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Neutrino Oscillations and Neutrino Mass

In five distinct measurements, Super-Kamiokande finds neutrinos apparently "disappearing". Since it is unlikely that momentum and energy are actually vanishing from the universe, a more plausible explanation is that the types of neutrinos we can detect are changing into types we cannot detect.  This phenomenon is known as neutrino oscillation. Neutrino oscillation is not black magic - there are very specific predictions for the behavior of our data if neutrinos oscillate, and we have uniformly found the data in good agreement with these predictions.  Unfortunately, a non-mathematical explanation of why neutrino oscillation and neutrino mass are inseparable is difficult. A more detailed, yet still non-mathematical explanation, and a full calculation, using basic quantum mechanics, are provided for those inquiring minds who want to know.

It is much easier to explain why our data appear to lead inexorably to the conclusion that neutrinos are oscillating. The secret lies in the fact that the neutrinos observed by Super-Kamiokande are without exception produced at great distances from the detector. Neutrinos produced in the atmosphere arrive at the detector from distances of about 40 km (if produced above it)  to 12,000 km (if produced on the other side of the Earth). These distances are significantly greater than any measurements made to date with neutrinos from accelerators or nuclear reactors on Earth. The Sun, clearly, is much, much further still. The great distances not only allow us to detect effects which would be invisible with a closer neutrino source, they also allow us to measure the behavior of neutrinos produced over a great range of distances. This ability in fact leads to some of the most dramatic evidence that oscillations are occurring.

The probability of a neutrino changing type is related to the distance travelled by the neutrino from its point of production to its point of detection.  As a general rule, neutrinos travelling greater distances will exhibit greater depletion from oscillation. Moreover, the oscillation probability varies smoothly over increasing distance. Hence, tests of the angular variation of the muon rate are the best to determine whether the overall deficit of muon neutrinos fits the hypothesis of oscillation as opposed to other some unaccounted-for systematic effect.  In all cases, the angular (neutrino pathlength) variation of the muon rate agrees with the oscillation hypothesis.

The oscillation probability is also a function of the neutrino energy, and here again we sample a large range of values, roughly a factor of 1000 from the Sub-GeV sample to the through-going upward muons. Although estimation of the neutrino energy giving rise to a given interaction is necessary approximate, there are no inconsistencies in the behavior of the different data sets, and all the atomospheric data agree well with the oscillation hypothesis regardless of energy.

Why the neutrino mass must be non-zero

The reason neutrino oscillation is relevant to the question of neutrino mass is that massless neutrinos cannot oscillate. Put another way, observation of oscillation implies that the masses of the neutrinos involved cannot be equal to one another. Since they cannot be equal to one another, they cannot both be zero. In fact it is quite likely that if any neutrinos have non-zero mass, all of them do.

 

Dave Casper