# Proof that neutrino flavor oscillation implies nonzero neutrino mass?

• A
[This is a reference request.]

I'm dissatisfied with the "proofs" I've found so far. E.g., in Kayser's review from 2008, in the paragraph following his eq(1.4), he assumes a propagation amplitude Prop##(\nu_i)## of ##\exp(-im_i \tau_i)##, where "##m_i## is the mass of the ##\nu_i## and ##\tau_i## is the proper time that elapses in the ##\nu_i## rest frame during its propagation". I.e., he assumes ##m_i \ne 0##. Thus, he proves only that nonzero neutrino masses imply neutrino flavor oscillation, but not the converse, afaict.

Can anyone point me to better references, pls?

Homework Helper
As far as I know, neutrino oscillation only depends on ##\Delta m^2##, i.e. the difference of the square of masses, so the fact that we observe ##\nu_e - \nu_\mu## and ##\nu_e - \nu_\tau## oscillation tells us that the masses of the neutrinos must be non-degenerate (and therefore at most only one can be 0).
I don't know what are good references, although neutrino oscillation is covered in a lot of books.

Orodruin and vanhees71
Staff Emeritus
Gold Member
[This is a reference request.]

I'm dissatisfied with the "proofs" I've found so far. E.g., in Kayser's review from 2008, in the paragraph following his eq(1.4), he assumes a propagation amplitude Prop##(\nu_i)## of ##\exp(-im_i \tau_i)##, where "##m_i## is the mass of the ##\nu_i## and ##\tau_i## is the proper time that elapses in the ##\nu_i## rest frame during its propagation". I.e., he assumes ##m_i \ne 0##. Thus, he proves only that nonzero neutrino masses imply neutrino flavor oscillation, but not the converse, afaict.

Can anyone point me to better references, pls?
Isn't this the way physics usually proceeds? Let ##T## be a particular theory, and ##E## be a particular experiment result. Now suppose that it can be show that ##T \Rightarrow E##. If an actual experiment is performed and ##E## is the result, we take this as evidence for, but not proof of, ##T##.

Theories involving massive neutrinos predict oscillations, which predict experiment results ##E_i##. Actual experiments produce some of these ##E_i##, which we take as evidence that (at least some) neutrinos have mass.

snorkack
Since oscillations only require mass difference, how does "neutrinos having mass", by implication all of them, lead to oscillations, or vice versa? If some neutrinos have nonzero mass and other/s zero, would oscillations still result? And vice versa, if neutrinos had masses but these were equal, it would still have no oscillations.

Staff Emeritus