Letter | Published:

Measurement of the multi-TeV neutrino interaction cross-section with IceCube using Earth absorption

Nature volume 551, pages 596600 (30 November 2017) | Download Citation

  • An Erratum to this article was published on 14 February 2018

This article has been updated

Abstract

Neutrinos interact only very weakly, so they are extremely penetrating. The theoretical neutrino–nucleon interaction cross-section, however, increases with increasing neutrino energy, and neutrinos with energies above 40 teraelectronvolts (TeV) are expected to be absorbed as they pass through the Earth. Experimentally, the cross-section has been determined only at the relatively low energies (below 0.4 TeV) that are available at neutrino beams from accelerators1,2. Here we report a measurement of neutrino absorption by the Earth using a sample of 10,784 energetic upward-going neutrino-induced muons. The flux of high-energy neutrinos transiting long paths through the Earth is attenuated compared to a reference sample that follows shorter trajectories. Using a fit to the two-dimensional distribution of muon energy and zenith angle, we determine the neutrino–nucleon interaction cross-section for neutrino energies 6.3–980 TeV, more than an order of magnitude higher than previous measurements. The measured cross-section is about 1.3 times the prediction of the standard model3, consistent with the expectations for charged- and neutral-current interactions. We do not observe a large increase in the cross-section with neutrino energy, in contrast with the predictions of some theoretical models, including those invoking more compact spatial dimensions4 or the production of leptoquarks5. This cross-section measurement can be used to set limits on the existence of some hypothesized beyond-standard-model particles, including leptoquarks.

Main

The cross-section for neutrino interactions with matter is very small. Neutrinos are usually regarded as particles that will go through anything6. However, the neutrino–nucleon interaction cross-section is expected to increase with energy. Until now, the cross-section has only been measured up to a neutrino energy of 370 GeV (Fig. 1; log(370) = 2.57) because it has been limited by the available accelerator neutrino beams1. In this range, the cross-section rises linearly with energy.

Figure 1: Neutrino cross-section measurements.
Figure 1

Measured neutrino charged-current interaction cross-sections σν, divided by the neutrino energy Eν, from accelerator experiments are shown, along with error bars showing their combined 1σ statistical and systematic uncertainty, from ref. 1 and from this work. The blue and green lines are the standard model predictions for muon neutrinos νμ and antineutrinos , respectively, with the uncertainties on the deep-inelastic cross-sections shown by the shaded bands3. The red line corresponds to the expected mixture of νμ and in the IceCube sample. The black line shows our result, assuming that the charged- and neutral-current cross-sections vary in proportion, and that the ratio between the actual cross-section and the standard model prediction does not depend on energy. The pink band shows the total 1σ (statistical plus systematic) uncertainty. The cross-section increases linearly with energy up to about 3 TeV (log(3,000) = 3.48), after which this increase is moderated and the cross-section becomes roughly proportional to (Eν)0.3 owing to the finite W± and Z0 masses.

In the standard model of particle physics, neutrinos interact with quarks through charged-current and neutral-current interactions, mediated by W± and Z0 bosons, respectively. At neutrino energies above 10 TeV, the finite W± and Z0 masses are expected to moderate the increase in cross-section, leading to a slower rise at higher energies. These cross-sections also reflect the densities of partons (quarks and gluons) within the nuclear targets. Accelerator neutrino experiments have mainly probed the densities of partons with Bjorken-x values (the fraction of the total nucleon momentum carried by a quark or gluon) above about 0.1. In this x range, there are more quarks than antiquarks, so the interaction cross-section of the antineutrino is about half that of the neutrino. Higher-energy experiments probe lower Bjorken-x values, where sea quarks predominate, and the difference between the neutrino and antineutrino cross-sections is reduced.

