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In 1998 there was an announcement of new evidence in favor of a nonzero mass for the neutrino. Here we summarize the experimental results that form the basis for that claim. See pages 394-95 in the text for the relevant background discussion.
The neutrino experiment is known as Super Kamiokande, and consists of a chamber located a kilometer underground, lined with sensitive light detecting photocells, and filled with 50 thousand tons of ultrapure water. Neutrinos reveal their presence by interacting with electrons and protons in the water to produce tiny flashes of light. The water has to be very pure to allow the photocells to see clearly through this vast volume of water. A smaller version of this experiment detected neutrinos from the 1987 Supernova in the Large Magellanic Cloud.
In the present experiment, the neutrinos to be detected come not from a distant supernova, but from the Earth's upper atmosphere. Neutrinos are produced there by the impact of cosmic-ray protons and nuclei. These cosmic-ray interactions generate many types of particles that rain down toward the Earth's surface. Among these particles are muon and electron neutrinos. Theory predicts that twice as many muon neutrinos should be produced by cosmic rays as electron neutrinos. Most particles are blocked by the Earth and do not reach the detector deep underground, but the neutrinos do. The experiment counts the number of muon neutrinos and electron neutrinos (they can be distinguished) and compares the results to the expected (roughly) 2:1 ratio.
What the Super Kamiokande found was a shortage of muon neutrinos, which suggests that some of the muon neutrinos have turned into something else between the time they were formed and when they pass through the detector. This provides evidence for neutrino oscillation which would only occur if the neutrino has mass. Interestingly the data do not support the idea that the muon neutrino is turning into the electron neutrino. It might be turning into the tau neutrino (which cannot be detected by Super Kamiokande) or into something else.
The experiment provides evidence that muon neutrinos can turn into something else and hence must have a nonzero mass. But it doesn't say for certain what that mass is, although the best evidence is consistent with a very small mass, too small to close the universe. But it is possible that the massive neutrino still serves as a "hot dark matter" component in the formation of galaxies and large-scale structure in the universe.