Abstract. Long assumed to be massless, the ubiquitous yet ghostly neutrino may have some substance after all. After a brief introduction to the tiny subatomic particle, I discuss two popular methods of measuring its mass: direct measurement and indirect via detection of so-called "neutrino oscillations." Promising claims of nonzero mass from indirect measurements are presented, along with implications for particle physics, solar dynamics, and the ultimate fate of the universe.
"Invented" in 1930 by Wolfgang Pauli to account for energy seemingly lost in the neutron decay process, the neutrino long evaded detection. The lengthy interval (almost twenty years) between Pauli's theoretical prediction and experimental detection is surprising, considering that the particle is copiously produced by nuclear fusion in the sun and by the decay of naturally occurring particles in the upper atmosphere. Indeed, hundreds of billions of solar neutrinos pass through each square inch of our bodies every second ! The elusive character of the neutrino is the result of its extremely weak interactions with matter, a consequence, in part, of being electrically neutral. If the neutrino were charged, it would interact with many more particles than it does and thus give more signs of its existence.
Pauli assumed a precisely zero neutrino mass. Testing this assumption is even harder than detecting a neutrino, primarily because the mass is zero or almost zero. Direct measurement, being limited to producing bounds on the mass, is particularly difficult and imprecise. Current bounds are about one ten thousandth of the electron mass! This is consistent with massless neutrinos but does not dismiss the possibility of mass. An example of the direct approach comes from the analysis of neutrinos from a supernova seen in 1987. This supernova produced a large burst of neutrinos with varying energies. While massless particles travel at the speed of light, massive particles travel at strictly smaller speeds, depending on their masses and energies. Hence, the neutrinos in this burst, if massive, traveled at varying speeds, rather than uniformly at the speed of light. Measurement of the difference in arrival times of these stellar neutrinos yields a bound on the mass but nothing definitive.
While direct approaches remain severely limited, indirect measurement has made substantial progress recently by successfully detecting the phenomenon called neutrino "mixing" or "oscillation" . Neutrinos come in three species or "flavors": electron neutrinos, muon neutrinos, and tau neutrinos. Mixing allows a neutrino to change its flavor sometime between creation and detection. Because the probability of this event is proportional to the difference in mass between the two flavors involved, a nonzero probability implies a mass difference . A difference requires at least one flavor to have nonzero mass; therefore, detection of neutrino mixing is detection of neutrino mass. These unequivocal results are clearly superior to those of direct techniques.
The principle seems clear enough theoretically, but how can these oscillations be detected in practice? The method varies with the type of experiment, which is essentially determined by the type of neutrino source. Experiments so far have used neutrinos from reactors and accelerators, the atmosphere, and the sun. Reactor and accelerator experiments typically generate a large number of neutrinos from a known reaction and then observe how many particles remain after traveling some distance. Neutrino mixing manifests itself in the disappearance of a large fraction of the neutrinos of a particular flavor . Similarly, experiments utilizing atmospheric neutrinos or solar neutrinos attempt to measure a difference between the number expected and the number actually detected.
Measuring a nonzero mass is significant for several reasons, not least of which is simply that particle physicists have assumed the contrary since 1930. Many theories naturally would need revision to accommodate the unexpected mass, if confirmed. Nonzero mass also could explain why the sun appears to produce fewer electron neutrinos than theorists predict: some oscillate into other flavors. Finally, massive neutrinos would have important cosmological implications. Because the universe contains a huge number of neutrinos, their mass would be a large fraction of the total mass in the universe. This total determines whether the universe will continue expanding or eventually collapse; so unexpected additional mass could change current predictions of the fate of the universe .
The idea of neutrino oscillations, long thought to be only of theoretical interest but now apparently vindicated by experiments, has carried mass measurements beyond conventional approaches. No longer limited to chipping away at already tiny mass bounds, experimenters can produce solid evidence of mass. Experiments to confirm the recent detections of neutrino oscillations should produce definitive results soon . This signals an exciting time in physics. Not only will much of particle physics need revision, predictions of the fate of the universe could be changed.
 David Griffiths, Introduction to Elementary Particles (Wiley, New York, 1987), pp. 22-28.
 John Learned, "Discovery of Neutrino Oscillations and Mass" (Online: http://www.phys.hawaii.edu/,jgl/neutrino news.html), June 1998.
 Wick C. Haxton and Barry R. Holstein, hep-ph/9905257, (1999).