At high energies, new processes beyond the standard model may appear. Some theories invoke new spatial dimensions, which are curled up on a distance scale r. At momentum transfers comparable to ħc/r, where ħ is the reduced Planck constant and c is the speed of light in vacuum, the neutrino cross-section rises dramatically4,7. In some grand unified or technicolour theories, leptoquarks may couple to both quarks and leptons; for example, a second-generation leptoquark couples to both muon neutrinos and quarks. The interaction cross-section increases considerably at neutrino–quark centre-of-mass energies that correspond to the mass of the leptoquark5.

Our measurement uses naturally occurring atmospheric and astrophysical neutrinos to extend neutrino interaction cross-section measurements to multi-teraelectronvolt energies by observing neutrino absorption in the Earth. Figure 2 shows the principle of the measurement. Atmospheric neutrinos, produced by cosmic-ray air showers below the Earth’s horizon, are the dominant source of neutrinos used for this analysis. Astrophysical neutrinos produced by distant sources are the largest contribution at energies above 300 TeV. High-energy neutrinos that deeply traverse the Earth are absorbed, whereas near-horizontal neutrinos provide an essentially absorption-free reference9. The contribution of atmospheric neutrino oscillations is negligible at teraelectronvolt energies and is not included here.

Figure 2: Neutrino absorption in the Earth.
Figure 2

a, Neutrino absorption is observed by measuring how the neutrino energy spectrum changes with the zenith angle. High-energy neutrinos transiting deep through the Earth are absorbed, whereas low-energy neutrinos are not. Neutrinos from just below the horizon provide a nearly absorption-free baseline at all relevant energies. b, Standard model prediction for the transmission probability of neutrinos through the Earth as a function of energy and zenith angle. Neutral-current interactions, which occur about 1/3 of the time, are included. When a neutral-current interaction occurs, a neutrino is replaced with one of lower energy. The horizontal white dotted line shows the trajectory (and zenith angle) of a neutrino that just passes through the core–mantle boundary.

The idea of studying neutrino absorption in the Earth dates back to 1974 (ref. 10), although most of the early papers on the subject proposed using absorption to probe the Earth’s interior11. However, the density uncertainty12,13,14,15 for long paths through the Earth is only 1%–2%; this leads to less than 1% systematic uncertainty in the cross-section measurement, below the total uncertainty of the cross-section. Early work on the subject envisioned using accelerator-produced neutrinos for Earth tomography; the idea of using natural (astrophysical or atmospheric) neutrinos came later16,17.

Neutrino absorption increases with neutrino energy, so that for 40-TeV neutrinos, the Earth’s diameter corresponds to one absorption length. By observing the change in the angular distribution of Earth-transiting neutrinos with increasing neutrino energy, one can measure the increasing absorption and, from that, determine the cross-section.

This analysis uses data collected with the IceCube detector18, which is installed in the Antarctic ice cap at the South Pole. The data were acquired during 2009 and 2010, when IceCube consisted of 79 vertical strings19, each supporting 60 optical sensors (Digital Optical Modules, DOMs20). The strings are arranged in a triangular grid, with 125 m between strings. The sensors are deployed at 17-m vertical intervals, at depths between 1,450 m and 2,450 m below the surface of the ice cap. Six of the strings are installed at the centre of the array, with smaller string spacing and with their DOMs clustered between 2,100 m and 2,450 m deep; this module is called ‘DeepCore’.

The DOMs detect Cherenkov light from the charged particles that are produced when neutrinos interact in the ice surrounding IceCube and the bedrock below. In this measurement, the 79-string detector recorded about 2,000 events per second. About 99.9999% of these were downward-going muons produced directly by cosmic-ray air showers above the horizon. The events were reconstructed using a series of algorithms of increasing accuracy and computational complexity21,22. At each stage of processing, a set of conditions was applied to eliminate background events. The final sample of 10,784 upward-going (zenith angle greater than 90°) events had an estimated background of less than 0.1%. Almost all of the background consisted of mis-reconstructed downward-going muons.

