††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: 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

# First measurement of the $\nu_{\mu}$ charged-current cross section on a
water target without pions in the final state

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  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  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  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  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.  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  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  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  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  UPMC, 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  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  D. Fukuda  Okayama
University, Department of Physics, Okayama, Japan  Y. Fukuda  Miyagi
University of Education, Department of Physics, Sendai, Japan  A. Garcia
Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science
and Technology, Campus UAB, Bellaterra (Barcelona) Spain  C. Giganti  UPMC,
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  L. Haegel
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland  J.T.
Haigh  University of Warwick, Department of Physics, Coventry, 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  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  A. Hillairet  University of Victoria, Department of
Physics and Astronomy, Victoria, British Columbia, Canada  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  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. 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  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.  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  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  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  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  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  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
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.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  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  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  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  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  Y. Petrov
University of British Columbia, Department of Physics and Astronomy,
Vancouver, British Columbia, Canada  TRIUMF, Vancouver, British Columbia,
Canada  L. Pickering  Michigan State University, Department of Physics and
Astronomy, East Lansing, Michigan, U.S.A.  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  A. Pritchard  University of Liverpool,
Department of Physics, Liverpool, United Kingdom  P. Przewlocki  National
Centre for Nuclear Research, Warsaw, Poland  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  P.N. Ratoff
Lancaster University, Physics Department, Lancaster, United Kingdom  M.A.
Rayner  University of Geneva, Section de Physique, DPNC, Geneva, 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  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.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  Institut de
Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science and
Technology, Campus UAB, Bellaterra (Barcelona) Spain  S. Sasaki  Tokyo
Metropolitan University, Department of Physics, Tokyo, 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  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  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  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  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  University of Toronto, Department of Physics,
Toronto, Ontario, Canada  TRIUMF, Vancouver, British Columbia, Canada  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  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.  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.  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  J. Walker  University of Winnipeg,
Department of Physics, Winnipeg, Manitoba, Canada  C.W. Walter  Duke
University, Department of Physics, Durham, North Carolina, U.S.A.  Y. Wang
State University of New York at Stony Brook, Department of Physics and
Astronomy, Stony Brook, New York, U.S.A.  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  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  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.  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
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

###### Abstract

This paper reports the first differential measurement of the charged-current
interaction cross section of $\nu_{\mu}$ on water with no pions in the final
state. This flux-averaged measurement has been made using the T2K experiment’s
off-axis near detector, and is reported in doubly-differential bins of muon
momentum and angle. The flux-averaged total cross section in a restricted
region of phase space was found to be
$\sigma=$(0.95\pm{}0.08(stat)\pm{}0.06(\mbox{det. syst.})\pm{}0.04(\mbox{model
syst.})\pm{}0.08(flux))\times
10^{-38}\text{\,}\mathrm{c}\mathrm{m}^{2}\mathrm{/}\mathrm{n}$$.

###### pacs:

14.60.Lm

###### pacs:

13.15.+g

###### pacs:

24.10.Lx

##  I Introduction

The T2K (Tokai-to-Kamioka) experimentAbe  _et al._ (2011) is a long-baseline
neutrino oscillation experiment, with a beam originating at J-PARC (Japan
Proton Accelerator Complex) which consists primarily of muon neutrinos. T2K
has measured the disappearance of muon neutrinos Abe  _et al._ (2012) and the
appearance of electron neutrinos Abe  _et al._ (2014a), using the off-axis
ND280 near detector on the J-PARC site, and the Super-Kamiokande detector
Fukuda  _et al._ (2003), located $295\text{\,}\mathrm{km}$ away.

At the energies of the T2K beamline, the main neutrino interaction process is
charged-current quasi-elastic interactions
($\nu_{\mu}+n\rightarrow\mu^{-}+p$). Because these neutrino interactions occur
within nuclear targets and not on free nuclei, additional nuclear effects and
final state interactions can modify the composition and kinematics of the
particles that are observed to be exiting the interaction. This paper focuses
on a measurement of CCQE-like events (in bins of the muon angle and momentum)
in which no pions (charged or neutral) are observed in the final state
(CC0$\pi$).

The active target regions of the ND280 near detector, as will be discussed in
Section II, are primarily composed of plastic scintillator, but the far
detector is water-based. While the near detector measurements on hydrocarbon
targets can help to greatly constrain the flux and cross section uncertainties
for the oscillation analyses, one of the dominant remaining uncertainties is
due to potential differences between the oxygen and carbon cross sections that
are not currently well-constrained by the ND280 detector Abe  _et al._
(2014b). The ND280 detector also contains water targets, and this paper
presents a measurement of the $\nu_{\mu}$ CC0$\pi$ interaction cross section
on water. This process is very important for T2K’s neutrino oscillation
measurements since this is the dominant reaction in the far detector.

