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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!

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    $\begingroup$ 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! $\endgroup$ Feb 22 at 14:52
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    $\begingroup$ @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. $\endgroup$
    – AXensen
    Feb 23 at 0:04
  • $\begingroup$ 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. $\endgroup$
    – AXensen
    Feb 23 at 0:06
  • $\begingroup$ @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. $\endgroup$ Feb 23 at 1:24
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    $\begingroup$ ...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. $\endgroup$ Feb 23 at 1:44

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Another source that could help you is the video from minute physics: https://www.youtube.com/watch?v=7fgKBJDMO54.

He distinguishes the types of neutrinos in interaction (flavor eigenstates) and traveling freely (mass eigenstates). But here again he doesn't detail why mass and flavor eigenstates should be different at first. The origin of this difference is pretty technical and painful to explain. It has to do with the fact that the weak interaction breaks its (U(1)xSU(2)) gauge symmetry. You can find a similar difference for the quarks. I am not sure that I understand it enough to explain it clearly, but here are some keywords that can help you in your search: the flavour/masses eigenstates are related by a matrix called a "mixing matrix". For neutrinos this matrix is called the "PMNS matrix", while for quarks it's the "CKM matrix". The existence of these matrix have to do with how the particles interact with the Higgs boson through the so called "Yukawa couplings", and so at the very end it has to do with the fact that the weak force comes from the spontaneous symmetry breaking of the electroweak force (you can find a complete review here for neutrinos https://pdg.lbl.gov/2020/reviews/rpp2020-rev-neutrino-mixing.pdf and https://arxiv.org/pdf/1710.00715.pdf and here for quarks: https://pdg.lbl.gov/2020/reviews/rpp2020-rev-ckm-matrix.pdf).

\textbf{Edit: I removed my mention to CP symmetry which was not needed}

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    $\begingroup$ Nice. Here is another video from PBS Space Time. It is between the level of Minute Physics and a complete review. Will A New Neutrino Change The Standard Model? $\endgroup$
    – mmesser314
    Feb 22 at 15:24
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    $\begingroup$ The Even Bananas series of videos from FermiLab has a lot on neutrinos. This one is a good follow on to Minute Physics. How do neutrino oscillations work? | Even Bananas 10 $\endgroup$
    – mmesser314
    Feb 22 at 15:33
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    $\begingroup$ CP violation is not required for neutrino mixing, and it is not necessary to mention it here. It is also, notably, not observable in the current generation of experiments that measure neutrino mixing. CP violation occurs because there are three generations of quarks/neutrinos, meaning the CKM and PMNS matrices are 3x3 and can have an imaginary phase in the upper right corner. But neutrino mixing would also occur if there were only two generations, and if the imaginary phase was zero in the PMNS. I upvoted anyway because the rest of your answer points generally in the right direction. $\endgroup$
    – AXensen
    Feb 23 at 0:00
  • $\begingroup$ Thanks for the clarification! I removed the part on CP symmetry in my comment to avoid creating more confusion. $\endgroup$ Feb 23 at 9:54
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Good morning. I am unaware of the exact prior level of knowledge possessed by your listeners, but I would proceed as follows: Before discussing self-state and oscillation itself, I would focus on the fact that apparently fewer electron neutrinos from the sun are detected than should be, explaining the issue of solar neutrinos. Then, without necessarily delving into self-states, I would explain how neutrinos can change flavor during their journey to Earth.

I realize this may not be a comprehensive clarification, but it is a complex concept. There is an excellent video in Spanish for outreach on YouTube by "Quantum Fracture", a theoretical physicst, in case it is of interest. I hope this helps!

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