# Neutrino mixing

## Main Question or Discussion Point

can any body explain what is the difference between neutrino flavour state and neutrino mass eigenstate?getting confuse on it again......

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It is aslo hard for me to understand their exact meanings. "flavor" eigenstates label their roles participating in various interactions. For example, W bosons couple electron with electron neutrinos, not muon neutrinos. And "mass" eigenstates determine their evolution with time. But still, it is very abstract. For example, a free electron neutrino will oscillate into muon neutrino or tauon neutrino or itself with time. But I can't find how it oscillates. I think there should be some external field, which combines with these "free" neutrino, forming a "Energy" eigenstate. But it is also a profound problem.

hmmm....flavor state is unphysical field i.e. no definite mass
mass eigenstate is physical field i.e. with definite mass
do the wave function or spinor contain any information of their mass to distinguish them?

The mass state are the actual physical neutrino states which remain diagonal under evolution by the free Hamiltonian. The flavor states are the superpositions of mass states which have charged current interactions with the respective charged leptons.

Because neutrinos interact so weakly and have such small mass differences, a superposition of neutrino mass states can retain quantum coherence over astrophysics (and even, possibly cosmological) distances. However, the small differences in mass mean that the free evolution of the different mass states will lead to energy and distance dependent phase differences between the eigenstates, changing both the overall phase and relative phases of the coefficients in the superposition. This, then, is how neutrino "flavors" change.

The mass state are the actual physical neutrino states which remain diagonal under evolution by the free Hamiltonian. The flavor states are the superpositions of mass states which have charged current interactions with the respective charged leptons.

Because neutrinos interact so weakly and have such small mass differences, a superposition of neutrino mass states can retain quantum coherence over astrophysics (and even, possibly cosmological) distances. However, the small differences in mass mean that the free evolution of the different mass states will lead to energy and distance dependent phase differences between the eigenstates, changing both the overall phase and relative phases of the coefficients in the superposition. This, then, is how neutrino "flavors" change.
“... The flavor states are the superpositions of mass states which have charged current interactions with the respective charged leptons. ..."

Here I have a question. Which states have charged current interactions, flavor eigenstates or mass eigenstates? If we use the former one, it is OK. But if we use the latter one, we have to multiply by $U_{\alpha i}$ 's at each vertex, which is like dealing with quarks using CKM matrix. (Sorry, I don't know how to insert mathematical symbols here!)

“... The flavor states are the superpositions of mass states which have charged current interactions with the respective charged leptons. ..."

Here I have a question. Which states have charged current interactions, flavor eigenstates or mass eigenstates? If we use the former one, it is OK. But if we use the latter one, we have to multiply by $U_{\alpha i}$ 's at each vertex, which is like dealing with quarks using CKM matrix. (Sorry, I don't know how to insert mathematical symbols here!)
The flavor states have diagonal charged current interactions with their respective charged leptons. However, it would be more physical to use the mass states and a mixing matrix element (in analogy to the quarks).

The flavor states have diagonal charged current interactions with their respective charged leptons. However, it would be more physical to use the mass states and a mixing matrix element (in analogy to the quarks).
Mass eigenstates correpond to diagonal elements in "free" Hamiltonians, while flavor eigenstates to diagonal elements in the "interaction" part. Could we combine mass eigenstate and flavor eigenstates to construct an eigenstates for the "whole" Hamiltonian? Maybe I go back to the beginning.