While there are differential measurements of the charged-current quasi-elastic
(CCQE) cross sections on carbon or hydrocarbon Aguilar-Arevalo  _et al._
(2010); Alcaraz-Aunion and Walding (2009); Fiorentini  _et al._ (2013); Abe
_et al._ (2016, 2015a), there are none on water. The K2K experiment has
published a measurement of the axial vector mass in neutrino-oxygen CCQE
interactions Gran  _et al._ (2006) using the SciFi detector, but not a
differential cross section measurement.

##  II The T2K Experiment

A high-intensity beam is produced at J-PARC at Tokai village, Ibaraki, Japan
and directed to Super-Kamiokande. In order to enhance the sensitivity to T2K’s
primary physics goals, the appearance of electron neutrinos and the
disappearance of muon neutrinos, the beam energy peaks at the oscillation
maximum of $0.6\text{\,}\mathrm{GeV}$, and this is achieved by adopting the
off-axis method Abe  _et al._ (2011).

###  II.1 The T2K Beamline

High-intensity $30\text{\,}\mathrm{GeV}$ protons from the J-PARC accelerator
strike a graphite target every 2.48 seconds and produce charged pions and
kaons. These pions and kaons are focused to the forward direction by three
horn magnets Sekiguchi  _et al._ (2015) and decay in the 96-m long decay
volume. Neutrinos (anti-neutrinos) are produced from decays of positively
(negatively) charged pions. Horn magnets select pions of either sign by
flipping the current direction.

T2K started data taking in 2010 with a beam of primarily muon neutrinos until
May 2014 and then started data taking with a primarily muon anti-neutrino beam
until May 2016, and is continuing to take data. The analysis presented here
uses data taken in the neutrino mode.

The neutrino flux is calculated based on the measurement of primary proton
beam profiles and hadron production data, including the measurement of the
pion and kaon yields Abgrall  _et al._ (2016) by the NA61/SHINE experiment
Abgrall  _et al._ (2014) at CERN. The total absolute flux uncertainty is about
10% at the peak energy, and details of the flux calculation are described in
Ref. Abe  _et al._ (2013).

###  II.2 The T2K ND280 Near Detector

This analysis looks for neutrino interactions in the T2K off-axis near
detector, shown in Figure 1, specifically for events in the pi-zero (PØD)
subdetector. This subdetector, described in more detail in Assylbekov  _et
al._ (2012) consists of alternating planes of scintillator bars, sandwiched
between lead or brass radiator layers. A more detailed schematic of the PØD is
shown in Figure 2. There are a total of 40 scintillator modules in the PØD,
each one composed of a vertical layer of triangular scintillator bars and a
layer of horizontal bars. In the upstream and downstream portions of the PØD
(the “upstream ECal” and the “central ECal”), the scintillator layers
alternate with lead sheets. The central 25 layers alternate the scintillator
layers with brass sheets and bladders which can be filled with water or air.
This analysis will use data taken in both configurations. The total mass of
water in the PØD in the fiducial volume is approximately 1902 kg. Downstream
of the PØD is a tracker with three TPCs Abgrall  _et al._ (2011) and two fine-
grained scintillator detectors Amaudruz  _et al._ (2012). The PØD and tracker
are surrounded by electromagnetic calorimeters Allan  _et al._ (2013) inside a
magnet with a 0.2 T field that is instrumented with muon detectors Aoki  _et
al._ (2013).

Figure 1: An exploded view of T2K’s off-axis near detector. Figure 2: A
schematic of the PØD, showing the structure of the layers. The beam travels
from the left to the right. The red box outlines the approximate fiducial
volume used for this analysis.

##  III Analysis

###  III.1 Event Selection

Hadrons produced within the nucleus are subject to final state interactions
(FSIs) that can reabsorb the hadron or alter their kinematics as they emerge
from the nucleus. Pion absorption for example can make a charged-current
resonant (CCRES) interaction appear as a CCQE final state. This forces the
selection to be based on a topology classified by the number and type of
outgoing particles from the nucleus in order to be less model dependent. A
single muon and zero pion topology is called CCQE-like or CC0$\pi$. The event
selection identifies CC0$\pi$-enhanced samples by selecting events where a
single track was reconstructed in the PØD. Identical selections are applied to
both the water-in and water-out samples.

