# 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?

Gaussian97
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
George Jones
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.

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.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
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.
It does not. It is a somewhat simplified statement. The conclusion is that there is flavor mixing in the lepton sector and that neutrinos have different masses. From that follows that at most one neutrino is massless. You can argue about how natural it would be to have a single massless neutrino when the others have non-zero masses, but there are indeed neutrino mass models where this could happen.

• ohwilleke and vanhees71
mfb
Mentor
If the masses are all the same (e.g. 0) then the flavor eigenstates (and every other state) are also mass eigenstates and no mixing happens. This is analogous to e.g. neutral meson mixing where we use the observed mixing to determine that there is a mass difference.

• • ohwilleke, strangerep and vanhees71