Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

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

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

This article has been updated


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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

Data availability

The likelihood surface data that support these findings will be made available for public access on

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.

Change history


  1. Christenson, J. H., Cronin, J. W., Fitch, V. L. & Turlay, R. Evidence for the 2π decay of the \({K}_{2}^{0}\) meson. Phys. Rev. Lett. 13, 138–140 (1964).

    ADS  Google Scholar 

  2. Tanabashi, M. et al. Review of particle physics. Phys. Rev. D 98, 030001 (2018).

    ADS  Google Scholar 

  3. Sakharov, A. D. Violation of CP invariance, C asymmetry, and baryon asymmetry of the Universe. Pis’ma Z. Eksp. Teor. Fiz. 5, 32–35 (1967); Sov. Phys. Usp. 34, 392–393 (1991).

    CAS  Google Scholar 

  4. Fukugita, M. & Yanagida, T. Baryogenesis without grand unification. Phys. Lett. B 174, 45–47 (1986).

    ADS  CAS  Google Scholar 

  5. Fukuda, Y. et al. Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett. 81, 1562–1567 (1998).

    ADS  CAS  Google Scholar 

  6. Ahmad, Q. R. et al. Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory. Phys. Rev. Lett. 89, 011301 (2002).

    ADS  CAS  PubMed  Google Scholar 

  7. Pascoli, S., Petcov, S. T. & Riotto, A. Connecting low energy leptonic CP-violation to leptogenesis. Phys. Rev. D 75, 083511 (2007).

    ADS  MATH  Google Scholar 

  8. Hagedorn, C., Mohapatra, R. N., Molinaro, E., Nishi, C. C. & Petcov, S. T. CP violation in the lepton sector and implications for leptogenesis. Int. J. Mod. Phys. A 33, 1842006 (2018).

    ADS  CAS  Google Scholar 

  9. Branco, G. C., González Felipe, R. & Joaquim, F. R. Leptonic cp violation. Rev. Mod. Phys. 84, 515–565 (2012).

    ADS  CAS  Google Scholar 

  10. Abe, K. et al. Observation of electron neutrino appearance in a muon neutrino beam. Phys. Rev. Lett. 112, 061802 (2014).

    ADS  CAS  PubMed  Google Scholar 

  11. Acero, M. A. et al. First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA. Phys. Rev. Lett. 123, 151803 (2019).

    ADS  CAS  PubMed  Google Scholar 

  12. Abe, K. et al. Search for CP violation in neutrino and antineutrino oscillations by the T2K experiment with 2.2 × 1021 protons on target. Phys. Rev. Lett. 121, 171802 (2018).

    ADS  CAS  PubMed  Google Scholar 

  13. Abe, S. et al. Precision measurement of neutrino oscillation parameters with KamLAND. Phys. Rev. Lett. 100, 221803 (2008).

    ADS  CAS  PubMed  Google Scholar 

  14. Adey, D. et al. Measurement of the electron antineutrino oscillation with 1958 days of operation at Daya Bay. Phys. Rev. Lett. 121, 241805 (2018).

    ADS  CAS  PubMed  Google Scholar 

  15. Aharmim, B. et al. Combined analysis of all three phases of solar neutrino data from the Sudbury Neutrino Observatory. Phys. Rev. C 88, 025501 (2013).

    ADS  Google Scholar 

  16. Maki, Z., Nakagawa, M. & Sakata, S. Remarks on the unified model of elementary particles. Prog. Theor. Phys. 28, 870–880 (1962).

    ADS  CAS  MATH  Google Scholar 

  17. Pontecorvo, B. Neutrino experiments and the problem of conservation of leptonic charge. Sov. Phys. JETP 26, 984–988 (1968); Zh. Eksp. Teor. Fiz. 53, 1717 (1967).

    ADS  Google Scholar 

  18. Krastev, P. I. & Petcov, S. T. Resonance amplification and t violation effects in three neutrino oscillations in the Earth. Phys. Lett. B 205, 84–92 (1988).

    ADS  Google Scholar 

  19. Jarlskog, C. A basis independent formulation of the connection between quark mass matrices, CP violation and experiment. Z. Phys. C 29, 491–497 (1985).

