Observation of an ultra-high-energy cosmic neutrino with KM3NeT

Abstract

The detection of cosmic neutrinos with energies above a teraelectronvolt (TeV) offers a unique exploration into astrophysical phenomena^1-3. Electrically neutral and interacting only by means of the weak interaction, neutrinos are not deflected by magnetic fields and are rarely absorbed by interstellar matter: their direction indicates that their cosmic origin might be from the farthest reaches of the Universe. High-energy neutrinos can be produced when ultra-relativistic cosmic-ray protons or nuclei interact with other matter or photons, and their observation could be a signature of these processes. Here we report an exceptionally high-energy event observed by KM3NeT, the deep-sea neutrino telescope in the Mediterranean Sea⁴, which we associate with a cosmic neutrino detection. We detect a muon with an estimated energy of $120_{-60}^{+110}$ petaelectronvolts (PeV). In light of its enormous energy and near-horizontal direction, the muon most probably originated from the interaction of a neutrino of even higher energy in the vicinity of the detector. The cosmic neutrino energy spectrum measured up to now^5-7 falls steeply with energy. However, the energy of this event is much larger than that of any neutrino detected so far. This suggests that the neutrino may have originated in a different cosmic accelerator than the lower-energy neutrinos, or this may be the first detection of a cosmogenic neutrino⁸, resulting from the interactions of ultra-high-energy cosmic rays with background photons in the Universe.

Fig. 1. Views of the event.

a, Side and top views of the event. The reconstructed trajectory of the muon is shown as a red line, along with an artist’s representation of the Cherenkov light cone. The hits of individual PMTs are represented by spheres stacked along the direction of the PMT orientations. Only the first five hits on each PMT are shown. As indicated in the legend, the spheres are coloured according to the detection time relative to the first triggered hit. The size of the spheres is proportional to the number of photons detected by the corresponding PMT. The locations of the secondary cascades, discussed in the Supplementary Material, are indicated by the black spheres along the muon trajectory. The north direction is indicated by a red arrow. A 100-m scale and the Eiffel Tower (330 m height, 125 m base width) are shown for size comparison. b, Zoomed-in view of the optical modules that are close to the first two observed secondary showers in the event. Here light-blue spheres represent hits that arrive within −5 to 25 ns of the expected Cherenkov arrival times.

Fig. 2. Number of PMTs in the event.

The normalized distributions of the number of PMTs participating in the triggering of the event for simulated muon energies of 10, 100 and 1,000 PeV. The vertical dashed line indicates the observed value in KM3-230213A, ${\widehat{\mathcal{N}}}_{\mathrm{trig}}^{\mathrm{PMT}}=\mathrm{3,672}$. The dashed histograms represent the distributions from the nominal simulations, whereas, in the filled histograms, systematic uncertainties are included by weighting the simulations according to a normal distribution, centred at the nominal value of the nuisance parameter and with a ±10% uncertainty. At the highest energy, the distributions seem to be truncated around ${\mathcal{N}}_{\mathrm{trig}}^{\mathrm{PMT}}=\mathrm{6,000}$ because the track crosses the detector in its periphery. Source Data

Fig. 3. Background rates.

a, Expected yearly rate of atmospheric muons and cosmic neutrinos (according to the best-fit flux of ref. ) in ARCA per bin of ${\mathcal{N}}_{\mathrm{trig}}^{\mathrm{PMT}}$ and cos(zenith angle). The solid (dashed) lines mark the boundary of the phase space outside which 5% (1%) of the muon and neutrino distributions are contained. KM3-230213A is shown by the cross. b, Number of events collected in the ARCA detector over the 287 days of data taking with 21 detection lines, with the same selection cuts. Two upgoing, lower-energy events are visible as well as KM3-230213A, which are candidate neutrino events, subject to future analysis.

Fig. 4. Sky map in the direction of KM3-230213A.

KM3-230213A is indicated by the red star, with the error regions within R(68%), R(90%) and R(99%) shown as dotted, dashed and solid contours, respectively. The directions of the selected source candidates are shown as coloured markers, whose colours and marker type indicate the criterion according to which the source was selected. The sources are numbered according to their proximity to KM3-230213A, as reported in Methods. Source Data

Fig. 5. Comparison with models and earlier measurements.

