertainty for the efficiency of the charge-
in-shower criterion is then the relative difference between the percentage of
control sample events passing the criterion relative to the expectation. For
the water-in configuration, $54.0\%$ of the simulated, and $51.3\pm{}2.2\%$ of
the data control sample events are selected, combining the difference and the
statistical error in quadrature leads to a systematic uncertainty of $6.6\%$
in the efficiency due to the charge-in-shower criterion. A similar calculation
is done for the water-out configuration. The procedure is then repeated for
the object separation and shower particle identification criteria. Because
these three uncertainties are estimated using statistically limited data sets
collected during independent water-in and water-out run periods they are
assumed to be uncorrelated between the configurations, and the uncertainty
will likely be reduced by the collection of additional data. The on-water
uncertainty for these uncertainties is estimated by combining the water-in and
water-out uncertainties in quadrature (summarized in Table 6).

After the best fit values were found in Section V, the fitted value and
uncertainty on the energy scale were used to estimate the effect of the energy
scale on the estimated efficiency. This effect was modeled by scaling the
NC1$\pi^{0}$ reconstruction efficiency shown in Figure 3 using many trials of
the energy scale parameter distributed according to the best fit parameter and
statistical uncertainty. The shifted efficiency curve represents a new
expectation for the trial energy scale parameter and is used to estimate the
expected number of saved signal events in the simulation. The fractional shift
and RMS of the distribution of the expected number of signal events are then
added in quadrature to estimate the uncertainty due to the energy scale for
the estimated efficiency. The time variation of the energy scale was tracked
using through-going minimum ionizing particles, and it introduces an
efficiency uncertainty of $1.8\%$ for both the water-in and water-out
configurations.

Several systematic uncertainties were associated with the fiducial volume.
Uncertainties on measurements of the detector mass were used to reweight the
selected events to extract the uncertainty due to fiducial mass. The effect of
alignment between detector elements on the efficiency was studied and found to
be negligible ($<0.1\%$). Additionally, there are two fiducial volume
uncertainties. One reflects how the result is affected by changing the
fiducial volume definition, while the other quantifies the uncertainty due to
a systematic shift between the simulated and true detector volumes. When
combined, the fiducial volume uncertainty is $1.9\%$ for water-in and $2.6\%$
for water-out.

The systematic uncertainty due to the background shape is estimated by
comparing the effect on the fitted signal rate with the shape parameter fixed
to when it is unconstrained. Following the procedure outlined in Section V,
the best values for the shape parameter with the water-in and water-out
configurations are found to be statistically consistent with the $\chi^{2}$
value for the invariant mass distribution being $47.5$ for $38$ degrees of
freedom for the water-in configuration and $38.7$ for $38$ degrees of freedom
for the water-out configuration. Because the backgrounds in both the water-in
and water-out configuration arise from the same physical processes, it is
assumed that this uncertainty is fully correlated between the water-in and
water-out configurations and the uncertainty is directly applied to the on-
water signal event rate. The change in the water-in and water-out event rates
between the case where the shape parameter is fixed to zero and where the
shape parameter is free leads to a $19.8\%$ uncertainty in the on-water rate
due to the background shape parameter.

While this analysis uses background-enriched control samples to minimize the
uncertainty due to the model of the cross sections, changes in the generated
event kinematics have an effect. This was studied using the neutrino flux
shape and cross section uncertainties detailed in Abe  _et al._ (2013a) and
Abe  _et al._ (2014). For the water-in configuration, the flux shape and cross
section introduce a $2.5\%$ uncertainty, and for the water-out configuration,
a $3.3\%$ uncertainty. Because rate of observed events is consistent with the
expectation, the full $12\%$ flux uncertainty is included and given as a
separate uncertainty.

##  VII  Number of Events on Water

The number of NC1$\pi^{0}$ events in the PØD measured using both the water-in
and water-out configuration (Table 5) can be used to determine the number of
events occurring directly on water. The measured number of NC1$\pi^{0}$ events
with water in the PØD is found to be
$342{}\pm{}33{}{}\textrm{\,(stat.)}{}\pm{}88{}\textrm{\,(sys.)}$ during an
exposure of $3.49\times 10^{20}$ POT, where the systematic uncertainty
includes effects that are correlated between the water-in and water-out
configurations. The ratio between the observed and expected rate is
$0.79{}\pm{}0.08{}\textrm{\,(stat.)}{}\pm{}0.20{}\textrm{\,(sys.)}{}$.
Similarly, with water out of the PØD, the measured number is
$246{}\pm{}26{}{}\textrm{\,(stat.)}{}\pm{}61{}\textrm{\,(sys.)}{}$ for an
exposure of $2.64\times 10^{20}$ POT, and the ratio between the observed and
expected rate is
$0.85{}\pm{}0.09{}\textrm{\,(stat.)}{}\pm{}0.21{}\textrm{\,(sys.)}{}$. To
allow direct comparison to the expected NC1$\pi^{0}$ event rate, the quoted
ratios include neither the $12\%$ flux normalization uncertainty nor the
NC1$\pi^{0}$ cross section uncertainty

