Over the past few decades, we have worked to measure their absolute masses, but so far have only determined a succession of ever-more-stringent upper limits. Most attention is focused on the electron neutrino, because it allows for the most stringent limits. The technology of choice is the beta decay of tritium - an isotope of hydrogen consisting of one proton and two neutrons. Tritium decays into helium three, plus an electron and an electron-neutrino, with a half life of 12.3 years. This is a low-energy decay, releasing about 18,590 electron volts of energy. For comparison, other, more typical beta decay reactions release ten to thirty times as much energy. Another point of comparison is an old-fashioned cathode-ray tube in a television receiver, which uses electrons accelerated to up to 25,000 volts - more than from tritium beta decay.
In these beta decay reactions, some of the energy is carried off by the neutrino, with most of the rest going into the electron; the recoiling helium-3 also carries off a bit of energy. Because beta decay is well understood, we can very accurately predict the distribution of energies carried off by the electron; this predicted spectrum has a small dependence on the neutrino mass;. The number of events where the electron carries off almost all of the energy decreases as the neutrino mass increases. We can fit the electron energy spectrum in this endpoint region to determine the neutrino mass.
The KATRIN collaboration has done this, and just released a new upper limit on the electron-neutrino mass; it is less than 0.45 electron volts, at a 90% confidence level. For comparison, this is less than one one-millionth of the mass of the electron. It is about a factor of 2 below previous measurements. The result is an enormous tour-de-force, since the change in the energy spectrum is tiny. The collaboration used an enormous spectrometer (pictured above) and studied 36 million electrons, which were already selected for being of particularly high energy.
Although KATRIN will release results with more data, and, likely, a tighter upper limit, this is near the end of the line for the spectrometric approach that we have used for the past few decades. A better spectrometer would also have to be a bigger spectrometer, and it is just not possible (economically, and probably technically) to build a much larger instrument. Instead, we are starting to investigate new approaches that involve trapping electrons in a uniform magnetic field, and observing the synchrotron radiation that they produce, using very sophisticated radio detectors.