Shown is the energy-squared per-flavour astrophysical flux derived from the observation of KM3-230213A with measurements and theoretical predictions, assuming equipartition (ν_e:ν_μ:ν_τ = 1:1:1). The blue cross corresponds to the flux needed to achieve one expected event after the track selection described in the text, in the central 90% neutrino energy range associated with KM3-230213A, illustrated with the horizontal span; the vertical bars represent the 1σ, 2σ and 3σ Feldman–Cousins confidence intervals on this estimate. The purple and pink shaded regions represent the 68% confidence level contours of the IceCube single-power-law (SPL) fits (Northern Sky Tracks, NST) and High-Energy Starting Events (HESE), respectively: the darker-shaded regions are the respective 90% central energy range at the best fit (dashed line), whereas the lighter-shaded regions are extrapolations to higher energies. The purple and pink crosses are the piece-wise fit from the same analyses, whereas the orange cross corresponds to the IceCube Glashow resonance event. The dotted lines are upper limits from ANTARES (95% confidence level), Pierre Auger (90% confidence level, for an E⁻² neutrino spectrum, corrected to convert from limits in half-decade to one-decade bins) and IceCube (90% confidence level, estimated assuming an E⁻¹ neutrino spectrum in sliding one-decade bins). The grey-shaded band comprises a variety of cosmogenic neutrino expectations following several models of cosmic-ray acceleration and propagation, whereas the yellow-shaded band comprises several scenarios of diffuse transient and variable extragalactic sources, both reported in the Supplementary Material. Source Data

Extended Data Fig. 1. Comparison between data and Monte Carlo simulations.

The distribution of the ${\mathcal{N}}_{\mathrm{trig}}^{\mathrm{PMT}}$ observable is shown on the left and the reconstructed zenith angle on the right. Simulated atmospheric muons are shown in blue and atmospheric neutrinos are shown in yellow. A 40% systematic uncertainty on their normalization is also included in the histograms. The expected distribution for a cosmic neutrino flux described by the best fit from the IceCube Northern Sky Tracks is shown for comparison in red.

Extended Data Fig. 2. Time residual distribution.

The time residual is defined as the difference between the time of arrival of the detected photons in the event and the expected time from Cherenkov radiation, induced by a relativistic muon. The distributions at various distances d from the track are shown, with coloured lines as indicated in the legend. In this figure, only the first hit on each PMT is used.

Extended Data Fig. 3. Energy measurement.

Left, the true muon energy E_μ maximizing the likelihood value for a given ${\mathcal{N}}_{\mathrm{trig}}^{\mathrm{PMT}}$ is shown as a blue line. The blue bands show the 1σ confidence level, computed from the likelihood distribution using Wilks’ theorem: in dark blue when only statistical uncertainties are considered, in light blue when systematic uncertainties are also included. The observed value ${\widehat{N}}_{\mathrm{trig}}^{\mathrm{PMT}}=\mathrm{3,672}$ corresponds to the horizontal dashed line. The resulting muon energy estimate is also reported (including systematic uncertainties). Right, log-likelihood profile for ${\widehat{\mathcal{N}}}_{\mathrm{trig}}^{\mathrm{PMT}}=\mathrm{3,672}$: the dashed blue curve represents the results when only the statistical uncertainty is considered, whereas the solid blue curve shows the results when including systematic uncertainties. The dashed horizontal lines represent the 1σ, 2σ and 3σ confidence level according to Wilks’ theorem.

Extended Data Fig. 4. Illustration of the topography.

Using bathymetric data from EMODnet, a sectional view along the incoming direction and position of the event is shown, with the sea shown in blue and the seabed and the rock beneath in brown. The x axis indicates the total distance from the ARCA site and the y axis and grey lines represent the depth with respect to the sea level. The shaded area shows the effect of a variation of ±1.5° in the direction reconstruction, corresponding to the 68% error region from the evaluation of systematic uncertainties.

Extended Data Fig. 5. All-flavour sky-averaged effective area for KM3NeT/ARCA.

The area in the 21 detection line configuration is shown as a function of neutrino energy. This effective area is computed after applying the event selection described in the text and is averaged between neutrinos and antineutrinos.