The neutrino zenith angles were determined from the reconstructed muon direction. The typical angular resolution was better than 0.6°, including the angular difference between the neutrino and muon directions. This small angular uncertainty does not affect the final result. The neutrino energies were much less well known than the zenith angles because we cannot determine how far from the detector the interaction occurred, so we do not know how much energy the muon lost before entering the detector. Therefore, this analysis used the muon energy as determined from the measured specific energy loss (dE/dx) of the muons. To improve the energy resolution, the muon tracks were divided into 120-m-long segments. The segments with the highest dE/dx values were excluded, and the truncated mean was determined from the remaining segments23. The removal of large stochastic losses led to better resolution than that obtained with the untruncated mean. The muon energy values were determined to within roughly a factor of 2.

The cross-section was found by a maximum-likelihood fit, which compared the data, binned by zenith angle and muon energy, with a model that included contributions from atmospheric and astrophysical neutrinos. The cross-section entered the fit through the energy- and zenith-angle-dependent probability for the neutrinos to be absorbed as they pass through the Earth. This absorption probability depends on the nucleon density, integrated along the path of the neutrino through the Earth. We used the Preliminary Reference Earth Model to determine the density of the Earth12. Thanks to seismic wave studies and tight constraints on the total mass of the Earth, the uncertainties in the integrated density were lower than a few per cent.

To account for neutral-current interactions, in which neutrinos lose a fraction of their energy, we modelled neutrino transmission through the Earth at each zenith angle in two dimensions: the incident neutrino energy and the neutrino energy near IceCube. The fit determined R = σmeas/σSM, where σmeas is the measured cross-section and σSM is the standard model cross-section from ref. 3. That calculation used quark and gluon densities derived from the Hadron-Electron Ring Accelerator (HERA) data to find the interaction cross-sections of neutrinos and antineutrinos with protons and neutrons, treating the Earth as an isoscalar target. The estimated uncertainty in the calculation was less than 5% for the energy range covered by this analysis. Because the calculation did not include nuclear shadowing, it might overestimate the cross-section for heavier elements, such as the iron in the core of the Earth. Experiments with 2–22-GeV neutrinos interacting with iron targets24 and 20–300-GeV neutrinos interacting with neon25 did not observe nuclear shadowing, but it may be present for higher-energy neutrinos26.

The fitted charged-current and neutral-current cross-sections were assumed to be the same multiples of their standard model counterparts, and we ignored nuclear shadowing. The fitting procedure was repeated for different cross-section values (varying in steps of ΔR = 0.2), leading to a parabolic curve of likelihood versus cross-section.

The flux model included conventional atmospheric neutrinos from π± and K± decay, prompt atmospheric neutrinos from the decay of charm/bottom hadrons and astrophysical neutrinos. Because the precise neutrino fluxes and spectra were imperfectly known, they were included as nuisance parameters in the fit, with the initial values and Gaussian uncertainties shown in Table 1. Five parameters accounted for the atmospheric, prompt and astrophysical neutrino fluxes (Φ) and two spectral indices, for the atmospheric and astrophysical fluxes (the prompt index is kept fixed). The other parameters were the kaon-to-pion (K/π) and muon neutrino-to-antineutrino () ratios in cosmic-ray air showers, plus one parameter to account for the overall optical efficiency of the IceCube DOMs.

Table 1: Fitting parameters for the cross-section fit

We used previous conventional and prompt atmospheric neutrino spectra from cosmic-ray air-shower simulations that were obtained from lower-energy neutrino data27 and a colour dipole model calculation28, respectively. We modified these spectra to account for the steepening of the cosmic-ray spectrum at the ‘knee’29 (a steepening of the cosmic-ray spectrum at a cosmic-ray energy of around 3 PeV). Recent perturbative quantum chromodynamics calculations30,31,32 have found a lower prompt flux than in ref. 26. However, the prompt component is small and has little effect on this analysis, and the fitting results are compatible with both calculations and with existing upper limits29 on the prompt flux. Finally, the astrophysical spectrum was obtained on the basis of a recent combined fit8. There is some disagreement between the spectral index derived from the combined fit and that obtained from a newer analysis29, which was focused on through-going muon tracks from muon neutrinos (νμ); this discrepancy was treated as a systematic uncertainty that was due to the uncertain spectral index.

