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Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations

Nature volume 580, pages 339–344 (2020)Cite this article

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A Publisher Correction to this article was published on 18 June 2020

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Abstract

The charge-conjugation and parity-reversal (CP) symmetry of fundamental particles is a symmetry between matter and antimatter. Violation of this CP symmetry was first observed in 19641, and CP violation in the weak interactions of quarks was soon established2. Sakharov proposed3 that CP violation is necessary to explain the observed imbalance of matter and antimatter abundance in the Universe. However, CP violation in quarks is too small to support this explanation. So far, CP violation has not been observed in non-quark elementary particle systems. It has been shown that CP violation in leptons could generate the matter–antimatter disparity through a process called leptogenesis4. Leptonic mixing, which appears in the standard model’s charged current interactions5,6, provides a potential source of CP violation through a complex phase δCP, which is required by some theoretical models of leptogenesis7,8,9. This CP violation can be measured in muon neutrino to electron neutrino oscillations and the corresponding antineutrino oscillations, which are experimentally accessible using accelerator-produced beams as established by the Tokai-to-Kamioka (T2K) and NOvA experiments10,11. Until now, the value of δCP has not been substantially constrained by neutrino oscillation experiments. Here we report a measurement using long-baseline neutrino and antineutrino oscillations observed by the T2K experiment that shows a large increase in the neutrino oscillation probability, excluding values of δCP that result in a large increase in the observed antineutrino oscillation probability at three standard deviations (3σ). The 3σ confidence interval for δCP, which is cyclic and repeats every 2π, is [−3.41, −0.03] for the so-called normal mass ordering and [−2.54, −0.32] for the inverted mass ordering. Our results indicate CP violation in leptons and our method enables sensitive searches for matter–antimatter asymmetry in neutrino oscillations using accelerator-produced neutrino beams. Future measurements with larger datasets will test whether leptonic CP violation is larger than the CP violation in quarks.

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Fig. 1: Observed νe and \({\bar{{\boldsymbol{\nu }}}}_{{\bf{e}}}\) candidate events at SK.
Fig. 2: Particle identification in the SK detector.
Fig. 3: Event prediction model tuning to near-detector data.
Fig. 4: Constraints on PMNS oscillation parameters.

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Data availability

The likelihood surface data that support these findings will be made available for public access on http://t2k-experiment.org/results/2020-constraint-cp-phase.

Code availability

The T2K collaboration develops and maintains the code used for the simulation of the experimental apparatus and statistical analysis of the raw data used in this result. This code is shared among the collaboration, but not publicly distributed. Inquiries regarding the algorithms and methods used in this result may be directed to the corresponding author.

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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 number SAPPJ-2014-00031), the NRC and CFI, Canada; the CEA and CNRS/IN2P3, France; the DFG, Germany; the INFN, Italy; the National Science Centre and Ministry of Science and Higher Education, Poland; the RSF (grant number 19-12-00325) and the Ministry of Science and Higher Education, Russia; MINECO and ERDF funds, Spain; the SNSF and SERI, Switzerland; the STFC, UK; and the 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 the ERC (FP7), “la Caixa” Foundation (ID 100010434, fellowship code LCF/BQ/IN17/11620050), the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement numbers 713673 and 754496, and H2020 grant numbers RISE-RISE-GA822070-JENNIFER2 2020 and RISE-GA872549-SK2HK; the JSPS, Japan; the Royal Society, UK; French ANR grant number ANR-19-CE31-0001; and the DOE Early Career programme, USA.

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Author notes

  1. Deceased: Y. Yamada, K. Nishikawa

Authors and Affiliations

  1. Institute for Cosmic Ray Research, Kamioka Observatory, University of Tokyo, Kamioka, Japan

    K. Abe, C. Bronner, Y. Hayato, M. Ikeda, J. Kameda, Y. Kataoka, Y. Kato, L. Marti-Magro, M. Miura, S. Moriyama, M. Nakahata, Y. Nakajima, S. Nakayama, H. Sekiya, M. Shiozawa, Y. Sonoda, A. Takeda, H. K. Tanaka & T. Yano

  2. Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos, University of Tokyo, Kashiwa, Japan