The total number of events on water is found using a statistical subtraction
by relating the event rate during the water-in exposure to the event rate
during the water-out exposure. The total number of signal events in the water-
in (WI) configuration can be divided into two parts,
$N_{\textrm{WI}}=N_{\textrm{On-Water}}+N_{\textrm{NW}}$, where
$N_{\textrm{NW}}$ is the number of signal events that occur on targets other
than water (referred to as “not-water” events) in the water-in configuration.
The number of not-water (NW) events, which is proportional to the number of
water-out (WO) events, can be subtracted from the total number of on-water
events by

$N_{\textrm{On-
Water}}=N_{\textrm{WI}}-\frac{\epsilon_{\textrm{NW}}\textrm{POT}_{\textrm{WI}}}{\epsilon_{\textrm{WO}}\textrm{POT}_{\textrm{WO}}}N_{\textrm{WO}},$
(1)

where the efficiencies, $\epsilon_{\textrm{NW}}$ and $\epsilon_{\textrm{WO}}$,
are given in Table 2, and the POT is given in Table 1. After the subtraction
in Equation 1, $106{}\pm{}41{}\textrm{\,(stat.)}{}\pm{}69\textrm{\,(sys.)}{}$
events were found, where the uncertainties that are correlated between the
water-in and water-out configurations have been taken into account. The
simulation predicts $157$ true NC1$\pi^{0}$ events on water.

The ratio of the number of measured to number of predicted on-water events,
including the correlated and uncorrelated uncertainties described in Section
VI is
$0.68{}\pm{}0.26{}\textrm{\,(stat.)}{}\pm{}0.44{}\textrm{\,(sys.)}{}\pm{}0.12{}\textrm{\,(flux)}{}$,
where the NC1$\pi^{0}$ cross section uncertainties are excluded.

##  VIII Conclusion

An on-water NC1$\pi^{0}$ rate measurement has been performed by combining data
from a $2.64\times 10^{20}$ POT neutrino beam exposure of the T2K ND280 PØD
using a water-in configuration with a $3.49\times 10^{20}$ POT exposure using
a water-out configuration. This is the first use of the subtraction method to
measure neutral current event rates with the T2K near detector.

The signal event rates are found using an extended maximum likelihood fit to
the reconstructed invariant mass for each sample in a range of 0-500
$\textrm{MeV}/\textrm{c}^{2}$. As described in Section III, the phase space of
the analysis has been limited to the region where the PØD has acceptance. The
analysis finds
$342{}\pm{}33{}{}\textrm{\,(stat.)}{}\pm{}88{}\textrm{\,(sys.)}$
($246{}\pm{}26{}{}\textrm{\,(stat.)}{}\pm{}61{}\textrm{\,(sys.)}{}$) signal
events in the PØD water-in (water-out) data compared to an expectation of
$433$ ($290$) events. Excluding the $12\%$ normalization and NC1$\pi^{0}$
cross section uncertainties, the resulting observed to expected ratios are
$0.79{}\pm{}0.08{}\textrm{\,(stat.)}{}\pm{}0.20{}\textrm{\,(sys.)}{}$ for
water-in and
$0.85{}\pm{}0.09{}\textrm{\,(stat.)}{}\pm{}0.21{}\textrm{\,(sys.)}{}$ for
water-out configurations. Subtracting the water-in and water-out samples after
correcting for the different POT and reconstruction efficiencies yields
$106{}\pm{}41{}\textrm{\,(stat.)}{}\pm{}69\textrm{\,(sys.)}{}$ signal events
on water compared to an expectation of $157$ events and an on-water
NC1$\pi^{0}$ production rate of
$0.68{}\pm{}0.26{}\textrm{\,(stat.)}{}\pm{}0.44{}\textrm{\,(sys.)}{}\pm{}0.12{}\textrm{\,(flux)}{}$
relative to the NEUT expectation. As noted in Section VI, the largest
systematic errors, for example, the uncertainty in the background shape, are
determined using statistically limited data sets and additional exposure is
expected to reduce these uncertainties. The observed event rates are
consistent with the expectation and indicate that the event rate from neutral
current $\pi^{0}$ production is not underestimated. This provides confidence
that the neutral current $\pi^{0}$ background to electron neutrino appearance
in T2K is not underestimated.

