Neutrinos are the lightest and quite possibly strangest of the Standard Model’s fundamental particles. It turns out that neutrinos can change their type or “flavor.” This has been demonstrated experimentally in the KamLAND, MINOS, Super-Kamiokande, KEK to Kamioka (K2K), and Sudbury Neutrino Observatory (SNO) experiments. Oscillations have been seen in neutrinos coming from the atmosphere, nuclear reactors, particle accelerators, space, and deep in the Earth. This oscillation of flavor is explained by the mixing of (at least) three unique mass states. The way these mass states mix is determined by unique mixing angles.
For a simplified example, a two (instead of three) flavor system can be examined. The following describes the two flavor states as a combination of two mass states:
where θ is the mixing angle. Through some quantum mechanics and general relativity, the probability of a neutrino changing flavor can be shown to be:
where L is the distance traveled by the neutrino and Eν is the energy of the neutrino. The important thing to recognize here is that the mixing angle can be measured in terms of the probability, distance and energy, all of which can also be measured. This model can be expanded to work for a three flavor system.
For a more detailed explanation of the theory and physics involved, check out the following:
Neutrino Oscillations (Wikipedia)
Neutrino Mass, Mixing, and Flavor Change (PDG Paper)