The result in this paper relies on a subset of the neutrino mode data as
broken down in Table 1 and totaling $5.52\text{\times}{10}^{20}$ protons on
the target (POT). The selection starts by identifying beam spills where the
spill information and all ND280 subdetectors are known to have high-quality
data. Each spill of the proton beam consists of several clearly-separated
bunches of protons. The selection then selects bunches containing tracks
reconstructed in the TPCs associated with vertices reconstructed within the
PØD fiducial volume, which extends from the middle of the scintillator of the
first water layer to the middle of the scintillator in the last water layer
and $25\text{\,}\mathrm{cm}$ in from the edges in the xy-plane (Fig. 2). In
practice, these tracks are reconstructed from segments found in the PØD and
TPC subdetector reconstruction processes. After identifying these bunches, the
analysis identifies the highest-momentum negatively-charged track as the muon
candidate. If no negatively charged track is found, the bunch is removed from
the selection. The selection then applies a TPC quality cut, removing tracks
with no more than 18 nodes in the TPC reconstruction. The final cut for the
selected CC0$\pi$ sample requires that only a single track was reconstructed
anywhere in the PØD in that bunch. The cross section reported here is
restricted to bins in the region of muon kinematics where
$\cos\theta_{\mu}\geq 0$ and $p_{\mu}\leq$5\text{\,}\mathrm{GeV}$$. The total
number of selected events in the water-in data sample is 12,777 (and based on
simulations it is expected that approximately 3860 of these events are true
interactions on water) and the total number in the water-out data (which has a
larger POT exposure) sample is 13,370. Due to the requirement of a negatively-
charged track, the $\bar{\nu}_{\mu}$ contamination is this sample is very
small and is estimated to be approximately 0.1% for both samples.

T2K Run | POT
---|---
2 Water | $4.29\times 10^{19}$
2 Air | $3.55\times 10^{19}$
3c Air | $1.35\times 10^{20}$
4 Water | $1.63\times 10^{20}$
4 Air | $1.76\times 10^{20}$
Total | 5.52 $\times 10^{20}$
Table 1: T2K runs and their associated POT, filtered for spills where all
ND280 detectors were flagged with good data quality. Figure 3: Data and MC
distributions of the water-in CC0$\pi$ signal selection. NEUT 5.3.2 MC has
been normalized to data POT and is sorted into various truth topologies.

Figure 3 shows distributions of events that pass the selection for the water-
in sample for data and a Monte Carlo detector simulation (MC). The MC
simulation chain primarily uses the NEUT neutrino event generator Hayato
(2002) to provide the kinematics for particles emerging from neutrino
interactions and a Geant4-based Agostinelli  _et al._ (2003) Allison  _et al._
(2006) package to simulate these particles moving through the detector (using
Geant version 4.9.4). The QGSP_BERT model is used for hadronic interactions.
The MC distribution is separated by interaction channel. A detailed review of
neutrino interactions can be found in Formaggio and Zeller (2012) for example.
The two largest sources of background are charged-current interactions with a
single outgoing $\pi$\+ (CC1$\pi^{+}$) and any other charged-current
interaction (CCOther) not categorized as CC0$\pi$ or CC1$\pi^{+}$. The
CC1$\pi^{+}$ topology is due primarily to pion resonance production and
CCOther to deep inelastic scattering (DIS) Formaggio and Zeller (2012).
Additionally, neutral current (NC) backgrounds are classified as “BKG” and
interactions occurring outside the PØD fiducial volume are classified as “out
of FV” or “OOFV”. Distributions for the water-out sample look similar.

Figure 4: Data and MC distributions of the water-in CC1$\pi^{+}$ sideband
selection. NEUT 5.3.2 MC has been normalized to data POT and is sorted into
various truth topologies. Figure 5: Data and MC distributions of the water-in
CCOther sideband selection. NEUT 5.3.2 MC has been normalized to data POT and
is sorted into various truth topologies.

To provide a data-driven constraint on the background, sideband selections are
used for the CC1$\pi^{+}$ and CCOther topologies. Their selection is identical
to the signal selection with the exception of the final cut. For the
CC1$\pi^{+}$ sideband, events with exactly two PØD reconstructed tracks in a
bunch along with at least one PØD reconstructed Michel electron are selected.
For the CCOther sideband, events with greater than two PØD reconstructed
tracks are selected. These cuts reduce overlap between the signal and sideband
selections as shown in Figs. 4 and 5 for the water-in samples. The water-out
sideband samples look very similar. The numbers of selected events in the
signal and sidebands regions are summarized in Tables 2 and 3.

| Water-Out Data
---|---
| Num of Selected Events
Cut | CC0$\pi$ | CC1$\pi^{+}$ | CC Oth
Data Quality and PØD+TPC |  |  |
$\mu^{-}$ candidate in Fid. Vol. | 33083 | 33083 | 33083
# PØD Tracks | 13370 | 8107 | 11606
# Michel e- | NA | 1710 | NA
Table 2: Number of water-out data events contained in the selected signal and sideband samples after each selection cut is applied. The cut on the number of Michel electrons is only applied to the CC1$\pi^{+}$ sample. | Water-In Data
---|---
| Num of Selected Events
Cut | CC0$\pi$ | CC1$\pi^{+}$ | CC Oth
Data Quality and PØD+TPC |  |  |
$\mu^{-}$ candidate in Fid. Vol. | 27713 | 27713 | 27713
# PØD Tracks | 12777 | 6297 | 8639
# Michel e- | NA | 1434 | NA
Table 3: Number of water-in data events contained in the selected signal and
sideband samples after each selection cut is applied. The cut on the number of
Michel electrons is only applied to the CC1$\pi^{+}$ sample.

