I am studying the neutrino oscillation phenomenom in which the flavour of a neutrino can change when it evolves in space-time.
What I understand is that this means that the 3 neutrino flavour states can be built in a common base of states. That is, if $$ \langle\nu_\mu|\nu_e\rangle \neq 0 \xrightarrow{} |\nu_\alpha\rangle = \sum_iU_{\alpha i}|\nu_i\rangle $$ With $\alpha$, and $i$ denoting the 3 possible flavours and base states respectively.
My question is, if this interpretation is correct, how do we know that this $|\nu_i\rangle$ states are mass states?

$$\textbf{Edit:}$$ Maybe what I'm trying to ask, is: how do we mathematically come up with the energy/mass eigenstates? Where do they come from?

  • 2
    $\begingroup$ How do you know that the $| \nu_i \rangle$ are the mass eigenstates? You diagonalize the neutrino mass matrix and determine the corresponding eigenvectors. $\endgroup$
    – Hyperon
    Mar 8 at 13:51
  • $\begingroup$ @Hyperon And by what magic do you know the neutrino mass matrix? $\endgroup$
    – John Doty
    Mar 10 at 17:32
  • $\begingroup$ @John Doty In the minimal version of the SM, the neutrinos are exactly massless and, as a consequence, there are no neutrino oscillations, clearly in conflict with the experimental evidence of the measured neutrino mass differences and mixing angles. Therefore, the SM must be extended by adding additional leptonic and/or scalar degrees of freedom. Presently, the ultimate form of this necessary extension is not known (there are numerous competing models), further experimental input (e.g. Majorana/Dirac nature of $\nu$, CP-violation in the lepton sector) will lead to further restrictions. / ctd $\endgroup$
    – Hyperon
    Mar 10 at 21:37
  • $\begingroup$ @John Doty But independently of the actual form of the extension of the standard model, you will have a mass matrix in the neutral lepton sector and the diagonalization of this mass matrix allows to identify the (neutrino) mass-eigenfields as linear combinations of the weak eigenfields. This allows a largely model-independendent discussion of neutrino oscillations in terms of neutrino mass differences, mixing angles and $CP$-violating phases. $\endgroup$
    – Hyperon
    Mar 10 at 21:45
  • $\begingroup$ @Hyperon OK, show me the values of the mass matrix elements. If you can't, then "You diagonalize the neutrino mass matrix and determine the corresponding eigenvectors." is empty of physical content. $\endgroup$
    – John Doty
    Mar 10 at 22:25

1 Answer 1


What we have is experiments that demonstrate neutrino oscillations. That's what we know. The rest is modeling, and in the model you quote, if the flavor states aren't a linear combination of mass eigenstates, there are no oscillations.

  • $\begingroup$ But with that answer, I could also create a model in which the neutrino states are a linear combination of momentum eigenstates, right? $\endgroup$
    – DavidUCM
    Mar 8 at 17:44
  • $\begingroup$ @DavidUCM Yes but you prefer to "localize" the creation and detection of the wave packet, and consider its three components created and annihilated at the same spot, so with huge momentum spreads. So you have three momenta constrained to a common energy by the three masses, and yielding the oscillation formula. Is this what you are asking? $\endgroup$ Mar 10 at 14:49
  • $\begingroup$ My question is more like: why do we choose the basis states in which the neutrino flavour states are built with to be mass states besides experimental evidence? The evidence is the change in the flavour, not directly the mass. So, how did we come up with the idea of introducing the mass to the problem? $\endgroup$
    – DavidUCM
    Mar 11 at 23:17
  • $\begingroup$ @DavidUCM That's how you get oscillations in the theory. The mass states evolve at different rates. $\endgroup$
    – John Doty
    Mar 11 at 23:59

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