Abstract
Along their long propagation from production to detection, neutrinos undergo flavour conversions that convert their types or flavours1,2. High-energy astrophysical neutrinos propagate unperturbed over a billion light years in vacuum3 and are sensitive to small effects caused by new physics. Effects of quantum gravity4 are expected to appear at the Planck energy scale. Such a high-energy universe would have existed only immediately after the Big Bang and is inaccessible by human technologies. On the other hand, quantum gravity effects may exist in our low-energy vacuum5,6,7,8, but are suppressed by inverse powers of the Planck energy. Measuring the coupling of particles to such small effects is difficult via kinematic observables, but could be observable through flavour conversions. Here we report a search with the IceCube Neutrino Observatory, using astrophysical neutrino flavours9,10 to search for new space–time structure. We did not find any evidence of anomalous flavour conversion in the IceCube astrophysical neutrino flavour data. We apply the most stringent limits of any known technologies, down to 10−42 GeV−2 with Bayes factor greater than 10 on the dimension-six operators that parameterize the space–time defects. We thus unambiguously reach the parameter space of quantum-gravity-motivated physics.
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Code availability
Much of the analysis code is IceCube proprietary and exists as part of the IceCube simulation and production framework. IceCube open-source code can be found at https://github.com/icecube. Additional information is available from analysis@icecube.wisc.edu upon request.
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Acknowledgements
We acknowledge support from the following agencies and institutions: USA—US National Science Foundation–Office of Polar Programs, US National Science Foundation–Physics Division, US National Science Foundation–EPSCoR, 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), Frontera computing project at the Texas Advanced Computing Center, US Department of Energy–National Energy Research Scientific Computing Center, Particle Astrophysics Research Computing Center 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 and Carlsberg Foundation; 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); United Kingdom—Department of Physics, University of Oxford, the Royal Society and the Science and Technology Facilities Council (STFC).
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The IceCube Collaboration acknowledges the significant contributions to this manuscript from C. Argüelles, K. Farrag and T. Katori. 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.
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Extended data
Extended Data Fig. 1 Example posterior distribution over the 14 nuisance parameters.
The plot is for \({{{\rm{Re}}}}({\mathring{c}}_{\tau\tau}^{(6)})=1{0}^{-44}\,Ge{V}^{-2}\) with source combination (0: 1: 0)S. Blue contours show two dimensional distribution slices, with one-dimensional projections above for each parameter. Three vertical lines indicate the lower quartile (25%), median (50%) and upper quartile (75%) for each parameter. Parameters are introduced in Ref. 9.
Extended Data Fig. 2 Example of the analysis Bayes factor as a function of one of the constrained parameters.
Horizontal lines show different hypothesis rejection strength levels according to Jeffreys’ scale. Here, we set the limit on \({{{\rm{Re}}}}({\mathring{c}}_{\tau\tau}^{(6)})\) with an assumed source flavour ratio (0: 1: 0)S. A substantial limit is obtained when the Bayes factor is greater than 10.0, and strong limits when the Bayes factor is greater than 31.6. Error bars indicate the error on the evidence computation via nested sampling.
Extended Data Fig. 3 Limits on the dimension-three new physics operator.
The hatched region is the limit obtained from the atmospheric neutrino data analysis on \({{{\rm{Re}}}}({\mathring{a}}_{\mu \tau }^{(3)})\)15. Limits determined by Bayes factors > 10 (dashed lines) and > 31.6 (solid lines) are presented as a function of the assumed astrophysical neutrino flavour ratio at the production source. The leftmost scenario is νμ dominant (0: 1: 0)S and the rightmost is νe dominant (1: 0: 0)S. The preferred scenario corresponds to (1/3: 2/3: 0)S (dashed vertical line). Limits on \({{{\rm{Re}}}}({\mathring{a}}_{ee}^{(3)})\) on (orange), \({{{\rm{Re}}}}({\mathring{a}}_{e\mu }^{(3)})\) (red), \({{{\rm{Re}}}}({\mathring{a}}_{e\tau }^{(3)})\) (green), \({{{\rm{Re}}}}({\mathring{a}}_{\mu \mu }^{(3)})\) (yellow), \({{{\rm{Re}}}}({\mathring{a}}_{\mu \tau }^{(3)})\) (purple), and \({{{\rm{Re}}}}({\mathring{a}}_{\tau \tau }^{(3)})\) (blue) are shown.
Extended Data Fig. 4 Limits on the dimension-four new physics operator.
The hatched region is the limit obtained from the atmospheric neutrino data analysis on \({{{\rm{Re}}}}({\mathring{c}}_{\mu \tau }^{(4)})\)15. Limits determined by Bayes factors > 10 (dashed lines) and > 31.6 (solid lines) are presented as a function of the assumed astrophysical neutrino flavour ratio at the production source. The leftmost scenario is νμ dominant (0: 1: 0)S and the rightmost is νe dominant (1: 0: 0)S. The preferred scenario corresponds to (1/3: 2/3: 0)S (dashed vertical line). Limits on \({{{\rm{Re}}}}({\mathring{c}}_{ee}^{(4)})\) on (orange), \({{{\rm{Re}}}}({\mathring{c}}_{e\mu }^{(4)})\) (red), \({{{\rm{Re}}}}({\mathring{c}}_{e\tau }^{(4)})\) (green), \({{{\rm{Re}}}}({\mathring{c}}_{\mu \mu }^{(4)})\) (yellow), \({{{\rm{Re}}}}({\mathring{c}}_{\mu \tau }^{(4)})\) (purple), and \({{{\rm{Re}}}}({\mathring{c}}_{\tau \tau }^{(4)})\) (blue) are shown.