    ADS  CAS  Google Scholar 

  20. Barger, V., Whisnant, K., Pakvasa, S. & Phillips, R. J. N. Matter effects on three-neutrino oscillations. Phys. Rev. D 22, 2718–2726 (1980).

    ADS  CAS  Google Scholar 

  21. Abe, K. et al. The T2K experiment. Nucl. Instrum. Methods A 659, 106–135 (2011).

    ADS  CAS  Google Scholar 

  22. Beavis, D., Carroll, A., Chiang, I. & the E889 Collaboration. Long Baseline Neutrino Oscillation Experiment At The AGS Physics design report BNL No. 52459 (Brookhaven National Laboratory, 1995).

  23. Otani, M. et al. Design and construction of INGRID neutrino beam monitor for T2K neutrino experiment. Nucl. Instrum. Methods A 623, 368–370 (2010).

    ADS  CAS  Google Scholar 

  24. Amaudruz, P. A. et al. The T2K fine-grained detectors. Nucl. Instrum. Methods A 696, 1–31 (2012).

    ADS  CAS  Google Scholar 

  25. Assylbekov, S. et al. The T2K ND280 off-axis pi-zero detector. Nucl. Instrum. Methods A 686, 48–63 (2012).

    ADS  CAS  Google Scholar 

  26. Abgrall, N. et al. Time projection chambers for the T2K near detectors. Nucl. Instrum. Methods A 637, 25–46 (2011).

    ADS  CAS  Google Scholar 

  27. Allan, D. et al. The electromagnetic calorimeter for the T2K near detector ND280. J. Instrum. 8, P10019 (2013).

    Google Scholar 

  28. Aoki, S. et al. The T2K Side Muon Range Detector (SMRD). Nucl. Instrum. Methods A 698, 135–146 (2013).

    ADS  CAS  Google Scholar 

  29. Fukuda, Y. et al. The Super-Kamiokande detector. Nucl. Instrum. Methods A 501, 418–462 (2003).

    ADS  CAS  Google Scholar 

  30. Nieves, J., Valverde, M. & Vicente Vacas, M. J. Inclusive nucleon emission induced by quasi-elastic neutrino-nucleus interactions. Phys. Rev. C 73, 025504 (2006).

    ADS  Google Scholar 

  31. Martini, M., Ericson, M., Chanfray, G. & Marteau, J. A unified approach for nucleon knock-out, coherent and incoherent pion production in neutrino interactions with nuclei. Phys. Rev. C 80, 065501 (2009).

    ADS  Google Scholar 

  32. Benhar, O., Farina, N., Nakamura, H., Sakuda, M. & Seki, R. Electron- and neutrino-nucleus scattering in the impulse approximation regime. Phys. Rev. D 72, 053005 (2005).

    ADS  Google Scholar 

  33. Salcedo, L. L., Oset, E., Vicente-Vacas, M. J. & Garcia-Recio, C. Computer simulation of inclusive pion nuclear reactions. Nucl. Phys. A 484, 557–592 (1988).

    ADS  Google Scholar 

  34. Böhlen, T. et al. The FLUKA code: developments and challenges for high energy and medical applications. Nucl. Data Sheets 120, 211–214 (2014).

    ADS  Google Scholar 

  35. Ferrari, A. Sala, P. R. Fasso, A. & Ranft, J. FLUKA: A Multi-Particle Transport Code Version 2005 CERN-2005–010, SLAC-R-773, INFN-TC-05–11 (FLUKA collaboration, 2005).

  36. Brun, R. et al. GEANT Detector Description and Simulation Tool Report CERN-W5013 (CERN, 1994).

  37. Abgrall, N. et al. Measurements of π±, K±, \({K}_{S}^{0}\), Λ and proton production in protoncarbon interactions at 31 GeV/c with the NA61/SHINE spectrometer at the CERN SPS. Eur. Phys. J. C 76, 84 (2016).

    Google Scholar 

  38. Abe, K. et al. Measurements of the T2K neutrino beam properties using the INGRID on-axis near detector. Nucl. Instrum. Methods A 694, 211–223 (2012).

