Atmospheric Neutrinos: From Cosmic Rays to Earth

Every second, about 100 atmospheric neutrinos cross each square metre of the Earth’s surface. They come from cosmic-ray interactions in the upper atmosphere — pions and kaons produced when high-energy cosmic rays strike air molecules, decaying in flight to produce muons and neutrinos. The flux is steady (varies only slightly with the solar cycle), free, omnidirectional, and spans an energy range of a billion-fold from sub-GeV to multi-PeV.

For neutrino physics, atmospheric neutrinos have been the gift that keeps on giving. The Kamiokande experiment first reported an unexpected deficit of muon neutrinos in 1988. The IMB experiment confirmed the deficit independently. Super-Kamiokande’s 1998 measurement of the zenith-angle-dependence transformed the deficit into definitive evidence of ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation — the discovery that earned Takaaki Kajita and Arthur McDonald the joint 2015 Nobel Prize. Twenty-eight years after the first observation, atmospheric neutrinos continue to provide some of the most precise oscillation measurements available.

This post is the comprehensive picture: how atmospheric neutrinos are produced, what they look like at Earth, how they’re detected, and what they tell us about neutrino physics today.

Production: from cosmic ray to neutrino

A high-energy cosmic ray (typically a proton, with ~10% admixture of heavier nuclei) entering the Earth’s atmosphere strikes an air molecule at an altitude of 15–30 km. The collision produces a shower of secondary particles, dominated by pions (${\pi }^{\pm }$, ${\pi }^0$) and kaons ($K^{\pm }$, $K_L^0$).

The neutral pion (${\pi }^0$) decays almost instantly to two photons and produces no neutrinos. The charged pions and kaons live long enough to decay before being absorbed: ${\pi }^{+}\to {\mu }^{+}+{\nu }_{\mu }(\text{lifetime: 26 ns})$ $K^{+}\to {\mu }^{+}+{\nu }_{\mu }(\text{lifetime: 12 ns, with similar branches to other channels})$

Each ${\pi }^{+}$ decay produces a ${\mu }^{+}$, which then decays: ${\mu }^{+}\to e^{+}+{\nu }_e+{\bar{\nu }}_{\mu }(\text{lifetime: 2.2 μs})$

The full chain produces, per pion: 1 ${\nu }_{\mu }$, 1 ${\bar{\nu }}_{\mu }$, 1 ${\nu }_e$. Antiparticles produced by ${\pi }^{-}$ decay produce the conjugate flux.

This explains the famous 2:1 muon-to-electron flavor ratio at production: $\frac{N({\nu }_{\mu })+N({\bar{\nu }}_{\mu })}{N({\nu }_e)+N({\bar{\nu }}_e)}\approx 2$ This ratio is essentially energy-independent over the GeV range, with departures at higher energies because muons are more likely to be absorbed before decaying.

The cosmic-ray spectrum

The atmospheric neutrino flux is convolved with the cosmic-ray spectrum at the top of the atmosphere. Cosmic-ray flux follows a broken power law:

• Below the “knee” ($\sim 10^{15}$ eV): galactic cosmic rays, accelerated by supernova remnants. Spectrum $\sim E^{-2.7}$.
• Knee ($\sim 10^{15}$ eV): a steepening, possibly indicating the maximum acceleration energy of galactic sources.
• Ankle ($\sim 10^{18}$ eV): a flattening, possibly the transition to extragalactic cosmic rays.
• GZK cutoff ($\sim 10^{19.5}$ eV): suppression from interactions with the cosmic microwave background.

The atmospheric neutrino flux inherits this structure, modified by the propagation/decay kinematics of pions and kaons. At low energies (below ~1 TeV), the flux falls as $E^{-2.7}$. At higher energies, kaons take over from pions as the dominant source (their longer interaction length means they decay before being absorbed at high energies), and the spectrum steepens to $E^{-3.7}$.

What the flux looks like

The atmospheric flux at Earth’s surface, integrated over zenith angle:

Energy range	Flux (m⁻² s⁻¹ sr⁻¹)
0.1 – 1 GeV	~$10^4$
1 – 10 GeV	~$10^2$
10 – 100 GeV	~$10$
100 GeV – 1 TeV	~$1$
1 – 10 TeV	~$0.1$
10 – 100 TeV	~$10^{-2}$

Above approximately 100 TeV, the atmospheric flux begins to be exceeded by the astrophysical neutrino flux (cosmic neutrinos from extragalactic sources, observed by IceCube). Below this transition, atmospheric neutrinos dominate.

The flux has a strong zenith-angle dependence. Neutrinos coming from directly overhead have only a few hundred grams per square centimetre of atmosphere to traverse before reaching a surface detector. Neutrinos coming from the opposite side of the Earth (“upward-going”) have travelled through approximately 10,000 km of rock and the full atmosphere — but Earth is essentially transparent to MeV-GeV neutrinos.

This zenith dependence is what enabled Super-Kamiokande’s 1998 oscillation measurement: by measuring the muon-to-electron flavor ratio as a function of zenith angle, they could probe oscillation across baselines from 10 km (downward-going) to 12,800 km (upward-going).