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), H2020 Grant No. RISE-GA644294-JENNIFER, EU; JSPS, Japan; Royal Society,
UK; the Alfred P. Sloan Foundation and the DOE Early Career program, USA.

## References

  * Abe  _et al._ (2011) K. Abe _et al._ (T2K), Nucl. Instrum. Meth. A659, 106 (2011), arXiv:1106.1238 [physics.ins-det] .
  * Abe  _et al._ (2013a) K. Abe _et al._ (T2K), Phys. Rev. D87, 012001 (2013a), [Addendum: Phys. Rev.D87,no.1,019902(2013)], arXiv:1211.0469 [hep-ex] .
  * Olive  _et al._ (2014) K. A. Olive _et al._ (Particle Data Group), Chin. Phys. C38, 090001 (2014).
  * Pohl  _et al._ (1979) M. Pohl _et al._ (Gargamelle anti-neutrino Propane), Phys. Lett. B82, 461 (1979).
  * Nakayama  _et al._ (2005) S. Nakayama _et al._ (K2K), Phys. Lett. B619, 255 (2005), arXiv:hep-ex/0408134 [hep-ex] .
  * Aguilar-Arevalo  _et al._ (2010) A. A. Aguilar-Arevalo _et al._ (MiniBooNE), Phys. Rev. D81, 013005 (2010), arXiv:0911.2063 [hep-ex] .
  * Kurimoto  _et al._ (2010a) Y. Kurimoto _et al._ (SciBooNE), Phys. Rev. D81, 033004 (2010a), arXiv:0910.5768 [hep-ex] .
  * Kurimoto  _et al._ (2010b) Y. Kurimoto _et al._ (SciBooNE), Phys. Rev. D81, 111102 (2010b), arXiv:1005.0059 [hep-ex] .
  * Assylbekov  _et al._ (2012) S. Assylbekov _et al._ , Nucl. Instrum. Meth. A686, 48 (2012), arXiv:1111.5030 [physics.ins-det] .
  * Abgrall  _et al._ (2011) N. Abgrall _et al._ (T2K ND280 TPC), Nucl. Instrum. Meth. A637, 25 (2011), arXiv:1012.0865 [physics.ins-det] .
  * Allan  _et al._ (2013) D. Allan _et al._ (T2K UK), JINST 8, P10019 (2013), arXiv:1308.3445 [physics.ins-det] .
  * Aoki  _et al._ (2013) S. Aoki _et al._ , Nucl. Instrum. Meth. A698, 135 (2013), arXiv:1206.3553 [physics.ins-det] .
  * Amaudruz  _et al._ (2012) P. A. Amaudruz _et al._ (T2K ND280 FGD), Nucl. Instrum. Meth. A696, 1 (2012), arXiv:1204.3666 [physics.ins-det] .
  * Hayato (2009) Y. Hayato,  _Neutrino interactions: From theory to Monte Carlo simulations. Proceedings, 45th Karpacz Winter School in Theoretical Physics, Ladek-Zdroj, Poland, February 2-11, 2009_ , Acta Phys. Polon. B40, 2477 (2009).
  * Abe  _et al._ (2013b) K. Abe _et al._ (T2K Collaboration), Phys. Rev. D 87, 092003 (2013b).
  * Abe  _et al._ (2014) K. Abe _et al._ (T2K), Phys. Rev. D89, 092003 (2014), [Phys. Rev.D89,099902(2014)], arXiv:1403.2552 [hep-ex] .
  * Agostinelli  _et al._ (2003) S. Agostinelli _et al._ (GEANT4), Nucl. Instrum. Meth. A506, 250 (2003).
  * Rein and Sehgal (1981) D. Rein and L. M. Sehgal, Annals Phys. 133, 79 (1981).
  * Gilje (2014) K. Gilje,  _Neutral Current $\pi^{0}$ Production Rate Measurement On-Water Using the $\pi^{0}$ Detector in the Near Detector of the T2K Experiment_, Ph.D. thesis, Stony Brook University, Stony Brook, NY (2014).