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Atmospheric neutrinos were first studied in the context of being background to nucleon decay searches. However, it was found that the above mentioned ratio of muon- to electron-neutrinos was significantly lower than the expected value from detailed predictions. It was tempting to entertain the notion that the muon neutrinos were oscilating either into an electron neutrino or some other flavor which the detectors were not sensitive to, such as a tau or sterile neutrino. However, until recently, when SuperK announced strong evidence for netrino oscilations there was always room for doubt. It still may be correct to doubt interpreting the atmospheric netrino problem as neutrino oscillations, but one would need to come up with an alternative and probably even odder solution.
Since water Cherenkov detectors do not see neutrinos directly, but rather see the products of the interaction of neutrinos and the nuclei in the water the ratio of muon neutrinos to electron neutrinos is not measured directly. Instead, the data is sampled for single ring only events and the type of particle which produced this single ring is determined. These events mostly preserve the type and direction of the original neutrino. That is, muon neutrino interaction products are usually identified as muon type rings and etc for electron neutrinos. Examples of a muon type ring and an electron type ring are shown at the top of this page. Muons tend to create sharp ring edges, but electrons induce an electromagnetic shower through brehmstrahlung and pair production and so have a fuzzy edged ring due to the many small overlapping rings from all the electron-positron pairs in the shower.
Once the particle type is identified, the ratio of muon type rings to electron type rings is found in the data. Finally, due to large systematics in the absolute flux and crossections in the theoretical predictions the so called ``double ratio'' or ``ratio of ratio'' (denoted by R), is formed. This is defined as the ratio of the ratio muon type rings to electron type rings for data to the same ratio for Monte Carlo simulations. This causes much of the theoretical systematic errors to cancel.
The current SuperK results on atmospheric neutrinos are separated in to two classes. Historically, from Kamiokande, the energy spectrum has been split into ``Sub GeV'' and ``Multi GeV'' ranges at 1.33 GeV. Recent results for these Sub GeV and Multi GeV regions are available from the LANL preprint server. These two reports have been submitted to PRB. SuperK's report on a neutrino oscillation interpretation of this data has been submitted to PRL and is available as a LANL preprint. In addition, all of the mentioned papers are available from SuperK's publication page.