Because past measurements of the neutrino flux were based on the assumption that the standard model cross-section is correct, this fit uses the product of each flux with that cross-section to apply constraints directly from the previous data. As the cross-section rises, the fluxes must drop to preserve the total number of events observed in previous experiments. The fit is thus sensitive to neutrino absorption in the Earth, and not to the total number of observed events.

The fit finds a cross-section times that of the standard model. The uncertainty is a mixture of the statistical uncertainty and the systematic errors from the uncertainties in the nuisance parameters. We isolate the statistical error by refitting with the nuisance parameters fixed to their preferred values, and find a statistical error of . The remainder of the fitting error, after quadrature subtraction, is attributed to systematic uncertainty sources in the fit.

Figure 3 compares the measured muon energy proxy spectrum for zenith angles between 110° and 180° (where absorption is substantial) with three fits: the best-fit result (using the cross-section given above) and two comparison fits with cross-sections 0.2 and 3.0 times the standard model prediction. The spectrum steepens noticeably as the cross-section increases. We use the term ‘energy proxy’ because of the limited energy resolution.

Figure 3: Cross-section data compared with Monte Carlo model predictions.
Figure 3

Energy spectrum of the data (black points) and the best-fit results (red curve) with the cross-sections fixed to 0.2 (green) and 3.0 (blue) times that predicted by the standard model for events with zenith angles between 110° and 180°, where absorption is substantial, are shown in the top panel. The bottom panel shows the ratios of the data to the three Monte Carlo predictions. The error bars show the 1σ (statistical only) errors.

The other major detector-related uncertainty is due to the optical properties of ice. This was studied with separate dedicated simulations, in which the scattering and absorption lengths were varied by ±10%. This led to a systematic uncertainty of in the standard model cross-section. Four other systematic uncertainties were considered: uncertainty in the density distribution of the Earth13,14,15 (±0.01), variations in atmospheric pressure at the neutrino production sites9  , uncertainties in the prompt and astrophysical neutrino spectral indices (±0.10) and uncertainties in the angular acceptance of the IceCube DOMs . These systematic errors were then added in quadrature to the systematic uncertainties from the fit, giving a total systematic uncertainty of times the prediction of the standard model.

The neutrino energy range in which this analysis is relevant was found by repeating the fit procedure with the absorption probability set to zero for neutrino energies below a certain threshold. As the threshold was gradually increased, the data and simulation diverged, and the quality of the fit was degraded. The threshold that corresponded to a likelihood increase of 1.0σ (−2ΔLLH = 1, where ΔLLH is the change in the natural logarithm of the likelihood) was the minimum energy to which this analysis was sensitive. We repeated the process by turning off neutrino absorption above a gradually decreasing high-energy threshold to find the upper end of the energy range and obtained the energy range 6.3–980 TeV. This wide range reflects the combination of a neutrino flux that decreases rapidly with energy (partially compensated by an increasing cross-section and detection probability) with the relatively rapid increase in absorption with increasing energy.

Figure 1 compares this measurement with previous measurements of neutrino cross-sections made at accelerator facilities. Ours is the first cross-section measurement at multi-teraelectronvolt energies, at which the effects of the finite W± and Z0 masses slow the increase of the cross-section with increasing energy. We measured the cross-section to be (statistical uncertainty) (systematic uncertainty) times the prediction of the standard model for charged- and neutral-current interactions in the energy range from 6.3 TeV to 980 TeV (log[Eν (GeV)] = 3.8–6.0). We did not see a dramatic increase in cross-section, as predicted by models of beyond-standard-model physics, such as those involving extra dimensions4 or leptoquarks5.

