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Neutrino interferometry for high-precision tests of Lorentz symmetry with IceCube


Lorentz symmetry is a fundamental spacetime symmetry underlying both the standard model of particle physics and general relativity. This symmetry guarantees that physical phenomena are observed to be the same by all inertial observers. However, unified theories, such as string theory, allow for violation of this symmetry by inducing new spacetime structure at the quantum gravity scale. Thus, the discovery of Lorentz symmetry violation could be the first hint of these theories in nature. Here we report the results of the most precise test of spacetime symmetry in the neutrino sector to date. We use high-energy atmospheric neutrinos observed at the IceCube Neutrino Observatory to search for anomalous neutrino oscillations as signals of Lorentz violation. We find no evidence for such phenomena. This allows us to constrain the size of the dimension-four operator in the standard-model extension for Lorentz violation to the \(10^{-28}\) level and to set limits on higher-dimensional operators in this framework. These are among the most stringent limits on Lorentz violation set by any physical experiment.

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  1. 1.

    Kostelecký, V. A. & Samuel, S. Spontaneous breaking of Lorentz symmetry in string theory. Phys. Rev. D 39, 683–685 (1989).

  2. 2.

    Carroll, S. M., Harvey, J. A., Kostelecký, V. A., Lane, C. D. & Okamoto, T. Noncommutative Field Theory and Lorentz Violation. Phys. Rev. Lett. 87, 141601 (2001).

  3. 3.

    Groot Nibbelink, S. & Pospelov, M. Lorentz violation in supersymmetric field theories. Phys. Rev. Lett. 94, 081601 (2005).

  4. 4.

    Kostelecký, A. & Mewes, M. Neutrinos with Lorentz-violating operators of arbitrary dimension. Phys. Rev. D 85, 096005 (2012).

  5. 5.

    Komatsu, E. et al. Five-year Wilkinson microwave anisotropy probe (WMAP) observations: cosmological interpretation. Astrophys. J. Suppl. 180, 330–376 (2009).

  6. 6.

    Kostelecký, V. A. & Mewes, M. Constraints on relativity violations from gamma-ray bursts. Phys. Rev. Lett. 110, 201601 (2013).

  7. 7.

    Kostelecký, V. A., Melissinos, A. C. & Mewes, M. Searching for photon-sector Lorentz violation using gravitational-wave detectors. Phys. Lett. B 761, 1–7 (2016).

  8. 8.

    Nagel, M. et al. Direct terrestrial test of Lorentz symmetry in electrodynamics to 10−18. Nat. Commun. 6, 8174 (2015).

  9. 9.

    Maccione, L., Taylor, A. M., Mattingly, D. M. & Liberati, S. Planck-scale Lorentz violation constrained by ultra-high-energy cosmic rays. J. Cosmol. Astropart. Phys. 0904, 022 (2009).

  10. 10.

    Allmendinger, F. et al. New limit on Lorentz-invariance- and CPT-violating neutron spin interactions using a free-spin-precession 3He-129Xe comagnetometer. Phys. Rev. Lett. 112, 110801 (2014).

  11. 11.

    Smiciklas, M., Brown, J. M., Cheuk, L. W. & Romalis, M. V. A new test of local Lorentz invariance using 21Ne-Rb-K comagnetometer. Phys. Rev. Lett. 107, 171604 (2011).

  12. 12.

    Heckel, B. R. et al. New CP-violation and preferred-frame tests with polarized electrons. Phys. Rev. Lett. 97, 021603 (2006).

  13. 13.

    Bennett, G. W. et al. Search for Lorentz and CPT violation effects in muon spin precession. Phys. Rev. Lett. 100, 091602 (2008).

  14. 14.

    Pruttivarasin, T. et al. A Michelson–Morley test of Lorentz symmetry for electrons. Nature 517, 592–595 (2015).

  15. 15.

    Kostelecký, V. A. & Tasson, J. D. Constraints on Lorentz violation from gravitational Čerenkov radiation. Phys. Lett. B 749, 551–559 (2015).

  16. 16.

    Abbasi, R. et al. Determination of the atmospheric neutrino flux and searches for new physics with AMANDA-II. Phys. Rev. D 79, 102005 (2009).

  17. 17.

    Abbasi, R. et al. Search for a Lorentz-violating sidereal signal with atmospheric neutrinos in IceCube. Phys. Rev. D 82, 112003 (2010).

  18. 18.

    Abe, K. et al. Test of Lorentz invariance with atmospheric neutrinos. Phys. Rev. D 91, 052003 (2015).

  19. 19.