    R. Akutsu, X. Junjie, T. Kajita & K. Okumura

  3. Department of Physics, Kyoto University, Kyoto, Japan

    A. Ali, Y. Ashida, S. Ban, T. Hayashino, A. Hiramoto, A. K. Ichikawa, M. Jiang, T. Kikawa, H. Kubo, S. Kuribayashi, K. G. Nakamura, T. Nakaya, T. Odagawa, M. Tajima, W. Uno, R. Wendell & K. Yasutome

  4. Institute for Particle Physics and Astrophysics, ETH Zurich, Zurich, Switzerland

    C. Alt, K. Fusshoeller, L. Molina Bueno, S. Murphy, B. Radics, A. Rubbia & C. M. Schloesser

  5. STFC, Rutherford Appleton Laboratory, Didcot, UK

    C. Andreopoulos, C. Densham, A. C. Kaboth, F. Nova, R. Shah, D. Wark & A. Weber

  6. Department of Physics, University of Liverpool, Liverpool, UK

    C. Andreopoulos, L. Anthony, C. Barry, F. Bench, J. Coleman, S. R. Dennis, K. Mavrokoridis, N. McCauley, C. Metelko, P. Paudyal, D. Payne, G. C. Penn, A. Pritchard, C. Touramanis & K. M. Tsui

  7. IFIC (CSIC and University of Valencia), Valencia, Spain

    M. Antonova, A. Cervera, P. Fernandez, A. Izmaylov & P. Novella

  8. Kobe University, Kobe, Japan

    S. Aoki, A. Suzuki & Y. Takeuchi

  9. Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP), University of Bern, Bern, Switzerland

    A. Ariga, A. Ereditato, C. Francois, C. Pistillo & C. Wilkinson

  10. Department of Physics, Tokyo Metropolitan University, Tokyo, Japan

    T. Arihara, Y. Awataguchi & H. Kakuno

  11. Faculty of Engineering, Yokohama National University, Yokohama, Japan

    Y. Asada, A. Minamino & G. Pintaudi

  12. Department of Physics, Imperial College London, London, UK

    E. T. Atkin, P. Dunne, P. Jonsson, P. B. Jurj, C. E. R. Naseby, T. S. Nonnenmacher, J. Pasternak, M. Scott, W. Shorrock, A. A. Sztuc, Y. Uchida & M. O. Wascko

  13. Department of Physics, University of Regina, Regina, Saskatchewan, Canada

    M. Barbi

  14. Department of Physics, University of Warwick, Coventry, UK

    G. J. Barker, S. B. Boyd, A. Chappell, P. F. Denner, D. R. Hadley, J. T. Haigh, A. Knight, S. Valder & W. G. S. Vinning

  15. Department of Physics, Oxford University, Oxford, UK

    G. Barr, D. Barrow, L. Cook, D. Coplowe, M. Kabirnezhad, L. Koch, X. Lu, R. Shah, T. Vladisavljevic, D. Wark & A. Weber

  16. H. Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland

    M. Batkiewicz-Kwasniak, A. Dabrowska, T. Wachala & A. Zalewska

  17. Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia

    A. Beloshapkin, A. Gorin, A. Izmaylov, M. Khabibullin, A. Khotjantsev, A. Kostin, Y. Kudenko,  V. Matveev, A. Mefodiev, O. Mineev, A. Shaikhiev, A. Shaykina, A. Shvartsman, A. Smirnov, S. Suvorov, V. V. Volkov, N. Yershov & A. Zykova

  18. Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Università e Politecnico di Bari, Bari, Italy

     V. Berardi, M. G. Catanesi, L. Magaletti & E. Radicioni

  19. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada

    S. Berkman, T. Feusels, K. Gameil, J. Kim & S. M. Oser

  20. TRIUMF, Vancouver, British Columbia, Canada

    S. Berkman, T. Feusels, K. Gameil, M. Hartz, D. Karlen, J. Kim, A. Konaka, T. Lindner, S. M. Oser, M. Pavin & S. Yen

  21. Department of Physics, Tokyo Institute of Technology, Tokyo, Japan

    L. Berns, M. Kuze & T. Yoshida

  22. Department of Physics and Astronomy, York University, Toronto, Ontario, Canada

    S. Bhadra, G. A. Fiorentini, M. McCarthy, E. S. Pinzon Guerra, G. Santucci & M. Yu

  23. Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Sorbonne Université, Université Paris Diderot, CNRS/IN2P3, Paris, France