Future optical Cherenkov experiments with IceCube or larger detectors, such as IceCube-Gen233 or Phase 2.0 of KM3NeT34, should be able to extend this measurement to higher energies and study the energy dependence of the interaction cross-section of neutrinos. Future experiments that detect the radio emission from neutrino showers over volumes exceeding 100 km3 using the ARA and ARIANNA technologies35,36 could observe the interactions of GZK neutrinos and extend the cross-section measurements up to energies of 1019 eV (ref. 37). Experiments at these energies will have sensitivity to phenomena (very heavy leptoquarks, or additional dimensions with small spatial extent) beyond the standard model that occur at higher energies than those that can be probed at CERN’s Large Hadron Collider.

Methods

The dataset used in this analysis was collected between 31 May 2010 and 13 May 2011, when the IceCube detector consisted of 79 strings. The data were processed with the standard IceCube calibration and reconstruction algorithms22, including energy determination using the truncated mean method9. A series of event selection criteria were applied to accept well-reconstructed upward-going track events with reconstructed muon-energy proxy22 above 1 TeV.

The events were then two-dimensionally binned in terms of zenith angle and muon-energy proxy and fitted by the combination of simulated events described in the main text. The simulated events were generated with standard IceCube programs that simulated the flux of neutrinos propagated through the Earth and forced to interact in or near IceCube. The resulting particle showers were simulated and reconstructed using standard IceCube simulation programs. Simulations were run for several assumed neutrino cross-sections, as described in the main text, and the results were interpolated between these cross-sections. Uncertainties in the different neutrino flux parameters listed in Table 1 were accounted for by using a weighting scheme for the simulated events. By adjusting the event weightings, different spectra could be simulated without rerunning the simulations.

Code availability

Proprietary codes used are embedded within the IceCube simulation framework and the IceTray framework. It is not practical to separate these and the codes are not therefore publicly available.

Data availability

The data used in this analysis are available online at http://icecube.wisc.edu/science/data/HE_NuMu_diffuse. The data were collected before 13 May 2011 (before run number 118175)22. That data release uses an energy proxy that is similar to, but not identical to, that used for the current analysis.

Change history

  • 14 February 2018

    Change history: Please see accompanying Erratum (http://doi.org/10.1038/nature25472). In this Letter, ‘HERA’ was wrongly expanded to ‘Hydrogen Epoch of Reionization Array’ instead of ‘Hadron-Electron Ring Accelerator’ on page 597. In addition, some author affiliations were wrongly assigned. The original Letter has been corrected online.

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Acknowledgements

We acknowledge support from the following agencies: United States Air Force Academy, US National Science Foundation, Office of Polar Programs; US National Science Foundation, Physics Division; University of Wisconsin Alumni Research Foundation; the Grid Laboratory of Wisconsin (GLOW) grid infrastructure at the University of Wisconsin, Madison; the Open Science Grid (OSG) grid infrastructure; US Department of Energy; National Energy Research Scientific Computing Center; the Louisiana Optical Network Initiative (LONI) grid computing resources; Natural Sciences and Engineering Research Council of Canada; WestGrid and Compute/Calcul Canada; Swedish Research Council; Swedish Polar Research Secretariat; Swedish National Infrastructure for Computing (SNIC); Knut and Alice Wallenberg Foundation; German Ministry for Education and Research (BMBF); Deutsche Forschungsgemeinschaft (DFG); Helmholtz Alliance for Astroparticle Physics (HAP); Initiative and Networking Fund of the Helmholtz Association, Germany; Fund for Scientific Research (FNRS-FWO), FWO Odysseus programme, Flanders Institute to encourage scientific and technological research in industry (IWT), Belgian Federal Science Policy Office (BELSPO); Marsden Fund; Australian Research Council; Japan Society for Promotion of Science (JSPS); Swiss National Science Foundation (SNSF); National Research Foundation of Korea (NRF); Villum Fonden, Danish National Research Foundation (DNRF).