###  III.2 Cross Section Extraction

The event selections described above are binned in the reconstructed double
differential $(p_{\mu},\cos\theta_{\mu})$ phase space. Reconstructed
kinematics are approximations to the true initial state of the muon. To
extract the true kinematics from the reconstructed, an unfolding technique is
used based on D’Agostini’s method with the MC truth as the prior D’Agostini
(1995). The purpose of unfolding is to remove detector reconstruction related
imperfections to achieve a more accurate representation of how the muon
emerged from the interaction. By correcting the data samples from PØD water-in
and water-out configurations separately, a subtraction procedure ultimately
gives a cross section on water. Additionally, the MC is tuned to account for
flux, interaction modeling, and detector corrections. The final tuned MC is
then used to calculate efficiency corrections, purity corrections, and the
unfolding matrix.

The exclusive CC0$\pi$ signal is evaluated by correcting the data selection
based on the CC0$\pi$ signal purity in the MC. The signal purity is calculated
using the MC truth information and the data from the sideband samples. As
described above, CC1$\pi^{+}$ interactions are the largest sources of
background, followed by CCOther interactions. Therefore, sideband samples for
these two backgrounds were selected as a data-driven background constraint.
The ratio of the overall data sideband normalization to the overall MC
sideband normalization is calculated and used to constrain the corresponding
background in the CC0$\pi$ MC selection as,

$B_{j}^{\prime}=B_{j}\frac{S_{d}}{S_{m}},$ (1)

where $j$ denotes a bin index, $B^{\prime}$ the sideband constrained
background, $B$ the original background in the MC signal selection, and
$S_{d}$ and $S_{m}$ the sideband normalizations from data and MC respectively.
This affects the signal purity used in the background correction,

$p_{j}^{\prime}=1-\frac{B_{j}^{\prime}}{N_{m,j}^{\prime}},$ (2)

where $N_{m,j}^{\prime}=N_{m,j}-B_{j}+B_{j}^{\prime}$ and $N_{m}$ is the
original number of events in the CC0$\pi$ MC selection.

For this analysis, the initial prior used in the D’Agostini unfolding
technique was taken from the MC truth and a single iteration is used. Fake-
data studies showed that multiple iterations did not improve results but
increased uncertainties. This increase is due to the correlation introduced
between the data and successive priors Adye (2011) and can produce large
fluctuations between neighboring bins. Additionally while in fake data tests
the total $\chi^{2}$ for the unfolded result was slightly larger than expected
($\sim$1.7 not including any systematics), it did not significantly decrease
with additional iterations. Thus a single iteration was chosen. This must be
regarded as a regularized result. With the MC truth as the prior, a single
iteration Bayesian unfolding matrix is equivalent to directly constructing an
unfolding matrix based on the MC. This means that the unfolding matrix is
calculated based on the mapping between truth and reconstructed kinematics in
the MC.

To extract the neutrino cross section on water an additional subtraction step
after the unfolding is required. The PØD fiducial volume contains plastic
scintillator layers and thin brass sheets sandwiched between layers of water
Assylbekov  _et al._ (2012). The water layers act as a passive target making
it difficult to know whether an interaction occurred on water or on some other
target nucleus. To work around this, the PØD was designed to be drained and
filled during different run periods. Everything being equal except for the
inclusion or exclusion of water, a subtraction of the true water-in and water-
out distributions should give the number of interactions on water. Since the
PØD is in two different detector configurations with and without water, it is
necessary to correct for detector smearing and inefficiencies before the
subtraction. A direct subtraction of the reconstructed event rates would give
an incorrect estimate for the actual event rate on water. Therefore, we first
unfold the reconstructed distribution for water-in and water-out separately to
get an approximation of their true distributions, then subtract the unfolded
distributions to get the distribution of interactions on water. Specifically,
this is given by,

$N_{i}^{\ce{H2O}}=\frac{U_{ij}^{w}N_{j}^{w}}{\epsilon_{i}^{w}}-R\frac{U_{ij}^{a}N_{j}^{a}}{\epsilon_{i}^{a}},$
(3)

where the indexes $i$ and $j$ indicate true and reconstructed bins
respectively, $w$ and $a$ indicate water-in and water-out periods
respectively, $N$ is the number of purity-corrected, signal events measured in
the data signal selection, $\epsilon$ the selection efficiency, and $R$ the
flux normalization factor between water-in and water-out periods. $U_{ij}$
represents the unfolding matrix. From this, the differential cross section on
water can be expressed as,

$\frac{d\sigma}{dx_{i}}=\frac{N_{i}^{\ce{H2O}}}{F^{w}N_{n}\Delta x_{i}},$ (4)

where $F^{w}$ is the integrated flux over the water-in period, $N_{n}$ the
number of neutrons, and $\Delta x_{i}$ the area of bin $i$ across the phase
space $x$. $F^{w}$ is the POT-weighted flux of all water-in periods and
calculated using flux simulations and from the constraints described above. As
the water-in and water-out periods have different beam exposures, total flux
for the water-out periods, $F^{a}$, is used to scale the flux normalization
ratio, $R=F^{w}/F^{a}$. Additionally, correlated errors between the water-in
and water-out periods are taken into account in the error propagation and
discussed in Section III.3.

