If neutrinos were massless, they would be always traveling at the speed light. This means that, as Einstein informed us, their clocks would not tick, and thus neutrinos could not change from one type to another. This stands in contradiction to neutrino oscillations observed in many neutrino experiments, such as the transformation of a muon neutrino into an electron neutrino recently reported by the Fermilab NOνA experiment.
Neutrinos are produced or detected as either an electron, muon or tau neutrino (νe, νμ or ντ); these are the neutrino flavors. By contrast the neutrinos that have a definite mass and travel unchanged in time are different admixtures of the neutrino flavors, and these massive neutrinos are unimaginatively called ν1, ν2 and ν3. Yes, quantum mechanics is weird, and for neutrinos it is applicable on macroscopic scales, from one to thousands of kilometers.
The flavor content and the mass of each of the massive neutrinos are the fundamental neutrino parameters. The size or amplitude of the oscillations tell us important information about the flavor content of the massive neutrinos, whereas the rate of the oscillations (the distance neutrinos travel divided by their energy) gives us important information about the mass-squared differences of the massive neutrinos.
Thus by measuring the rate and amplitude of the oscillations, we can extract information on the mixings and mass squared differences of the massive neutrinos.
Fermilab is not the only producer of person-made neutrinos in Illinois. The electric power companies also produce neutrinos in their nuclear power plants, hundreds of megawatts of neutrinos actually, or 2×1020 neutrinos per gigawatt of thermal power per second.
The neutrinos produced in these reactors are electron antineutrinos. Physicists from around the globe are involved in three large reactor neutrino experiments: Daya Bay (China), Double Chooz (France) and RENO (South Korea). Each of these experiments has both near (0.3-0.5 kilometers) and far (1-2 kilometers) detectors. The near detector(s) are used for both the normalization and the energy spectrum of the neutrinos coming from the reactors, thereby reducing the systematic uncertainties.
In 2012, each of these experiments measured the amplitude of neutrino oscillation, which tells us the νe fraction of the massive neutrino with the least amount of this flavor, this neutrino we call ν3. This fraction is denoted by sin2θ13 and is approximately 2.2 percent. More recently both Daya Bay and RENO have reported on a precision measurement how this oscillation varies as a function of baseline divided by neutrino energy, which gives us a precision measurement of the difference of the mass squared of ν3 and some combination of the mass squareds of ν1 and ν2. This mass squared difference is denoted as Δm2ee.
What combination of the mass squareds of ν1 and ν2 is used to form this mass squared difference? Since Δm231 and Δm232 differ in size by 3 percent, and the measurement uncertainties are approaching 4 percent, to extract the most information on the fundamental neutrino parameters, precision theoretical knowledge of what combination is measured in such experiments is crucial. This is where the Fermilab Theory Department is involved.
Ten years ago, two guest scientists, Hiroshi Nunokawa and Renata Zukanovich Funchal from Brazil, and I showed, by a detailed study of the neutrino survival oscillation probability, that the Δm2 measured in such reactor experiments, Δm2ee, is nothing more complicated than “the νe average of Δm231 and Δm232.” A surprisingly simple result with a direct physical meaning!