Detection

Atmospheric neutrinos are detected primarily via charged-current scattering in detector materials: ${\nu }_{\mu }+N\to {\mu }^{-}+X,{\nu }_e+N\to e^{-}+X$

The outgoing charged lepton produces an observable signal. Energy spectroscopy and direction reconstruction depend on the detector technology.

Water Cherenkov (Super-Kamiokande, Hyper-Kamiokande): GeV-scale neutrinos produce muons or electrons that emit Cherenkov rings. Muons make sharp rings; electrons make fuzzy ones. The rings are reconstructed to give particle direction and energy. Sensitive to ~0.1 to ~50 GeV neutrinos.

Liquid argon TPC (DUNE): Sub-millimetre track reconstruction. Best identification of multi-particle final states. Sensitive to ~0.1 to ~50 GeV.

Liquid scintillator (KamLAND, JUNO): Limited spatial resolution but excellent energy resolution. Sensitive to the lowest energies.

Underground/Underwater Cherenkov (IceCube, KM3NeT): Very large volume but coarse spatial resolution. Sensitive to TeV–PeV neutrinos.

The combination of these technologies gives complementary measurements across the full energy spectrum.

Atmospheric oscillation

The fundamental phenomenon: muon neutrinos produced in atmospheric showers oscillate into tau neutrinos during their flight through the Earth. The oscillation probability depends on: $P({\nu }_{\mu }\to {\nu }_{\tau })\approx {\sin }^2(2{\theta }_{23}){\sin }^2\left(\frac{\Delta m_{31}^{2}L}{4E_{\nu }}\right)$

For atmospheric neutrinos:

• $L$ = baseline (10 km for downward, up to 12,800 km for upward)
• $E_{\nu }$ = neutrino energy (a few hundred MeV to ~50 GeV typically)

The first oscillation maximum occurs at $L/E\sim 500$ km/GeV. For 1 GeV neutrinos, this is 500 km — well within the Earth’s diameter. So upward-going ${\nu }_{\mu }$ have largely oscillated to ${\nu }_{\tau }$, while downward-going have not.

Super-K’s 1998 zenith-angle plot showed exactly this pattern: the muon-neutrino flux deficit is maximal for upward-going events (around $L\sim 10,000$ km) and absent for downward-going (around $L\sim 10$ km). This was the smoking-gun evidence for atmospheric oscillation.

Mass-ordering sensitivity

Atmospheric neutrinos provide unique sensitivity to the mass ordering through matter-induced resonance. As atmospheric neutrinos traverse the Earth’s mantle, the Mikheyev-Smirnov-Wolfenstein effect modifies the oscillation probability. In the mantle, the effective mixing is enhanced for ${\nu }_{\mu }\to {\nu }_e$ (in normal ordering) or for ${\bar{\nu }}_{\mu }\to {\bar{\nu }}_e$ (in inverted ordering).

The signature is a resonance at energies around 5–10 GeV for neutrinos travelling through the deepest part of the mantle (zenith angles around 145°). The presence or absence of this resonance, and its sign, distinguishes the two mass orderings.

ORCA at KM3NeT is specifically designed for this measurement. Hyper-K and DUNE will also contribute via their atmospheric channels. By the early 2030s, atmospheric data from all three experiments combined should determine the mass ordering at high statistical significance.

Other physics enabled

Atmospheric neutrinos contribute to several ongoing physics programmes:

Sterile-neutrino searches: Long-baseline atmospheric data tightly constrain mixing of active neutrinos with eV-scale sterile states. The lack of unexplained anomalies in atmospheric data is one of the strongest constraints on the sterile-neutrino interpretation of LSND/MiniBooNE.

Atmospheric flavor ratio: The 2:1 expected production ratio, combined with measurements at IceCube and Super-K, tests both the cosmic-ray composition and oscillation effects. Unexpected ratios at high energies could indicate beyond-Standard-Model physics like sterile-neutrino oscillations or non-standard interactions.

Tau-neutrino appearance: Atmospheric beam offers clean tests of the matrix element $|U_{\tau 3}{|}^2$. Both Super-K and IceCube have observed tau-neutrino-like events in their atmospheric samples.

Dark-matter capture in the Sun: Some dark-matter scenarios predict that WIMPs in the Sun annihilate to produce neutrinos at GeV energies. Searches in the atmospheric-neutrino-rich GeV regime constrain these models. Current limits are dominated by Super-K and IceCube atmospheric data.

Why this source endures

Three decades after the Kamiokande deficit measurement, atmospheric neutrinos remain one of the most-used neutrino sources. Several reasons:

Free. No accelerator, no reactor, no purification — just cosmic rays and the atmosphere.

Omnidirectional. Sample the full sky at all times, no scheduling required.

Broad spectrum. GeV to PeV in a single source.

Large baseline range. From a few km to ~13,000 km, accessible to any underground detector.

Constant. Annual variation under 5%, no time-of-day variation. Long-term integration gives high statistics.

The 1998 atmospheric oscillation discovery was a result of patient cosmic-ray-neutrino observation over many years. The same discipline continues to yield new physics today and will into the 2030s and beyond.