    S. Bienstock, A. Blondel, J. Dumarchez, C. Giganti, M. Guigue, B. Popov & M. Zito

  24. Section de Physique, DPNC, University of Geneva, Geneva, Switzerland

    A. Blondel, A. Bravar, L. Maret, E. Noah, S. Parsa & F. Sánchez

  25. IRFU, CEA Saclay, Gif-sur-Yvette, France

    S. Bolognesi, S. Emery-Schrenk, S. Hassani, E. Mazzucato, L. Munteanu, S. Suvorov & G. Vasseur

  26. Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain

    B. Bourguille, C. Jesús-Valls, T. Lux & D. Vargas

  27. Physics Department, Lancaster University, Lancaster, UK

    D. Brailsford, T. Dealtry, T. A. Doyle, A. J. Finch, A. Knox, L. L. Kormos, M. Lawe, J. Nowak, H. M. O’Keeffe, P. N. Ratoff & J. G. Walsh

  28. Department of Theoretical Physics, University Autonoma Madrid, Madrid, Spain

    D. Bravo Berguño & L. Labarga

  29. Institute of Physics, University of Silesia, Katowice, Poland

    A. Bubak, J. Holeczek, J. Kisiel & K. Porwit

  30. Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France

    M. Buizza Avanzini, O. Drapier, M. Gonin, M. Licciardi & Th. A. Mueller

  31. Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA

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  32. Department of Physics, University of Colorado at Boulder, Boulder, CO, USA

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  33. High Energy Accelerator Research Organization (KEK), Tsukuba, Japan

    S. Cao, M. Friend, Y. Fujii, T. Hasegawa, N. C. Hastings, T. Ishida, T. Ishii, M. Jakkapu, T. Kobayashi, T. Maruyama, T. Matsubara, T. Nakadaira, K. Nakamura, K. Nakayoshi, K. Nishikawa, Y. Oyama, K. Sakashita, T. Sekiguchi, S. Y. Suzuki, M. Tada, T. Tsukamoto & Y. Yamada

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  35. Dipartimento di Fisica e Astronomia, INFN Sezione di Padova and Università di Padova, Padua, Italy

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  36. Department of Physics, University of Houston, Houston, TX, USA

    D. Cherdack

  37. Department of Physics, University of Tokyo, Tokyo, Japan

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  38. CERN European Organization for Nuclear Research, Geneva, Switzerland

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  39. Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, University of Tokyo, Chiba, Japan

    L. Cook, M. Hartz, Y. Hayato, T. Kajita, E. Kearns, Y. Koshio, L. Marti-Magro, M. Miura, S. Moriyama, M. Nakahata, K. Nakamura, S. Nakayama, T. Nakaya, K. Okumura, B. Quilain, K. Scholberg, H. Sekiya, M. Shiozawa, H. Sobel, Y. Suzuki, Y. Takeuchi, H. K. Tanaka, M. Vagins, T. Vladisavljevic, R. Wendell & M. Yokoyama

  40. Dipartimento di Fisica, INFN Sezione di Napoli and Università di Napoli, Naples, Italy

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  41. Department of Physics, King’s College London, London, UK

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  44. Department of Physics, Okayama University, Okayama, Japan

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  45. Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Chiba, Japan

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  49. Department of Physics, Colorado State University, Fort Collins, CO, USA

    M. Hogan, E. Reinherz-Aronis, J. Schwehr, W. Toki & R. J. Wilson

  50. Institute For Interdisciplinary Research in Science and Education (IFIRSE), ICISE, Quy Nhon, Vietnam

    N. T. Hong Van & T. V. Ngoc

  51. International Centre of Physics, Institute of Physics (IOP), Vietnam Academy of Science and Technology (VAST), Hanoi, Vietnam