    Kostelecký, V. A. & Russell, N. Data tables for Lorentz and CPT violation. Rev. Mod. Phys. 83, 11–31 (2011).

  20. 20.

    Liberati, S. Tests of Lorentz invariance: a 2013 update. Class. Quant. Grav. 30, 133001 (2013).

  21. 21.

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

  22. 22.

    Ahmad, Q. R. et al. Measurement of the rate of ν e + dp + p + e− interactions produced by 8 B solar neutrinos at the Sudbury Neutrino Observatory. Phys. Rev. Lett. 87, 071301 (2001).

  23. 23.

    Ahn, M. H. et al. Indications of neutrino oscillation in a 250 km long baseline experiment. Phys. Rev. Lett. 90, 041801 (2003).

  24. 24.

    Eguchi, K. et al. First results from KamLAND: Evidence for reactor anti-neutrino disappearance. Phys. Rev. Lett. 90, 021802 (2003).

  25. 25.

    Abe, K. et al. Indication of electron neutrino appearance from an accelerator-produced off-axis muon neutrino beam. Phys. Rev. Lett. 107, 041801 (2011).

  26. 26.

    An, F. P. et al. Observation of electron-antineutrino disappearance at Daya Bay. Phys. Rev. Lett. 108, 171803 (2012).

  27. 27.

    Esteban, I., Gonzalez-Garcia, M. C., Maltoni, M., Martinez-Soler, I. & Schwetz, T. Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity. J. High Energy Phys. 1701, 087 (2017).

  28. 28.

    Aartsen, M. G. et al. Evidence for astrophysical muon neutrinos from the northern sky with IceCube. Phys. Rev. Lett. 115, 081102 (2015).

  29. 29.

    Gonzalez-Garcia, M. C., Halzen, F. & Maltoni, M. Physics reach of high-energy and high-statistics IceCube atmospheric neutrino data. Phys. Rev. D 71, 093010 (2005).

  30. 30.

    Abbasi, R. et al. The IceCube data acquisition system: signal capture, digitization, and timestamping. Nucl. Instrum. Meth. A 601, 294–316 (2009).

  31. 31.

    Aartsen, M. G. et al. The IceCube Neutrino Observatory: instrumentation and online systems. J. Instrum. 12, P03012 (2017).

  32. 32.

    Weaver, C. N. Evidence for Astrophysical Muon Neutrinos from the Northern Sky. PhD thesis, Univ. Wisconsin–Madison (2015).

  33. 33.

    Fedynitch, A., Engel, R., Gaisser, T. K., Riehn, F. & Stanev, T. Calculation of conventional and prompt lepton fluxes at very high energy. Eur. Phys. J. Web Conf. 99, 08001 (2015).

  34. 34.

    Jones, B. J. P. Sterile Neutrinos in Cold Climates. PhD thesis, MIT (2015).

  35. 35.

    Argüelles Delgado, C. A. New Physics with Atmospheric Neutrinos. PhD thesis, Univ. Wisconsin–Madison (2015).

  36. 36.

    Cooper-Sarkar, A. & Sarkar, S. Predictions for high energy neutrino cross-sections from the ZEUS global PDF fits. J. High Energy Phys. 0801, 075 (2008).

  37. 37.

    Aartsen, M. G. et al. Searches for sterile neutrinos with the IceCube detector. Phys. Rev. Lett. 117, 071801 (2016).

  38. 38.

    Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013).

  39. 39.

    Aartsen, M. G. et al. Determining neutrino oscillation parameters from atmospheric muon neutrino disappearance with three years of IceCube DeepCore data. Phys. Rev. D 91, 072004 (2015).

  40. 40.

    Harris, R. A. & Stodolsky, L. Two state systems in media and “Turing’s paradox”. Phys. Lett. B 116, 464–468 (1982).

  41. 41.

    Abraham, J. et al. Observation of the suppression of the flux of cosmic rays above 4 x 1019eV. Phys. Rev. Lett. 101, 061101 (2008).

  42. 42.

    Aab, A. et al. Evidence for a mixed mass composition at the ‘ankle’ in the cosmic-ray spectrum. Phys. Lett. B 762, 288–295 (2016).

  43. 43.

    Chalmers, M. Interview: Steven Weinberg. CERN Courier 57, 31–35 (2017).

  44. 44.

    Aartsen, M. G. et al. Evidence for high-energy extraterrestrial neutrinos at the IceCube detector. Science 342, 1242856 (2013).

  45. 45.