Author information

Affiliations

  1. Department of Physics, University of Adelaide, Adelaide, 5005, Australia

    • M. G. Aartsen
    • , G. C. Hill
    • , A. Kyriacou
    • , S. Robertson
    • , A. Wallace
    •  & B. J. Whelan
  2. DESY, D-15738 Zeuthen, Germany

    • M. Ackermann
    • , E. Bernardini
    • , S. Blot
    • , F. Bradascio
    • , H.-P. Bretz
    • , J. Brostean-Kaiser
    • , A. Franckowiak
    • , E. Jacobi
    • , T. Karg
    • , T. Kintscher
    • , M. Kowalski
    • , S. Kunwar
    • , R. Nahnhauer
    • , K. Satalecka
    • , C. Spiering
    • , J. Stachurska
    • , A. Stasik
    • , N. L. Strotjohann
    • , A. Terliuk
    • , M. Usner
    •  & J. van Santen
  3. Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    • J. Adams
    •  & H. Bagherpour
  4. Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium

    • J. A. Aguilar
    • , I. Ansseau
    • , D. Heereman
    • , K. Meagher
    • , T. Meures
    • , A. O’Murchadha
    • , E. Pinat
    •  & C. Raab
  5. Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark

    • M. Ahlers
    • , D. J. Koskinen
    • , M. J. Larson
    • , M. Medici
    • , M. Rameez
    •  & S. Sarkar
  6. Oskar Klein Centre and Department of Physics, Stockholm University, SE-10691 Stockholm, Sweden

    • M. Ahrens
    • , C. Bohm
    • , J. P. Dumm
    • , C. Finley
    • , S. Flis
    • , K. Hultqvist
    • , C. Walck
    •  & M. Zoll
  7. Département de physique nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland

    • I. Al Samarai
    • , S. Bron
    • , T. Carver
    • , A. Christov
    •  & T. Montaruli
  8. Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany

    • D. Altmann
    • , G. Anton
    • , T. Glüsenkamp
    • , U. Katz
    • , T. Kittler
    •  & M. Tselengidou
  9. Department of Physics, Marquette University, Milwaukee, Wisconsin 53201, USA

    • K. Andeen
    •  & M. Plum
  10. Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA

    • T. Anderson
    • , D. F. Cowen
    • , J. J. DeLaunay
    • , M. Dunkman
    • , P. Eller
    • , F. Huang
    • , A. Keivani
    • , J. L. Lanfranchi
    • , D. V. Pankova
    • , C. F. Turley
    •  & M. J. Weiss
  11. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • C. Argüelles
    • , S. Axani
    • , G. H. Collin
    • , J. M. Conrad
    • , M. Moulai
    •  & G. Tešić
  12. III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany

    • J. Auffenberg
    • , M. Brenzke
    • , T. Glauch
    • , C. Haack
    • , P. Kalaczynski
    • , J. P. Koschinsky
    • , M. Leuermann
    • , L. Rädel
    • , R. Reimann
    • , M. Rongen
    • , T. Sälzer
    • , S. Schoenen
    • , L. Schumacher
    • , J. Stettner
    • , M. Vehring
    • , E. Vogel
    • , M. Wallraff
    • , A. Waza
    •  & C. H. Wiebusch
  13. Physics Department, South Dakota School of Mines and Technology, Rapid City, South Dakota 57701, USA

    • X. Bai
  14. Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada

    • J. P. Barron
    • , W. Giang
    • , D. Grant
    • , C. Kopper
    • , R. W. Moore
    • , S. C. Nowicki
    • , S. E. Sanchez Herrera
    • , S. Sarkar
    • , F. D. Wandler
    • , C. Weaver
    • , T. R. Wood
    • , E. Woolsey
    •  & J. P. Yanez
  15. Department of Physics and Astronomy, University of California, Irvine, California 92697, USA

