# How can I understand neutrino mixing and the difference between flavour and mass eigenstates?

I understand that if neutrino flavour is just a superposition of mass eigenstates, the probabilities of detecting a particular flavour of neutrino will vary as they propagate since the time evolution factors of the mass eigenstates advance differently. The problem I'm having is understanding why the flavour and mass eigenstates are different and mix this way in the first place.

I need to be able to explain this in a way suitable for students at the end of an undergraduate course, as well as academics who are not familiar with this area. I think this may be the issue, since at best I have a very vague, "pop-science" understanding of the standard model, so likely lack the required knowledge to really see how it works. Most explanations I have read are way over my head, or too vague and hand-wavy. "Because flavour states are superpositions of mass states, the detection rates of a particular flavour change over distance". That's obvious! Why are they like this to begin with?

Edit: thank you everyone for your helpful contributions, I certainly have plenty more reading to do now!

• Nobody knows why! There are no good theories compelling it. But people are used to this phenomenon from K-$\bar K$ mixing. They "grew up" with it! Feb 22 at 14:52
• @CosmasZachos I think you're underselling the theoretical motivation for neutrino mixing. There is good reason to motivate an arbitrary 3x3 unitary matrix that relates the flavor eigenstates to the mass eigenstates. This unitary matrix was clearly observed a long time ago in the quark system. It is entirely expected. Anything else would be evidence of fine tuning. What was unexpected is that the neutrinos even have mass. Feb 23 at 0:04
• Read the wiki en.wikipedia.org/wiki/… in the section "Classical analogue of neutrino oscillation." The gist is that neutrino oscillations are essentially the same phenomenon as a coupled oscillator oscillating between two different kinds of oscillation. Feb 23 at 0:06
• @AXensen We are not on the same page. The OP appreciates the technical structure leading to generic non diagonal mass matrices, for quarks and leptons, obviously: it is in all books. He is asking why that structure is necessary and inevitable, "in the first place". Nobody knows: all texture motivational models have shown no sign of success. Feb 23 at 1:24
• ...It is the underlying assumptions of that WP article that are asked about: once the skewed diagonalization of mass matrices is established, all else is determined and computable and straightforward. What is a total mystery is how these mass matrices arise. Dressing them up in Yukawa couplings is again 1-to-1 and a distraction... He is asking why so. Nobody knows. I am not underselling bad models. If a theorist tried to sell you a plausible theory underlying the (complex) pattern of Yukawa couplings, take cover. Feb 23 at 1:44