The neutrino is a fundamental particle that is generated in particle decays and nuclear reactions and that, in the standard model, interacts only via the weak force. At Earth's distance from the Sun, about 65 billion solar neutrinos pass through every square centimeter every second, and the vast majority of them pass right through the planet. Neutrinos interact so rarely that they were originally assumed to be massless, but in the last two decades several clever experiments showed that they do have mass. Neutrinos' three different flavor states -- electron, muon, and tau, named for the charged leptons they're associated with -- are admixtures of three different mass states, m1, m2, and m3. The quantum mechanics of this scenario leads to the phenomenon of mixing: a neutrino created as an electron neutrino has some probability of being detected, some distance away, as a muon neutrino. Oscillation experiments, which study this mixing as a function of neutrino flavor, energy, and distance, have told us how far apart these three mass states are, but cannot tell us the absolute mass scale.
The absolute neutrino mass scale is interesting for several reasons. We know that neutrinos are very light: electrons, the next lightest known particles, weigh at least 500,000 times more. This points to the possibility that neutrino masses arise from a different sort of process compared to other particles. We also know that the universe is filled with neutrinos, streaming through, and these neutrinos will have affected the way that structures formed in the chaos after the Big Bang. Neutrino mass is an important input to cosmological models.
It's a hard thing to measure, though. There are a few different ways to access the mass, but the best direct limits, with the least model dependence, have come from precision measurements of tritium beta decay. When tritium -- a radioactive isotope of hydrogen with one proton and two neutrons -- decays, it leaves behind a 3He daughter nucleus, a beta electron, and an electron antineutrino. The mass energy of the initial T nucleus is divided up among the masses and kinetic energies of all three daughters. We can calculate the kinetic energy given to the 3He daughter and we can, separately, measure the masses of the two nuclei to fairly high precision, leaving us with the beta and the neutrino. The neutrino mass represents energy that the beta electron cannot carry away. If we measure the high-energy tail of the beta spectrum, examining the distribution of the betas that carry away the very largest amounts of energy, we will see the signature of that neutrino mass.
In the late 1990s and early 2000s, two experiments, Mainz (2005 publication) and Troitsk (2003 publication, 2011 publication), used this strategy to set the best pre-KATRIN direct limit on the neutrino mass, less than 2 eV at 90% confidence. The KATRIN experiment, now running in Karlsruhe, Germany, will improve on that limit by an order of magnitude. The principle of KATRIN is simple, but its execution is complex. A windowless, gaseous T2 source will supply betas at a rate of 1011 decays every second, but only 1/1013 of those is useful for the measurement. The rest will be filtered out by a pair of spectrometers, electromagnetic integrating filters that collimate the betas and reject those with kinetic energy below a certain threshold. Varying the threshold will allow us to map out the shape of the spectrum as a function of energy. A 148-pixel silicon detector watches the output from the main spectrometer, which has a design energy resolution of 1 eV. An extensive transport system, between the source and the spectrometers, will pump out tritium while allowing beta electrons to pass through. An electron gun, mounted behind the source, allows regular systematic checks, while the spectrometer from the Mainz experiment and two high-precision voltage dividers constantly monitor the main spectrometer energy threshold. Every system poses its own challenges and every systematic must be studied, from the operating temperature of the detector to the molecular physics of the source.
In its first two measurement campaigns, KATRIN has dramatically improved on past limits. First, we established that the effective neutrino mass is less than 1.1 eV at 90% confidence (short paper in Physical Review Letters; long paper on analysis methods). Now, combining these data with a larger data set from Fall 2019, we've found that the effective neutrino mass is less than 0.8 eV at 90% confidence (preprint paper on arXiv). We are continuing to run the experiment, learn more about our systematics, and close in on the neutrino mass! There's also research and development on the farther future of KATRIN: the TRISTAN project would upgrade KATRIN's detector system to enable a sensitive search for keV-scale sterile neutrinos, which (if they exist) could help explain the dark matter in the universe. (Here's a short paper on the TRISTAN detector development so far.)