###  III.3 Systematic Uncertainties

As in previous T2K analyses, the systematic uncertainties can be separated
into three principal categories: flux uncertainties, cross section model
uncertainties, and detector uncertainties Abe  _et al._ (2016, 2015b).

The flux and cross section errors are calculated by reweighting the individual
simulated events. Once the events are reweighted, the unfolding matrix is
regenerated and the cross section is recalculated using the new weights. The
uncertainties for flux and cross section parameters are taken from the same
covariance matrices used as inputs to the near detector fit in the T2K
oscillation analysis Abe  _et al._ (2015b). There are 46 total parameters in
the covariance matrix: 25 for flux, 6 for final-state interactions, and 15
other cross section parameters. By generating many throws for the model
parameters and calculating the resulting event weights, we can calculate a
covariance matrix for the final result. If $\frac{d\sigma_{O}}{dx_{i;k}}$
gives the cross section result for bin $i$ and parameter throw $k$ which has
$n$ throws, then the covariance between bins $i$ and $j$ is

$\mathrm{cov}(i,j)=\frac{1}{n}\sum\limits_{k=0}^{n-1}\left(\frac{d\sigma_{O}}{dx_{i;k}}-\bar{\frac{d\sigma_{O}}{dx_{i}}}\right)\left(\frac{d\sigma_{O}}{dx_{j;k}}-\bar{\frac{d\sigma_{O}}{dx_{j}}}\right)$
(5)

where

$\bar{\frac{d\sigma_{O}}{dx_{i}}}=\frac{1}{n}\sum\limits_{k=0}^{n-1}\frac{d\sigma_{O}}{dx_{i;k}}$
(6)

The flux uncertainty is dominated by the uncertainty in the total flux
normalization and is found to be 8.76%. Flux uncertainties are due in large
part to uncertainties in the hadron production model but are affected by
beamline uncertainties as well Abe  _et al._ (2013). A parameterization in
neutrino energy and flavor is used to propagate flux uncertainties. Cross
section model uncertainties include both uncertainties in basic neutrino-
nucleus scattering and uncertainties from FSI Abe  _et al._ (2015b).
Parameters that govern the neutrino interaction and nuclear description models
used in the NEUT generator Hayato (2002) are used to propagate cross section
uncertainties.

Neutrino-nucleus scattering depends on nucleon form factors and the nuclear
medium model. Neutrino generators typically assume a dipole form factor
governed by an axial mass parameter for QE and resonant charged-current
interactions. Additionally, many of the interaction parameters tune the
normalization on certain interaction channels that are poorly understood.
These include 2p2h contributions that arise from multinucleon correlations
inside the nucleus. The current understanding of these multinucleon
interactions is based on the meson exchange model where two nucleons exchange
a meson current such that the charged-current interaction involves both
nucleons. This is expected to enhance the CCQE-like cross section. Thus,
instead of a single final state nucleon, two or more nucleons may be ejected
out of the nucleus. Other parameters, such as the nuclear binding energy and
the Fermi momentum describe the nuclear medium.

An intranuclear cascade model describes secondary pion propagation within the
nucleus Salcedo  _et al._ (1988). Uncertainties on FSI are calculated by
tuning the pion production, absorption, rescattering and charge-exchange
probabilities.

The primary neutrino generator used for this analysis is a tuned version of
NEUT 5.3.2 Hayato (2002) Hayato (2009).The tuning is applied based on best-fit
values from a fit of three models implemented in NEUT to external MINERA and
MiniBooNE CCQE measurements Wilkinson  _et al._ (2016). The NEUT model uses
the Smith-Moniz relativistic Fermi gas (RFG) model Smith and Moniz (1972) with
a relativistic random phase approximation (RPA) Nieves  _et al._ (2011) and a
multinucleon exchange (2p2h) model Nieves  _et al._ (2011) Gran  _et al._
(2013). An axial mass of $M_{A}^{QE}=$1.15\pm
0.03\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}^{2}$$, the amplitude of
the multinucleon effects $\text{2p2h norm.}=$27\pm 12\text{\,}\mathrm{\char
37\relax}$$, and Fermi momentum $p_{F}=$223\pm
5\text{\,}\mathrm{M}\mathrm{eV}\mathrm{/}\mathrm{c}$$ were used. The
uncertainties in these parameters are propagated to the final cross section
measurement. A secondary neutrino generator used for testing is GENIE 2.8.0
Andreopoulos  _et al._ (2015).

