Atmospheric Neutrinos

When a high-energy cosmic ray — predominantly a proton — strikes a nucleus in the upper atmosphere, it produces a cascade of secondary particles. Most of the subsequent charged pions and kaons decay in flight: ${\pi }^{+}\to {\mu }^{+}{\nu }_{\mu },{\mu }^{+}\to e^{+}{\nu }_e{\bar{\nu }}_{\mu }$ (and charge-conjugate processes). Each pion decay chain produces two muon neutrinos (one prompt, one from the muon) and one electron neutrino, yielding the famous 2:1 flavor ratio at production: $\frac{N({\nu }_{\mu }+{\bar{\nu }}_{\mu })}{N({\nu }_e+{\bar{\nu }}_e)}\approx 2$ This ratio was known precisely from pion and muon decay kinematics long before atmospheric neutrinos were used as a probe of oscillation.

Energy range and flux

Atmospheric neutrinos span a very wide energy range. The conventional flux from pion and muon decays peaks below 1 GeV and falls steeply (roughly $E^{-3}$) at high energy. Above about 100 GeV, muons reach the ground before decaying and the flux becomes “prompt” — dominated by short-lived charmed mesons whose rapid decays still contribute. At the highest energies relevant to IceCube (10 TeV and above) the conventional flux drops below the astrophysical neutrino flux, allowing extragalactic sources to dominate.

Typical rates:

• Kamiokande, 1 GeV range: a few hundred atmospheric events per year per kiloton
• IceCube, > 100 GeV: about $10^5$ events per year across 1 km³ of ice

The 1998 discovery

Super-Kamiokande analyzed the zenith-angle distribution of atmospheric neutrinos. Upward-going neutrinos have traversed the full Earth diameter (~12,800 km); downward-going neutrinos have traveled only the atmospheric depth (~15 km). In the absence of oscillation the two fluxes should be equal (modulo small geomagnetic effects).

Super-K found the up-down ratio for electron-like events consistent with one, but the ratio for muon-like events significantly below one for upward-going events — a clear zenith-angle-dependent deficit. The kinematics matched ${\nu }_{\mu }$ oscillating into ${\nu }_{\tau }$ with $\Delta m^2\sim 2\times 10^{-3}$ eV² and near-maximal mixing.

Announced in June 1998 at the Neutrino ‘98 conference in Takayama, the result was the first convincing oscillation observation. Takaaki Kajita shared the 2015 Nobel Prize for this work.

Current use as a probe

Atmospheric neutrinos continue to provide a uniquely broadband probe. At a given detector, they span six orders of magnitude in $L/E$, allowing multiple oscillation channels to be studied simultaneously. Relevant applications include:

• Mass ordering determination through matter-enhanced MSW resonances in the Earth’s mantle and core (IceCube-DeepCore, PINGU, ORCA, INO)
• Constraints on non-standard interactions via the energy and zenith dependence of the survival probability
• Tests of Lorentz invariance and CPT symmetry through any anomalous zenith- or azimuth-dependence
• Sterile neutrino searches in the eV–keV mass range

Astrophysical component

Above a few tens of TeV, the atmospheric flux becomes sub-dominant to astrophysical neutrinos. IceCube’s 2013 discovery of a high-energy astrophysical flux was made possible by this crossover: events up to the PeV range can be cleanly attributed to extragalactic sources. This astrophysical component is discussed separately under neutrino astronomy rather than here.

The atmospheric flux remains the foreground — and the most statistical — component in any neutrino telescope.