    • S. W. Barwick
    •  & G. Yodh
  16. Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany

    • V. Baum
    • , S. Böser
    • , V. di Lorenzo
    • , B. Eberhardt
    • , T. Ehrhardt
    • , L. Köpke
    • , G. Krückl
    • , G. Momenté
    • , P. Peiffer
    • , J. Sandroos
    • , A. Steuer
    •  & K. Wiebe
  17. Department of Physics, University of California, Berkeley, California 94720, USA

    • R. Bay
    • , G. Binder
    • , K. Filimonov
    • , S. R. Klein
    • , S. Miarecki
    • , T. Palczewski
    • , P. B. Price
    • , J. Tatar
    •  & K. Woschnagg
  18. Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, Ohio 43210, USA

    • J. J. Beatty
    •  & M. Sutherland
  19. Department of Astronomy, Ohio State University, Columbus, Ohio 43210, USA

    • J. J. Beatty
  20. Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

    • J. Becker Tjus
    • , F. Bos
    • , B. Eichmann
    • , M. Kroll
    • , S. Schöneberg
    •  & F. Tenholt
  21. Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany

    • K.-H. Becker
    • , D. Bindig
    • , K. Helbing
    • , S. Hickford
    • , R. Hoffmann
    • , F. Lauber
    • , U. Naumann
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    •  & D. Soldin
  22. Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA

    • S. BenZvi
    •  & R. Cross
  23. Department of Physics, University of Maryland, College Park, Maryland 20742, USA

    • D. Berley
    • , E. Blaufuss
    • , E. Cheung
    • , J. Felde
    • , E. Friedman
    • , R. Hellauer
    • , K. D. Hoffman
    • , R. Maunu
    • , A. Olivas
    • , T. Schmidt
    • , M. Song
    •  & G. W. Sullivan
  24. Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA

    • D. Z. Besson
  25. Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • G. Binder
    • , L. Gerhardt
    • , A. Goldschmidt
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    • , S. Miarecki
    • , D. R. Nygren
    • , T. Palczewski
    • , G. T. Przybylski
    • , T. Stezelberger
    • , R. G. Stokstad
    •  & J. Tatar
  26. Department of Physics, TU Dortmund University, D-44221 Dortmund, Germany

    • M. Börner
    • , T. Fuchs
    • , M. Hünnefeld
    • , M. Meier
    • , T. Menne
    • , D. Pieloth
    • , W. Rhode
    • , T. Ruhe
    • , A. Sandrock
    • , P. Schlunder
    • , J. Soedingrekso
    •  & J. Werthebach
  27. Department of Physics, Sungkyunkwan University, Suwon 440-746, South Korea

    • D. Bose
    • , H. Dujmovic
    • , S. In
    • , M. Jeong
    • , W. Kang
    • , J. Kim
    •  & C. Rott
  28. Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden

    • O. Botner
    • , A. Burgman
    • , A. Hallgren
    • , C. Pérez de los Heros
    •  & E. Unger
  29. Department of Physics and Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin, Madison, Wisconsin 53706, USA

    • J. Bourbeau
    • , J. Braun
    • , J. Casey
    • , D. Chirkin
    • , M. Day
    • , P. Desiati
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    •  & T. Yuan
  30. Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium

    • L. Brayeur
    • , M. Casier
    • , C. De Clercq
    • , K. D. de Vries
    • , G. de Wasseige
    • , J. Kunnen
    • , J. Lünemann
    • , G. Maggi
    • , S. Toscano
    •  & N. van Eijndhoven
  31. SNOLAB, 1039 Regional Road 24, Creighton Mine 9, Lively, Ontario P3Y 1N2, Canada

    • K. Clark
  32. Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany

    • L. Classen
    •  & A. Kappes
  33. Physik-department, Technische Universität München, D-85748 Garching, Germany