Table 4 shows the individual contributions of several interaction model
parameters to the total cross section. Note that the 2p2h normalization,
binding energy $E_{b}$, and Fermi momentum $p_{F}$ are nuclei-dependent. These
are calculated with $100$ throws without taking correlations into account.
This illustrates and identifies the effects of a single parameter on the cross
section result. For the final result, 800 throws were used along with
covariances across the full parameter-space to generate the interaction and
other systematic uncertainties, and 2000 throws were used for statistical
errors. The lower number of throws used in Table 4 means there is a larger
statistical error on the uncertainty itself.

Source | Uncertainty [%]
---|---
| on cross sec.
$M_{A}^{QE}$ | $0.8$
$M_{A}^{RES}$ | $0.3$
CA5 single-pion interaction | $0.5$
2p2h normalization (^16O) | $2.8$
$E_{b}$ (^16O) | $0.05$
$p_{F}$ (^16O) | $0.2$
Table 4: The fractional uncertainties on the restricted phase space cross
section due to several of the individual cross section parameters.

Detector systematics describe uncertainties in reconstructed properties of
events rather than the underlying physics. These are separated into weight
systematics and variation systematics. Weight systematics modify the weight to
be applied to simulated events. These include effects such as differences in
tracking efficiencies between data and simulation. Variation systematics
modify observables such as the reconstructed particle momentum of a simulated
event. These allow for migration of events between different kinematic bins.
Systematics related to the uncertainty on the fiducial mass must be treated in
a different manner, as these affect both the expected number of events and the
total mass used to normalize the cross section measurement.

The event reconstruction in the PØD uses a Kalman filter algorithm to
calculate the properties of tracks found in the detector. The reconstructed
momentum will primarily be influenced by two main effects: the curvature of
the track in the tracker and the energy loss within the PØD. Because
relatively little information about the track curvature can be obtained by the
PØD and because the small amount of energy loss in the tracker will have
little effect on the reconstructed initial momentum, the systematics for these
two effects are treated separately. Uncertainties in the energy loss in the
PØD are estimated from a sample of cosmic ray muons that pass through the
tracker and stop in the PØD. To propagate these uncertainties, the
reconstructed momentum in the simulation is altered by

$(\Delta p)^{P\O{}D{}}_{scale}=(x_{s}\sigma_{s})(p^{reco}-p^{reco}_{TPC1})$
(7)

for the scale uncertainty and

$(\Delta
p)^{P\O{}D{}}_{res}=(x_{r}\sigma_{r})(p^{reco}-p^{reco}_{TPC1}-p^{truth}+p^{truth}_{TPC1})$
(8)

for the resolution uncertainty. In these equations $\sigma$ represents the
uncertainty and $x$ is a normally distributed random number that changes for
each systematics throw. Similar numbers are obtained for both the water-out
and water-in geometries, and a 1.4% uncertainty is applied to the energy loss
scale and a 7% uncertainty to the resolution. Tracker curvature systematics
follow the same procedure as for previous T2K analyses Abe  _et al._ (2015b).
Scale and resolution uncertainties are applied to the momentum extrapolated
from the track curvature. Additional uncertainties are applied to account for
distortions in the magnetic field, charge misidentification, TPC cluster
reconstruction, and TPC track reconstruction. Studies have shown that the PØD
track reconstruction and matching PØD tracks to TPC tracks have an efficiency
greater than 99.8%, so no correction or uncertainty is applied due to this.

In some cases, an interaction that occurred outside the fiducial volume will
be reconstructed in the fiducial volume. Using the nominal NEUT simulation,
such out of fiducial volume events represent 2.89% of events in the water-in
sample and 3.95% of events in the water-out sample. An analysis of the spatial
distribution of events in the layers of the PØD central electromagnetic
calorimeter, immediately downstream of the water target, suggests that there
may be as much as a factor of two discrepancy in the amount of migration
between data and simulation (but this is a small fraction of the total number
of events). To account for this, we increase the weights of events originating
in the central electromagnetic calorimeter by a factor of two and add an
uncertainty of 50% of the initial weight. The distributions of these events in
the two PØD geometries are identical, as there is no water in these layers.
These events will cancel out up to small differences in statistics and the
detector response, so a large uncertainty corresponds to a small effect on the
final result. The detector systematics are summarized in Table 5

Systematic | Uncertainty [%]
---|---
PØD Energy Loss Scale | 1.3
PØD Energy Loss Resolution | 6.7
Tracker Momentum Scale | 1.5
Tracker Momentum Resolution | 0.2
Magnetic Field Distortion | 0.04
Charge ID Efficiency | 0.1
TPC Cluster Efficiency | 0.3
TPC Track Efficiency | 0.4
Out of Fiducial Volume | 0.8
Detector Mass | 1.5
Table 5: Detector systematic uncertainties considered in this analysis. The
uncertainty in each category gives the overall uncertainty on the restricted
phase space cross section, calculated for 100 throws. The final result in Eq.
9 throws all uncertainties simultaneously and uses a larger number of throws.

