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Neutrino oscillations indicate that neutrino have little bit mass. Among three neutrinos - electron, muon and tau neutrino - which is heavier? What is the mass range of these neutrino?

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The cause for neutrino oscillations is that the flavour eigenstates are not the same as the mass eigenstates. Therefore, once you know the flavour of a neutrino, i.e. whether it is a electron, muon, or tau neutrino, the mass is not well defined. And the other way around: Once you know the mass, the outcome of a flavour measuring experiment is uncertain.

The mass differences measured in an neutrino experiment are differences between the mass eigenstates and thus say nothing about the mass of for instance the tau neutrino. Note that even the masses of the mass eigenstates are not known as only mass differences are measured.

The situtation is similar to a particle in a double-well potential. If you know in which well the particle sits, you do not know it's energy and when you know it's energy you do not know in which well the particle is. To complete the analogy with the neutrino case, there would need to be three wells with different depths.

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