    Stecker, F. W., Scully, S. T., Liberati, S. & Mattingly, D. Searching for traces of Planck-scale physics with high energy neutrinos. Phys. Rev. D 91, 045009 (2015).

  46. 46.

    Argüelles, C. A., Katori, T. & Salvado, J. New physics in astrophysical neutrino flavor. Phys. Rev. Lett. 115, 161303 (2015).

  47. 47.

    Aartsen, M. G. et al. Measurement of South Pole ice transparency with the IceCube LED calibration system. Nucl. Instrum. Meth. A 711, 73–89 (2013).

  48. 48.

    Aartsen, M. G. et al. Measurement of the atmospheric ν e spectrum with IceCube. Phys. Rev. D 91, 122004 (2015).

  49. 49.

    Adrian-Martinez, S. et al. Letter of intent for KM3NeT 2.0. J. Phys. G 43, 084001 (2016).

  50. 50.

    Aartsen, M. G. et al. IceCube-Gen2: a vision for the future of neutrino astronomy in Antarctica. Preprint at (2014).

  51. 51.

    Altmann, M. et al. GNO solar neutrino observations: Results for GNO I. Phys. Lett. B 490, 16–26 (2000).

  52. 52.

    Abdurashitov, J. N. et al. Solar neutrino flux measurements by the Soviet–American Gallium Experiment(SAGE) for half the 22 year solar cycle. J. Exp. Theor. Phys. 95, 181 (2002).

  53. 53.

    Hosaka, J. et al. Solar neutrino measurements in super-Kamiokande-I. Phys. Rev. D. 73, 112001 (2006).

  54. 54.

    Aharmim, B. et al. Electron energy spectra, fluxes, and day–night asymmetries of B-8 solar neutrinos from measurements with NaCl dissolved in the heavy-water detector at the Sudbury Neutrino Observatory. Phys. Rev. C 72, 055502 (2005).

  55. 55.

    Arpesella, C. et al. Direct measurement of the Be-7 solar neutrino flux with 192 days of Borexino data. Phys. Rev. Lett. 101, 091302 (2008).

  56. 56.

    Ashie, Y. et al. Evidence for an oscillatory signature in atmospheric neutrino oscillation. Phys. Rev. Lett. 93, 101801 (2004).

  57. 57.

    Adamson, P. et al. Combined analysis of ν μ disappearance and ν μν e appearance in MINOS using accelerator and atmospheric neutrinos. Phys. Rev. Lett. 112, 191801 (2014).

  58. 58.

    Aartsen, M. G. et al. Measurement of atmospheric neutrino oscillations at 6–56 GeV with IceCube DeepCore. Phys. Rev. Lett. 120, 071801 (2018).

  59. 59.

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

  60. 60.

    Abe, Y. et al. Indication of reactor disappearance in the Double Chooz experiment. Phys. Rev. Lett. 108, 131801 (2012).

  61. 61.

    Ahn, J. K. et al. Observation of reactor electron antineutrino disappearance in the RENO experiment. Phys. Rev. Lett. 108, 191802 (2012).

  62. 62.

    An, F. P. et al. Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay. Phys. Rev. Lett. 112, 061801 (2014).

  63. 63.

    Abe, K. et al. Combined analysis of neutrino and antineutrino oscillations at T2K. Phys. Rev. Lett. 118, 151801 (2017).

  64. 64.

    Adamson, P. et al. Constraints on oscillation parameters from ν e appearance and ν μ disappearance in NOvA. Phys. Rev. Lett. 118, 231801 (2017).

  65. 65.

    Coleman, S. R. & Glashow, S. L. High-energy tests of Lorentz invariance. Phys. Rev. D 59, 116008 (1999).

  66. 66.

    Amelino-Camelia, G., Ellis, J. R., Mavromatos, N. E., Nanopoulos, D. V. & Sarkar, S. Tests of quantum gravity from observations of gamma-ray bursts. Nature 393, 763–765 (1998).

  67. 67.

    Colladay, D. & Kostelecký, V. A. CPT violation and the standard model. Phys. Rev. D. 55, 6760–6774 (1997).

  68. 68.

    Colladay, D. & Kostelecký, V. A. Lorentz violating extension of the standard model. Phys. Rev. D. 58, 116002 (1998).

  69. 69.

    Kostelecký, V. A. Gravity, Lorentz violation, and the standard model. Phys. Rev. D. 69, 105009 (2004).

  70. 70.

    Auerbach, L. B. et al. Tests of Lorentz violation in \({\bar{\nu }}_{\mu }\to {\bar{\nu }}_{e}\) oscillations. Phys. Rev. D 72, 076004 (2005).