    • S. Coenders
    • , M. Huber
    • , K. Krings
    • , I. C. Rea
    • , E. Resconi
    •  & A. Turcati
  34. Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA

    • D. F. Cowen
  35. Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

    • J. P. A. M. de André
    • , T. DeYoung
    • , J. Hignight
    • , D. Lennarz
    • , K. B. M. Mahn
    • , J. Micallef
    • , G. Neer
    •  & D. Rysewyk
  36. Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA

    • H. Dembinski
    • , P. A. Evenson
    • , T. K. Gaisser
    • , J. G. Gonzalez
    • , R. Koirala
    • , H. Pandya
    • , D. Seckel
    • , T. Stanev
    •  & S. Tilav
  37. Department of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium

    • S. De Ridder
    • , M. Labare
    • , D. Ryckbosch
    • , W. Van Driessche
    • , S. Vanheule
    •  & M. Vraeghe
  38. Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany

    • M. de With
    • , D. Hebecker
    • , H. Kolanoski
    •  & M. Kowalski
  39. Department of Physics, Southern University, Baton Rouge, Louisiana 70813, USA

    • A. R. Fazely
    • , S. Ter-Antonyan
    •  & X. W. Xu
  40. Department of Astronomy, University of Wisconsin, Madison, Wisconsin 53706, USA

    • J. Gallagher
  41. Earthquake Research Institute, University of Tokyo, Bunkyo, Tokyo 113-0032, Japan

    • K. Hoshina
  42. Dept. of Physics and Institute for Global Prominent Research, Chiba University, Chiba 263-8522, Japan

    • A. Ishihara
    • , M. Kim
    • , T. Kuwabara
    • , L. Lu
    • , K. Mase
    • , M. Relich
    • , A. Stößl
    •  & S. Yoshida
  43. CTSPS, Clark-Atlanta University, Atlanta, Georgia 30314, USA

    • G. S. Japaridze
  44. Department of Physics, University of Texas at Arlington, 502 Yates Street, Science Hall Room 108, Box 19059, Arlington, Texas 76019, USA

    • B. J. P. Jones
  45. Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA

    • J. Kiryluk
    • , M. Lesiak-Bzdak
    • , H. Niederhausen
    •  & Y. Xu
  46. Université de Mons, 7000 Mons, Belgium

    • G. Kohnen
  47. Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA

    • S. Kopper
    • , P. Nakarmi
    • , J. A. Pepper
    • , P. A. Toale
    •  & D. R. Williams
  48. Department of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, Pennsylvania 19104, USA

    • N. Kurahashi
    • , B. Relethford
    • , M. Richman
    •  & L. Wills
  49. Department of Physics, University of Wisconsin, River Falls, Wisconsin 54022, USA

    • J. Madsen
    • , S. Seunarine
    •  & G. M. Spiczak
  50. Department of Physics, Yale University, New Haven, Connecticut 06520, USA

    • R. Maruyama
  51. Department of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Drive, Anchorage, Alaska 99508, USA

    • K. Rawlins
  52. Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK

    • S. Sarkar
  53. School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    • I. Taboada
    •  & C. F. Tung

Consortia

  1. The IceCube Collaboration

Authors

    Contributions

    The IceCube neutrino observatory was designed and constructed by the IceCube Collaboration and the IceCube Project, which continues to operate it. Data processing and calibration, Monte Carlo simulations of the detector and of theoretical models, and data analyses were performed by a large number of IceCube Collaboration members, who also discussed and approved the scientific results. The analysis presented here was performed by S.Mi. with input from G.B. The paper was written by S.Mi., G.B. and S.R.K. and reviewed by the collaboration. All authors approved the final version of the manuscript.

    Competing interests

    The author declare no competing financial interests.

    Corresponding author

    Correspondence to S. R. Klein.

    Reviewer Information Nature thanks A. De Gouvea 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.

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    DOI

    https://doi.org/10.1038/nature24459

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