    N. T. Hong Van

  52. Department of Physics, University of Winnipeg, Winnipeg, Manitoba, Canada

    B. Jamieson, F. Shaker & J. Walker

  53. Department of Physics, Royal Holloway University of London, Egham, UK

    A. C. Kaboth & W. C. Parker

  54. Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada

    D. Karlen

  55. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, USA

    S. P. Kasetti, T. Kutter & M. Tzanov

  56. Department of Physics, Boston University, Boston, MA, USA

    E. Kearns

  57. Department of Physics, Osaka City University, Osaka, Japan

    H. Kim, N. Kukita, T. Okusawa, Y. Seiya, S. Tanaka & K. Yamamoto

  58. National Centre for Nuclear Research, Warsaw, Poland

    K. Kowalik, J. Lagoda, E. Rondio, J. Zalipska & G. Zarnecki

  59. National Research Nuclear University “MEPhI”, Moscow Institute of Physics and Technology, Moscow, Russia

    Y. Kudenko

  60. Institute of Radioelectronics and Multimedia Technology, Warsaw University of Technology, Warsaw, Poland

    R. Kurjata, A. Rychter, K. Zaremba & M. Ziembicki

  61. INFN Sezione di Roma and Università di Roma “La Sapienza”, Rome, Italy

    L. Ludovici

  62. Department of Physics and Astronomy, University of Rochester, Rochester, NY, USA

    S. Manly, K. S. McFarland & C. Wret

  63. Department of Physics, University of Toronto,, Toronto, Ontario, Canada

    J. F. Martin, C. Nantais, H. A. Tanaka & T. Towstego

  64. University of California, Irvine, Department of Physics and Astronomy, Irvine, CA, USA

    S. Mine, M. Smy, H. Sobel & M. Vagins

  65. Department of Physics, Keio University, Kanagawa, Japan

    Y. Nishimura

  66. School of Physics and Astronomy, Queen Mary University of London, London, UK

    R. A. Owen

  67. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA

     V. Paolone

  68. Faculty of Physics, University of Warsaw, Warsaw, Poland

    M. Posiadala-Zezula

  69. Department of Physics, Duke University, Durham, NC, USA

    K. Scholberg

  70. SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA, USA

    H. A. Tanaka

Consortia

The T2K Collaboration

  • K. Abe
  • , R. Akutsu
  • , A. Ali
  • , C. Alt
  • , C. Andreopoulos
  • , L. Anthony
  • , M. Antonova
  • , S. Aoki
  • , A. Ariga
  • , T. Arihara
  • , Y. Asada
  • , Y. Ashida
  • , E. T. Atkin
  • , Y. Awataguchi
  • , S. Ban
  • , M. Barbi
  • , G. J. Barker
  • , G. Barr
  • , D. Barrow
  • , C. Barry
  • , M. Batkiewicz-Kwasniak
  • , A. Beloshapkin
  • , F. Bench
  • ,  V. Berardi
  • , S. Berkman
  • , L. Berns
  • , S. Bhadra
  • , S. Bienstock
  • , A. Blondel
  • , S. Bolognesi
  • , B. Bourguille
  • , S. B. Boyd
  • , D. Brailsford
  • , A. Bravar
  • , D. Bravo Berguño
  • , C. Bronner
  • , A. Bubak
  • , M. Buizza Avanzini
  • , J. Calcutt
  • , T. Campbell
  • , S. Cao
  • , S. L. Cartwright
  • , M. G. Catanesi
  • , A. Cervera
  • , A. Chappell
  • , C. Checchia
  • , D. Cherdack
  • , N. Chikuma
  • , M. Cicerchia
  • , G. Christodoulou
  • , J. Coleman
  • , G. Collazuol
  • , L. Cook
  • , D. Coplowe
  • , A. Cudd
  • , A. Dabrowska