  71. 71.

    Aguilar-Arevalo, A. A. et al. Test of Lorentz and CPT violation with short baseline neutrino oscillation excesses. Phys. Lett. B 718, 1303–1308 (2013).

  72. 72.

    Adamson, P. et al. Testing Lorentz invariance and CPT conservation with NuMI neutrinos in the MINOS near detector. Phys. Rev. Lett. 101, 151601 (2008).

  73. 73.

    Adamson, P. et al. A search for Lorentz invariance and CPT violation with the MINOS far detector. Phys. Rev. Lett. 105, 151601 (2010).

  74. 74.

    Adamson, P. et al. Search for Lorentz invariance and CPT violation with muon antineutrinos in the MINOS near detector. Phys. Rev. D 85, 031101 (2012).

  75. 75.

    Rebel, B. & Mufson, S. The search for neutrino-antineutrino mixing resulting from Lorentz invariance violation using neutrino interactions in MINOS. Astropart. Phys. 48, 78–81 (2013).

  76. 76.

    Abe, Y. et al. First test of Lorentz violation with a reactor-based antineutrino experiment. Phys. Rev. D 86, 112009 (2012).

  77. 77.

    Díaz, J. S., Katori, T., Spitz, J. & Conrad, J. M. Search for neutrino-antineutrino oscillations with a reactor experiment. Phys. Lett. B 727, 412 (2013).

  78. 78.

    Diaz, J. S. & Schwetz, T. Limits on CPT violation from solar neutrinos. Phys. Rev. D 93, 093004 (2016).

  79. 79.

    Abe, K. et al. Search for Lorentz and CPT violation using sidereal time dependence of neutrino flavor transitions over a short baseline. Phys. Rev. D 95, 111101 (2017).

  80. 80.

    Feroz, F., Hobson, M. P. & Bridges, M. MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009).

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We acknowledge the support from the following agencies: USA—US National Science Foundation–Office of Polar Programs, US National Science Foundation–Physics Division, Wisconsin Alumni Research Foundation, Center for High Throughput Computing (CHTC) at the University of Wisconsin–Madison, Open Science Grid (OSG), Extreme Science and Engineering Discovery Environment (XSEDE), US Department of Energy–National Energy Research Scientific Computing Center, Particle astrophysics research computing centre at the University of Maryland, Institute for Cyber-Enabled Research at Michigan State University and Astroparticle physics computational facility at Marquette University; Belgium—Funds for Scientific Research (FRS-FNRS and FWO), FWO Odysseus and Big Science programmes, and Belgian Federal Science Policy Office (Belspo); Germany—Bundesministerium für Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG), Helmholtz Alliance for Astroparticle Physics (HAP), Initiative and Networking Fund of the Helmholtz Association, Deutsches Elektronen Synchrotron (DESY), and High Performance Computing cluster of the RWTH Aachen; Sweden—Swedish Research Council, Swedish Polar Research Secretariat, Swedish National Infrastructure for Computing (SNIC), and Knut and Alice Wallenberg Foundation; Australia—Australian Research Council; Canada—Natural Sciences and Engineering Research Council of Canada, Calcul Québec, Compute Ontario, Canada Foundation for Innovation, WestGrid and Compute Canada; Denmark—Villum Fonden, Danish National Research Foundation (DNRF); New Zealand—Marsden Fund; Japan—Japan Society for Promotion of Science (JSPS) and Institute for Global Prominent Research (IGPR) of Chiba University; Korea—National Research Foundation of Korea (NRF); Switzerland—Swiss National Science Foundation (SNSF); UK—Science and Technology Facilities Council (STFC) and The Royal Society.

Author information

The IceCube Collaboration designed, constructed and now operates the IceCube Neutrino Observatory. Data processing and calibration, Monte Carlo simulations of the detector and of theoretical models, and data analyses were performed by a large number of collaboration members, who also discussed and approved the scientific results presented here. The main authors of this manuscript were C. Argüelles, A. Kheirandish, G. Collin, S. Mandalia, J. Conrad and T. Katori. It was reviewed by the entire collaboration before publication, and all authors approved the final version of the manuscript.

Competing interests

The authors declare no competing interests.

Correspondence to C. Argüelles or G. H. Collin or J. M. Conrad or A. Kheirandish or T. Katori or S. Mandalia.

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Further reading

Fig. 1: Test of LV with atmospheric neutrinos.
Fig. 2: The ratio of vertical to horizontal neutrino transition probabilities at IceCube.
Fig. 3: The excluded parameter space region for the dimension-six SME coefficients.