# What Are Atmospheric Neutrinos?

Returning to the subject of the Nobel Prize, you might be wondering what the physics prize this year was actually about.

What matters for these experiments is (1) neutrino flavor, (2) neutrino baseline (distance traveled from being in a more or less known flavor configuration) and (3) neutrino energy. Atmospheric neutrinos are one of the several different ways that we can study oscillations.

High energy particles coming in from space (i.e. cosmic rays) are generally nuclei (most often just protons). Upon reaching the atmosphere, these particles often have enough energy to undergo inelastic collisions with the particles in the atmosphere. The most common types of events would be hadronic showers, where the strong force allows for more hadrons to be created. The most common hadrons created in showers are pions, which are the lightest mesons (bound quark-antiquark states). Charged pions decay through the weak force into neutrinos and charged leptons. It turns out that pions decay to muons and muon neutrinos well over 99% of the time. Thus, cosmic rays create muon neutrinos (and antineutrinos) within the atmosphere. Typical energies are also much higher than is found in nuclear processes, so atmospheric neutrinos can be distinguished from solar and beta decay neutrinos.

Because neutrinos don’t really interact much with anything else, cosmic ray neutrinos can also pass straight through Earth. If a neutrino detector can reconstruct the direction of the neutrino, it can then look for short baseline neutrinos (from above) and long baseline neutrinos (from below). A pretty broad energy spectrum is also found. It also happens that neutrino oscillations (in a simplified two-neutrino case) evolve like:

$P(\nu_\ell\rightarrow\nu_{\ell'})\propto \sin^2 \frac{\Delta m^2 L}{4E}$

Theshape of the oscillations depends on the mass splitting and on the ratio of baseline to neutrino energy. If the mass splitting is too small, then not enough oscillations will happen to measure them. If the mass splitting is too large, the oscillations will be happening so fast that any realistic detector will just measure the unoscillated spectrum with an extra scaling constant of 1/2.

Fortunately, it just so happens that one of the mass splittings relevant to a sample of nearly pure muon neutrinos leads to oscillations that are readily measurable to the GeV-scale atmospheric neutrinos. So, the oscillations should be apparent if one looks at the ratio of the upward-going (long baseline/oscillated) neutrinos to downward-going (short baseline/unoscillated) neutrinos. A characteristic sinusoidal shape should be seen if this ratio is plotted as a function of L/E. This allows for precision fits of oscillation parameters using atmospheric neutrino data.