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## 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......

- Thread starter thoms2543
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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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mathman

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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?

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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.

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“... 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.

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!)

- #7

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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 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!)

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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.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).

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