The three (distinct) neutrino flavors had been discovered before neutrino oscillations were discovered. Until then, it seems to have been logical to think of them as three types of distinct particles because their (weak) interaction with matter produces different secondary particles depending on the neutrino flavor. But now that neutrino oscillations have been discovered, why do we still need keep the notion of three different neutrino particles rather than just one? To my understanding, the only way to measure the flavor of a neutrino is by observing the products of their interaction with matter; different neutrino flavors will produce different particles (e.g., the electron neutrino produces an electron and the muon neutrino produces a muon). However, couldn't we model this with just a single neutrino that has different probabilities of producing either an electron, muon, or tau during an interaction?
1 Answer
Those probabilities depend on how far the neutrinos have travelled. And the formula for how they do precisely matches the model that treats the three neutrino flavours as different linear combinations of mass eigenstates.
Edit To say more about this, a neutrino in a mass eigenstate will stay in this mass eigenstate until it interacts. It just evolves according to a phase factor which doesn't affect a quantum mechanical measurement.
But you already said that each reaction we use to detect a neutrino only happens for a specific one of the three flavours. The counterpart to this statement is that every experiment we can do to produce neutrinos also produces them as a specific flavour eigenstate. So freely propagating neutrinos start off as a linear combination of mass eigenstates and each one evolves with a different phase factor. This is what leads to oscillation. Letting the evolution happen for some time and then re-projecting this state onto each flavour typically does not yield 100% for the initial flavour and 0% for the others anymore. It yields probabilities which depend on time, mass differences and the precise coefficients that relate mass and flavour eigenstates.
Experiments have verified many parts of this model but there is still more to measure. In particular, we would like to know the coefficients above which are components of the PMNS matrix. This is like the CKM matrix for quarks but it is much further from being diagonal. The magnitudes of the elements are comparatively easy to measure but to truly learn what they are, we would need to know their real and imaginary parts which have to be extracted from a more subtle interference effect.
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$\begingroup$ Does that mean a neutrino will always only be in one mass eigenstate and retain that mass for its entire lifetime? Only the probability to measure a particular flavor - i.e., corresponding secondaries - changes over time? If my understanding is correct, then it seems that the mass (eigenstates) is the differentiating property of neutrinos, not the flavor? I.e., it seems misleading to label the three neutrinos as electron-, muon-, tau-neutrino, which differentiates them based on the secondaries they produce but every neutrino can produce any of them, revealing any flavor during an interaction. $\endgroup$– a_guestCommented May 14 at 19:59
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$\begingroup$ Wouldn't it therefore be more intuitive to label the neutrinos as, e.g., $\nu_{1}, \nu_{2}, \nu_{3}$ rather than $\nu_{e}, \nu_{\mu}, \nu_{\tau}$ to differentiate them based on their combination of mass eigenstates? $\endgroup$– a_guestCommented May 14 at 20:00
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2$\begingroup$ Good questions. I've edited the answer. Whether people prefer the $1,2,3$ labels to the $e,\mu\,\tau$ labels depends on the application. $\endgroup$ Commented May 14 at 21:32