flavor eigenstates vs mass eigenstates

Here is the heart of why neutrinos oscillate, told as plainly as possible. There are two different ways to describe a neutrino, and they do not line up. One way labels it by the company it keeps in weak interactions — electron, muon, or tau flavor. The other way labels it by its definite mass. The puzzle is that a neutrino with a definite flavor does not have a definite mass, and one with a definite mass does not have a definite flavor.

Think of it like describing a colour. You could name a paint by its everyday label — 'electron', 'muon', 'tau' — or by the pure primary pigments mixed to make it. A 'flavor' neutrino is really a specific recipe blending three pure 'mass' neutrinos, each a different shade and a different weight. When a neutrino is born in a weak interaction it comes out as a flavor recipe. But as it travels through space it is the pure mass ingredients that move with steady, slightly different rhythms. Over distance the ingredients drift out of step, the recipe re-mixes, and what was an electron recipe gradually looks like a muon one.

This mismatch between the flavor basis and the mass basis is the entire mechanism of oscillation, and it only exists because the three mass states have different masses — if they were all equal there would be no drifting and no oscillation. The fixed relationship between the two descriptions, the exact recipe for blending mass states into flavor states, is captured by a table of numbers called the PMNS mixing matrix. The same flavor-versus-mass idea also appears for quarks, where it is encoded in a sibling table called the CKM matrix.