The one-track selection is sensitive to pileup where particles from several
interactions are reconstructed in the PØD in the same bunch. The main pileup
sources are cosmic ray muons, multiple neutrino interactions in the same beam
bunch, and interactions occurring in the material outside ND280 (called sand
events) that produce tracks in the PØD. The cosmic ray muon pileup rate is
estimated to be approximately $2\times 10^{-4}$ per bunch, which is
negligible. The beam-related pileup rate is dominated by sand events, and is
calculated separately for each ND280 run period. The sand muon corrections are
given in Table 6.

Run |  $p_{sand}$ [bunch-1]
---|---
2 water | 0.0144
2 air | 0.0173
3c | 0.0188
4 water | 0.0217
4 air | 0.0245
Table 6: Sand event pileup rates for each ND280 run period. The weights of
simulated events are reduced by a factor of $1-p_{sand}$.

Finally, there is some uncertainty in the total target mass. Mass
uncertainties change the total number of events expected as well as the total
number of target nuclei used to obtain the correct cross section
normalization. Because the PØD is composed of several materials, the mass
uncertainty also has a small effect on the smearing matrix, since the cross
section shape will not necessarily have the exact same shape for different
materials. In the case of the water in the fiducial volume, the total mass of
the water is known very well, but there is still uncertainty in how the water
is distributed throughout the different layers. Measurements have shown that
there is approximately 15% more water in the most downstream water layer
compared to more centrally located layers. There is also a smaller uncertainty
on the amount of water in individual layers away from the edges. To estimate
the uncertainty due to the mass, a 0.8% uncertainty on the total water mass is
applied with additional 15% uncertainties in the layers at the ends of the
water target and 5% uncertainties on the remaining layers. The layer-by-layer
variations are performed keeping the total mass fixed. These give us an
uncertainty of 1.5% due to the target mass.

For all systematic errors, correlations between the water-in and water-out
periods were taken into consderation in Eq. 3. This was done by ensuring
identical seeding for throws in calculating Eq. 5. Since flux uncertainties do
not distinguish between water-in and water-out samples the flux uncertainties
should be fully correlated. The oxygen binding energy parameter affects only
the water-in sample, which means that the overall cross section uncertainties
are not fully correlated. Some PØD-specific detector systematics, such as the
PØD target mass systematic, have dependence on the water state. Thus detector
systematics are not fully correlated either. Further, any differences between
water-in and water-out detectors are taken into account with different
standard deviations on the underlying variations. Statistical errors are
treated as uncorrelated.

##  IV Results

The result shown in Fig. 6 uses data from T2K Runs $24$. It is reported as a
double differential cross section in the outgoing muon kinematics
$(p_{\mu},\cos\theta_{\mu})$. Black data points taken from Eq. 4 show the
double differential result with full error bars. The colored error bars show
the cumulative uncertainties from various sources, starting with the data
statistics and ending with the detector systematics. Errors from each source
are added in quadrature. MC predictions from NEUT 5.3.2 (tuned) and GENIE
2.8.0 are shown as solid and dashed blue lines.

(a)  (b)

(c)  (d)

(e)  (f)

(g)  (h)

Figure 6: The double differential $\nu$_$\mu$ CC0$\pi$ cross section on water
for each slice in $\cos\theta_{\mu}$.

The fractional contribution from each source of uncertainty is shown in Fig.
7, binned and plotted in the same scheme as Fig. 6. In most regions, the
statistical error from the data is the single most dominant source of bin-by-
bin uncertainty, but overall the statistical errors are comparable to the
total systematic uncertainty. Aside from the low sensitivity bins, the
fractional bin-by-bin errors lie on the order of $1020\text{\,}\mathrm{\char
37\relax}$.

(a)  (b)

(c)  (d)

(e)  (f)

(g)  (h)

Figure 7: The fractional error from each source of uncertainty on the double
differential $\nu$_$\mu$ CC0$\pi$ cross section on water.

This result is compared to the T2K CC0$\pi$ cross section on C8H8 Abe  _et
al._ (2016) in Fig. 8. Since both results were obtained using the T2K flux,
the error bars shown do not include the flux uncertainty. The binnings do not
exactly match between the two analyses, but when overlaid, both results appear
to be consistent within uncertainties for most of the phase space. The largest
areas of discrepancy are in the high-angle regions, where the CC0$\pi$ water
cross section is higher than the hydrocarbon cross section.