    ADS  CAS  Google Scholar 

  39. Abgrall, N. et al. Measurements of π± differential yields from the surface of the T2K replica target for incoming 31 GeV/c protons with the NA61/SHINE spectrometer at the CERN SPS. Eur. Phys. J. C 76, 617 (2016).

    ADS  Google Scholar 

  40. Abgrall, N. et al. Measurements of π±, K± and proton double differential yields from the surface of the T2K replica target for incoming 31 GeV/c protons with the NA61/SHINE spectrometer at the CERN SPS. Eur. Phys. J. C 79, 100 (2019).

    ADS  MathSciNet  Google Scholar 

  41. Hayato, Y. A neutrino interaction simulation program library NEUT. Acta Phys. Pol. B 40, 2477 (2009).

    ADS  CAS  Google Scholar 

  42. Llewellyn Smith, C. H. Neutrino reactions at accelerator energies. Phys. Rep. 3, 261–379 (1972).

    ADS  Google Scholar 

  43. Nieves, J., Amaro, J. E. & Valverde, M. Inclusive quasielastic charged-current neutrino-nucleus reactions. Phys. Rev. C 70, 055503 (2004).

    ADS  Google Scholar 

  44. Benhar, O. & Fabrocini, A. Two nucleon spectral function in infinite nuclear matter. Phys. Rev. C 62, 034304 (2000).

    ADS  Google Scholar 

  45. Nieves, J., Simo, I. R. & Vacas, M. J. V. Inclusive charged-current neutrino-nucleus reactions. Phys. Rev. C 83, 045501 (2011).

    ADS  Google Scholar 

  46. Gran, R., Nieves, J., Sanchez, F. & Vicente Vacas, M. J. Neutrino-nucleus quasi-elastic and 2p2h interactions up to 10 GeV. Phys. Rev. D 88, 113007 (2013).

    ADS  Google Scholar 

  47. Rein, D. & Sehgal, L. M. Neutrino-excitation of baryon resonances and single pion production. Ann. Phys. 133, 79–153 (1981).

    ADS  CAS  Google Scholar 

  48. Sjöstrand, T. High-energy physics event generation with PYTHIA 5.7 and JETSET 7.4. Comput. Phys. Commun. 82, 74–89 (1994).

    ADS  Google Scholar 

  49. Oset, E., Salcedo, L. L. & Strottman, D. A theoretical approach to pion nuclear reactions in the resonance region. Phys. Lett. B 165, 13–18 (1985).

    ADS  Google Scholar 

  50. Day, M. & McFarland, K. S. Differences in quasi-elastic cross sections of muon and electron neutrinos. Phys. Rev. D 86, 053003 (2012).

    ADS  Google Scholar 

  51. Rein, D. Angular distribution in neutrino induced single pion production processes. Z. Phys. C 35, 43–64 (1987).

    ADS  CAS  Google Scholar 

  52. Kabirnezhad, M. Single pion production in neutrino-nucleon interactions. Phys. Rev. D 97, 013002 (2018).

    ADS  CAS  Google Scholar 

  53. Yang, T., Andreopoulos, C., Gallagher, H., Hoffmann, K. & Kehayias, P. A hadronization model for few-GeV neutrino interactions. Eur. Phys. J. C 63, 1–10 (2009).

    ADS  CAS  Google Scholar 

  54. Jiang, M. et al. Atmospheric neutrino oscillation analysis with improved event reconstruction in Super-Kamiokande IV. Prog. Theor. Exp. Phys. 2019, 053F01 (2019).

    CAS  Google Scholar 

  55. Wilks, S. S. The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62 (1938).

    MATH  Google Scholar 

  56. Feldman, G. J. & Cousins, R. D. A unified approach to the classical statistical analysis of small signals. Phys. Rev. D 57, 3873–3889 (1998).

    ADS  CAS  Google Scholar 

  57. Hastings, W. K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970).

    MathSciNet  MATH  Google Scholar 

Download references


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.

Author information

Authors and Affiliations



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.

Ethics declarations

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.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Table 1 Systematic uncertainties

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

The T2K Collaboration. Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations. Nature 580, 339–344 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing