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The puzzle of the missing solar neutrinos is supposedly solved by neutrino oscillations. I understand the mechanism, but there is still one point which I find unclear.

For the energy range and dispersion of solar neutrinos, the mixing by the time they reach the Earth is total. But unless I am mistaken, for neutrinos detected through charged current interaction (transmutation of a neutron into a proton) that can only involve electron neutrinos, the ratio to the estimated number produced by the Sun is 1/3 with the accepted solar models. This ratio 1/3 has been confirmed by the NSO results which involve all three flavours of neutrinos by detecting neutral current interactions (inelastic collisions on deuterons that break them up), independently of a solar model.

But if one looks at the figures on neutrino mixing one can see that from what are originally electron neutrinos (which are the only ones produced in the Sun), if one averages over the oscillations, one gets proportions roughly just a bit more than 1/2 electron-, just a bit less than 1/3 muon- and about 1/6 tau-neutrinos. One does not get equipartition in all three flavours;

So how come the ratio of electron neutrinos to the total, when they reach Earth, is close to 1/3 instead of just a bit more than 1/2?

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    $\begingroup$ The right keyword to look up is "MSW effect". The Sun's electron density affects the neutrinos' properties as they pass through it. By the time they exit the Sun, they're actually in the second mass eigenstate which has a squared projection of $1/3$ on the electron flavor eigenstate. $\endgroup$
    – knzhou
    Commented Nov 2, 2023 at 17:52
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    $\begingroup$ This $1/3$ has absolutely nothing to do with the fact that there are $3$ flavors; instead it depends on detail on the PMNS matrix's elements. So yes, the way it's described in popsci is a big oversimplification. $\endgroup$
    – knzhou
    Commented Nov 2, 2023 at 17:53
  • $\begingroup$ @knzhou Your second remark goes in my direction. Indeed, what comes from the PMNS matrix' elements is 1/2, not 1/3, that would be a naive equipartition. As far as the first one, I'll check the "MSW" effect. As you describe it, it would indeed make sense. Why don't you make it an answer ? $\endgroup$
    – Alfred
    Commented Nov 2, 2023 at 18:07
  • $\begingroup$ It looks like this is what @knzhou described. $\endgroup$
    – J.G.
    Commented Nov 2, 2023 at 18:23
  • $\begingroup$ @J.G. Yes, I did check that wiki page just after posting my remark on knzhou remark. Neutrinos emerging from the sun in the second mass eigenstate because of interaction with matter. If knzhou makes it an answer, I'll accept it. $\endgroup$
    – Alfred
    Commented Nov 2, 2023 at 18:28

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