  • , G. De Rosa
  • , T. Dealtry
  • , P. F. Denner
  • , S. R. Dennis
  • , C. Densham
  • , F. Di Lodovico
  • , N. Dokania
  • , S. Dolan
  • , T. A. Doyle
  • , O. Drapier
  • , J. Dumarchez
  • , P. Dunne
  • , A. Eguchi
  • , L. Eklund
  • , S. Emery-Schrenk
  • , A. Ereditato
  • , P. Fernandez
  • , T. Feusels
  • , A. J. Finch
  • , G. A. Fiorentini
  • , G. Fiorillo
  • , C. Francois
  • , M. Friend
  • , Y. Fujii
  • , R. Fujita
  • , D. Fukuda
  • , R. Fukuda
  • , Y. Fukuda
  • , K. Fusshoeller
  • , K. Gameil
  • , C. Giganti
  • , T. Golan
  • , M. Gonin
  • , A. Gorin
  • , M. Guigue
  • , D. R. Hadley
  • , J. T. Haigh
  • , P. Hamacher-Baumann
  • , M. Hartz
  • , T. Hasegawa
  • , S. Hassani
  • , N. C. Hastings
  • , T. Hayashino
  • , Y. Hayato
  • , A. Hiramoto
  • , M. Hogan
  • , J. Holeczek
  • , N. T. Hong Van
  • , F. Iacob
  • , A. K. Ichikawa
  • , M. Ikeda
  • , T. Ishida
  • , T. Ishii
  • , M. Ishitsuka
  • , K. Iwamoto
  • , A. Izmaylov
  • , M. Jakkapu
  • , B. Jamieson
  • , S. J. Jenkins
  • , C. Jesús-Valls
  • , M. Jiang
  • , S. Johnson
  • , P. Jonsson
  • , C. K. Jung
  • , X. Junjie
  • , P. B. Jurj
  • , M. Kabirnezhad
  • , A. C. Kaboth
  • , T. Kajita
  • , H. Kakuno
  • , J. Kameda
  • , D. Karlen
  • , S. P. Kasetti
  • , Y. Kataoka
  • , T. Katori
  • , Y. Kato
  • , E. Kearns
  • , M. Khabibullin
  • , A. Khotjantsev
  • , T. Kikawa
  • , H. Kikutani
  • , H. Kim
  • , J. Kim
  • , S. King
  • , J. Kisiel
  • , A. Knight
  • , A. Knox
  • , T. Kobayashi
  • , L. Koch
  • , T. Koga
  • , A. Konaka
  • , L. L. Kormos
  • , Y. Koshio
  • , A. Kostin
  • , K. Kowalik
  • , H. Kubo
  • , Y. Kudenko
  • , N. Kukita
  • , S. Kuribayashi
  • , R. Kurjata
  • , T. Kutter
  • , M. Kuze
  • , L. Labarga
  • , J. Lagoda
  • , M. Lamoureux
  • , M. Laveder
  • , M. Lawe
  • , M. Licciardi
  • , T. Lindner
  • , R. P. Litchfield
  • , S. L. Liu
  • , X. Li
  • , A. Longhin
  • , L. Ludovici
  • , X. Lu
  • , T. Lux
  • , L. N. Machado
  • , L. Magaletti
  • , K. Mahn
  • , M. Malek
  • , S. Manly
  • , L. Maret
  • , A. D. Marino
  • , L. Marti-Magro
  • , J. F. Martin
  • , T. Maruyama
  • , T. Matsubara
  • , K. Matsushita
  • ,  V. Matveev
  • , K. Mavrokoridis
  • , E. Mazzucato
  • , M. McCarthy
  • , N. McCauley
  • , J. McElwee
  • , K. S. McFarland
  • , C. McGrew
  • , A. Mefodiev
  • , C. Metelko
  • , M. Mezzetto
  • , A. Minamino
  • , O. Mineev
  • , S. Mine
  • , M. Miura
  • , L. Molina Bueno
  • , S. Moriyama
  • , J. Morrison
  • , Th. A. Mueller
  • , L. Munteanu
  • , S. Murphy
  • , Y. Nagai
  • , T. Nakadaira
  • , M. Nakahata
  • , Y. Nakajima
  • , A. Nakamura
  • , K. G. Nakamura
  • , K. Nakamura
  • , S. Nakayama
  • , T. Nakaya
  • , K. Nakayoshi
  • , C. Nantais
  • , C. E. R. Naseby
  • , T. V. Ngoc
  • , K. Niewczas
  • , K. Nishikawa
  • , Y. Nishimura
  • , E. Noah
  • , T. S. Nonnenmacher
  • , F. Nova
  • , P. Novella
  • , J. Nowak
  • , J. C. Nugent
  • , H. M. O’Keeffe
  • , L. O’Sullivan
  • , T. Odagawa
  • , K. Okumura
  • , T. Okusawa
  • , S. M. Oser
  • , R. A. Owen