(a)  (b)

(c)  (d)

(e)  (f)

(g)  (h)

Figure 8: Here, the CC0$\pi$ water cross section from the PØD is overlaid with
the CC0$\pi$ C8H8 cross section previously measured by T2K Abe  _et al._
(2016). The error bars shown include all sources of uncertainty _except_ the
flux. In regions where $\cos\theta_{\mu}$ slices are different between the
water and hydrocarbon result, the bin edges are noted in the legend.

Finally, the result is compared to the Martini _et al._ Martini  _et al._
(2009) model predictions on carbon in Fig. 9 and the SuSAv2 model predictions
on water Amaro  _et al._ (2005); Megias  _et al._ (2016) in Fig. 10. Both
models are shown with and without 2p2h. Overall, our result agrees better with
an inclusion of 2p2h in most regions of phase space. This is consistent with a
similar comparison performed for the measurement on C8H8 Abe  _et al._ (2016).

(a)  (b)

(c)  (d)

(e)  (f)

(g)  (h)

Figure 9: A comparison of the CC0$\pi$ water cross section against two Martini
model predictions on carbon, one with 2p2h contributions and one without.

(a)  (b)

(c)  (d)

(e)  (f)

(g)  (h)

Figure 10: A comparison of the CC0$\pi$ water cross section against the SuSAv2
model. Predictions for CCQE and 2p2h on oxygen are shown separately along with
their sums and average over the bins.

The unfolding procedure allows events to migrate into and out of regions in
the phase space outside the binned area. Specifically, this “out-of-range”
region refers to where $\cos\theta_{\mu}<0$ or
$p_{\mu}>$5\text{\,}\mathrm{GeV}$$. As the selection efficiency here is very
low, we calculated a reduced, total cross section by integrating over only to
the explicitly binned areas of the $(p_{\mu},\cos\theta_{\mu})$ phase space.
The reduced, total cross section was found to be,

$\begin{split}\sigma^{\mathrm{CC0\pi}}_{\ce{$\nu$_{$\mu$}}{}\ce{H2O}}=0.95\pm{}0.08(\mbox{stat})\pm{}0.06(\mbox{det.
syst.})\\\ $\pm{}0.04(\mbox{model syst.})\pm{}0.08(\mbox{flux})\times
10^{-38}\text{\,}\mathrm{c}\mathrm{m}^{2}\mathrm{/}\mathrm{n}$.\end{split}$
(9)

This is significantly higher than the NEUT (GENIE) prediction of
$0.66(0.68)\times
10^{-38}\text{\,}\mathrm{c}\mathrm{m}^{2}\mathrm{/}\mathrm{n}$ primarily due
to the disagreement between data and MC in the high-angle regions, which cover
a large portion of the reduced phase space. The breakdown of the fractional
uncertainties on Eq. 9 are given in Table 7.

Source | Uncertainty [%]
---|---
Statistics (data) | $7.7$
Statistics (MC) | $1.8$
Detector mass | $1.5$
Detector other | $6.3$
FSI | $3.4$
Cross Section | $3.2$
Flux | $8.7$
Table 7: Fractional uncertainties on the total cross section.

##  V Conclusion

Using the T2K near detector, ND280, a CCQE-like, flux-integrated cross section
on water was reported here in the double-differential phase space of the
outgoing muon. Since the $\bar{\nu_{\mu}}$ contribution to this sample is
insignificant, this is effectively a measurement on oxygen. The result
complements previous T2K cross section measurements. The fluxes used for this
result, the extracted cross section values and covariance matrices for the
errors are available at the following website: http://t2k-experiment.org/wp-
content/uploads/nd280data-numu-cc0pi-xs-on-h2o-2017.tar.gz.

A comparison to a double-differential cross section result on carbon Abe  _et
al._ (2016) shows good agreement with the exception of a few low momentum bins
in the high-angle region. Comparisons were also performed to T2K simulations
using NEUT Hayato (2002) and GENIE Andreopoulos  _et al._ (2015). Overall it
appears that the tuned NEUT prediction is favored over GENIE, but in the
angular regions of $0.7<\cos{\theta_{\mu}}<0.85$ it shows better agreement
with GENIE. Another comparison to the Martini _et al._ Martini  _et al._
(2009) CCQE prediction with and without 2p2h prefers the 2p2h contribution. A
comparison to the SuSAv2 model predictionsAmaro  _et al._ (2005); Megias  _et
al._ (2016) also generally agrees with the data within errors, though the data
points tend to be lower than the model in the more forward regions.

New techniques for CCQE measurements, such as exploring the transverse
kinematics space, or incorporating proton kinematics are ongoing in T2K.
Future analyses from T2K will have the benefit of higher statistics and can
also include antineutrino cross sections.

##  VI 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.

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