Extended Data Fig. 5 Limits on the dimension-five new physics operator.
The hatched region is the limit obtained from the atmospheric neutrino data analysis on \({{{\rm{Re}}}}({\mathring{a}}_{\mu \tau }^{(5)})\)15. Limits determined by Bayes factors > 10 (dashed lines) and > 31.6 (solid lines) are presented as a function of the assumed astrophysical neutrino flavour ratio at the production source. The leftmost scenario is νμ dominant (0: 1: 0)S and the rightmost is νe dominant (1: 0: 0)S. The preferred scenario corresponds to (1/3: 2/3: 0)S (dashed vertical line). Limits on \({{{\rm{Re}}}}({\mathring{a}}_{ee}^{(5)})\) on (orange), \({{{\rm{Re}}}}({\mathring{a}}_{e\mu }^{(5)})\) (red), \({{{\rm{Re}}}}({\mathring{a}}_{e\tau }^{(5)})\) (green), \({{{\rm{Re}}}}({\mathring{a}}_{\mu \mu }^{(5)})\) (yellow), \({{{\rm{Re}}}}({\mathring{a}}_{\mu \tau }^{(5)})\) (purple), and \({{{\rm{Re}}}}({\mathring{a}}_{\tau \tau }^{(5)})\) (blue) are shown.
Extended Data Fig. 6 Limits on the dimension-seven new physics operator.
The hatched region is the limit obtained from the atmospheric neutrino data analysis on \({{{\rm{Re}}}}({\mathring{a}}_{\mu \tau }^{(7)})\)15. Limits determined by Bayes factors > 10 (dashed lines) and > 31.6 (solid lines) are presented as a function of the assumed astrophysical neutrino flavour ratio at the production source. The leftmost scenario is νμ dominant (0: 1: 0)S and the rightmost is νe dominant (1: 0: 0)S. The preferred scenario corresponds to (1/3: 2/3: 0)S (dashed vertical line). Limits on \({{{\rm{Re}}}}({\mathring{a}}_{ee}^{(7)})\) on (orange), \({{{\rm{Re}}}}({\mathring{a}}_{e\mu }^{(7)})\) (red), \({{{\rm{Re}}}}({\mathring{a}}_{e\tau }^{(7)})\) (green), \({{{\rm{Re}}}}({\mathring{a}}_{\mu \mu }^{(7)})\) (yellow), \({{{\rm{Re}}}}({\mathring{a}}_{\mu \tau }^{(7)})\) (purple), and \({{{\rm{Re}}}}({\mathring{a}}_{\tau \tau }^{(7)})\) (blue) are shown.
Extended Data Fig. 7 Limits on the dimension-eight new physics operator.
The hatched region is the limit obtained from the atmospheric neutrino data analysis on \({{{\rm{Re}}}}({\mathring{c}}_{\mu \tau }^{(8)})\)15. Limits determined by Bayes factors > 10 (dashed lines) and > 31.6 (solid lines) are presented as a function of the assumed astrophysical neutrino flavour ratio at the production source. The leftmost scenario is νμ dominant (0: 1: 0)S and the rightmost is νe dominant (1: 0: 0)S. The preferred scenario corresponds to (1/3: 2/3: 0)S (dashed vertical line). Limits on \({{{\rm{Re}}}}({\mathring{c}}_{ee}^{(8)})\) on (orange), \({{{\rm{Re}}}}({\mathring{c}}_{e\mu }^{(8)})\) (red), \({{{\rm{Re}}}}({\mathring{c}}_{e\tau }^{(8)})\) (green), \({{{\rm{Re}}}}({\mathring{c}}_{\mu \mu }^{(8)})\) (yellow), \({{{\rm{Re}}}}({\mathring{c}}_{\mu \tau }^{(8)})\) (purple), and \({{{\rm{Re}}}}({\mathring{c}}_{\tau \tau }^{(8)})\) (blue) are shown.
Extended Data Table 1 Limits on new physics operators extracted from this analysis.
These limits on new physics operators are derived from Bayes factor > 10.0 (Bayes factor > 31.6) which corresponds to 1 in 10.0 (31.6) likelihood ratio for a uniform prior. They are for characteristic source flavour ratios, (1: 0: 0)S, (1/3: 2/3: 0)S, and (0: 1: 0)S. We list only operators where limits are set.
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The IceCube Collaboration. Search for quantum gravity using astrophysical neutrino flavour with IceCube. Nat. Phys. 18, 1287–1292 (2022). https://doi.org/10.1038/s41567-022-01762-1
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DOI: https://doi.org/10.1038/s41567-022-01762-1
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