mixing angles and mass-squared differences

Neutrino oscillation has a handful of dials that nature has set to particular values, and measuring those settings has been a decades-long quest. There are two families of numbers. The first family, the mixing angles, says how thoroughly the flavors and mass states are blended — how far the recipes overlap. The second family, the mass-squared differences, sets the rhythm — how quickly the oscillation cycles as a neutrino flies.

There are three mixing angles, usually written theta-12, theta-23, and theta-13. Theta-12, measured with solar neutrinos, is large; theta-23, measured with atmospheric and accelerator neutrinos, is large and close to maximal; theta-13, the smallest, was the hardest to find and was finally measured around 2012 with reactor neutrinos. The two mass-squared differences are the gaps between the squares of the three masses: a smaller 'solar' splitting and a larger 'atmospheric' one, the larger being roughly thirty times the smaller. Crucially, oscillation depends only on these squared differences, never on the raw masses, which is why it can prove neutrinos have mass without revealing how heavy they are.

These six or so numbers are now the core inputs of neutrino physics, measured to increasing precision by experiments around the world. Yet they raise as many questions as they answer. The values look oddly different from the quark sector, the absolute mass scale stays hidden, and the sign of one splitting (the mass ordering) is still unknown. Together with the unmeasured CP phase, the oscillation parameters are a small, sharp window onto whatever new physics gives neutrinos their masses.