  • , Y. Oyama
  • ,  V. Palladino
  • , J. L. Palomino
  • ,  V. Paolone
  • , M. Pari
  • , W. C. Parker
  • , S. Parsa
  • , J. Pasternak
  • , P. Paudyal
  • , M. Pavin
  • , D. Payne
  • , G. C. Penn
  • , L. Pickering
  • , C. Pidcott
  • , G. Pintaudi
  • , E. S. Pinzon Guerra
  • , C. Pistillo
  • , B. Popov
  • , K. Porwit
  • , M. Posiadala-Zezula
  • , A. Pritchard
  • , B. Quilain
  • , T. Radermacher
  • , E. Radicioni
  • , B. Radics
  • , P. N. Ratoff
  • , E. Reinherz-Aronis
  • , C. Riccio
  • , E. Rondio
  • , S. Roth
  • , A. Rubbia
  • , A. C. Ruggeri
  • , C. A. Ruggles
  • , A. Rychter
  • , K. Sakashita
  • , F. Sánchez
  • , G. Santucci
  • , C. M. Schloesser
  • , K. Scholberg
  • , J. Schwehr
  • , M. Scott
  • , Y. Seiya
  • , T. Sekiguchi
  • , H. Sekiya
  • , D. Sgalaberna
  • , R. Shah
  • , A. Shaikhiev
  • , F. Shaker
  • , A. Shaykina
  • , M. Shiozawa
  • , W. Shorrock
  • , A. Shvartsman
  • , A. Smirnov
  • , M. Smy
  • , J. T. Sobczyk
  • , H. Sobel
  • , F. J. P. Soler
  • , Y. Sonoda
  • , J. Steinmann
  • , S. Suvorov
  • , A. Suzuki
  • , S. Y. Suzuki
  • , Y. Suzuki
  • , A. A. Sztuc
  • , M. Tada
  • , M. Tajima
  • , A. Takeda
  • , Y. Takeuchi
  • , H. K. Tanaka
  • , H. A. Tanaka
  • , S. Tanaka
  • , L. F. Thompson
  • , W. Toki
  • , C. Touramanis
  • , T. Towstego
  • , K. M. Tsui
  • , T. Tsukamoto
  • , M. Tzanov
  • , Y. Uchida
  • , W. Uno
  • , M. Vagins
  • , S. Valder
  • , Z. Vallari
  • , D. Vargas
  • , G. Vasseur
  • , C. Vilela
  • , W. G. S. Vinning
  • , T. Vladisavljevic
  • , V. V. Volkov
  • , T. Wachala
  • , J. Walker
  • , J. G. Walsh
  • , Y. Wang
  • , D. Wark
  • , M. O. Wascko
  • , A. Weber
  • , R. Wendell
  • , M. J. Wilking
  • , C. Wilkinson
  • , J. R. Wilson
  • , R. J. Wilson
  • , K. Wood
  • , C. Wret
  • , Y. Yamada
  • , K. Yamamoto
  • , C. Yanagisawa
  • , G. Yang
  • , T. Yano
  • , K. Yasutome
  • , S. Yen
  • , N. Yershov
  • , M. Yokoyama
  • , T. Yoshida
  • , M. Yu
  • , A. Zalewska
  • , J. Zalipska
  • , K. Zaremba
  • , G. Zarnecki
  • , M. Ziembicki
  • , E. D. Zimmerman
  • , M. Zito
  • , S. Zsoldos
  •  & A. Zykova

Contributions

The operation, Monte Carlo simulation, and data analysis of the T2K Experiment are carried out by the T2K Collaboration with contributions from all collaborators listed as authors on this manuscript. The scientific results presented here have been presented to and discussed by the full collaboration, and all authors have approved the final version of the manuscript.

Corresponding author

Correspondence to M. Hartz.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Anatael Cabrera, Alexandre Sousa and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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The T2K Collaboration. Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations. Nature 580, 339–344 (2020). https://doi.org/10.1038/s41586-020-2177-0

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  • DOI: https://doi.org/10.1038/s41586-020-2177-0

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