## The Atmospheric Neutrino Anomaly

IMB found a ratio of ratios equal to (0.54 +/- 0.13) and Kamiokande found a ratio of ratios equal to (0.57 +/- 0.10). This significant difference implies one of two things. Either the simulation is wrong or the standard model prediction of 2:1 muon to electron neutrinos from pion decay is wrong. A third possibility is that the data is simply misinterpreted. Whatever the cause, this difference of the ratio of ratios from 1 is called the Atmospheric Neutrino Anomaly.

It seems unlikely the simulation is wrong. The largest source of uncertainties comes from an ignorance of the energy dependent neutrino cross sections. However, these uncertainties tend to cancel out in the ratio of ratios. It also seems unlikely the data has been misinterpreted. This could happen if muon events were misidentified as electron events or vice versa. But the chances of several different experiments making the same misidentification are rather small. None the less, this possibility has been tested at the KEK accelerator in Japan. There specific particles with known energies were shot into a small water cerenkov tank. The particles were electrons, muons and pions which are the bulk of the products that come from neutrino interactions. Initial results from this test show there is very little misidentification.

## Neutrino Oscillations

This leaves the possibility of new physics. Current theory holds that lepton number is conserved. Lepton number indicates the type of neutrino so this basically means that muon neutrino will always be a muon neutrino. But what if this is not the case? What if neutrinos changed type as they moved through space? This is possible if neutrinos have even a small mass and if that mass is different for each type. In this theory the probability for a neutrino to change type varies periodically with distance and is referred to as neutrino oscillations. This is one possibility for the atmospheric neutrino anomaly. Neutrino oscillations are not included in the simulation. If the muon or electron neutrinos are changing type before they enter the detector that would cause a discrepancy between the measured and predicted ratios.

## Recent Results

Actually, neutrino oscillations depend on the quantity distance over energy. Energy refers to energy of the neutrino. Neutrinos can easily pass through the entire earth, so the distances vary from the height of the atmosphere to the diameter of the earth. The distances are related to zenith angle which is the angle the neutrino makes with a line perpendicular to the ground. Basically, the larger the zenith angle the larger the distance.

At low energies, no matter what the zenith angle, the neutrinos travel over many periods of the oscillation and so an average of the curve is observed. This means the discrepancy between measured and predicted ratios (the ratio of ratios) will be constant no matter from what direction the neutrinos come. However, at high energies the amount of oscillation depends mainly on the distance and thus zenith angle. Downward going neutrinos, which have the smallest zenith angle the smallest distance, should be less effected by neutrino oscillations than upward going neutrinos. Likewise, the ratio of ratios should be close to 1 for neutrinos with small zenith angles but much different from 1 for neutrinos with large zenith angles.

Initially, the neutrinos collected in both IMB and Kamiokande were low energy. Low in this case means that less than 1 GeV of energy was visible in the detector. Higher energy events were ignored since it is impossible for the products from proton decay to have more than 1 GeV total energy. The ratio of ratios for both detectors was less than 1 and independent of zenith angle. This agrees with the theory of neutrino oscillations but could also be true of a number of other explanations.

Once it became clear that neutrinos were about as interesting as proton decay, IMB and Kamiokande began saving the high energy events. The Kamiokande collaboration recently analyzed their high energy set and found that the ratio of ratios decreases with increasing zenith angle exactly as expected for neutrino oscillations.

--Russell Clark