# Neutrino oscillations

A neutron plus a W particle yield a proton an electron an antineutrino and a W- particle.

The reactants - the neutron and W particle do not have oscillating masses.
One of the products does - the antineutrino.
Shouldn't there be an oscillating mass on both sides of the equation?

## Answers and Replies

vanesch
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kurious said:
The reactants - the neutron and W particle do not have oscillating masses.
One of the products does - the antineutrino.

I don't know what you imagine being "oscillating masses". I think you're confusing with neutrino "oscillations" which is nothing else but saying that the neutrinos which are "multiplet eigenstates" are not pure energy (or mass) eigenstates, but are linear combinations of it (or, vice versa, that mass eigenstates of neutrinos are linear combinations of "multiplet eigenstates" (the things we call electron neutrino, muon neutrino and tau neutrino and which enter into feynman diagrams).
The term "oscillation" comes then from the following fact:
imagine that in the sun there's a process going on. It will produce neutrinos in the "multiplet" eigenstate, because the sun is mainly composed of up and down quarks (not a lot of strange, charm etc...), so the main feynman diagrams will produce pure "electron neutrinos". But as said above, an "electron neutrino" is a superposition of several "energy eigenstates" (or mass eigenstates). If this quantum object evolves freely in space, you know that each energy eigenstate has a phase evolution exp(-i E t) associated to it.
So the relative phases of the components of the "electron neutrino" as seen in the mass basis, change over time, because the masses (energies) are different.
After a while, you get a completely different superposition, and this might then correspond not to an "electron neutrino" but to a "muon neutrino" (which is simply ANOTHER superposition of the same mass eigenstates). Because there are only 3 terms involved (maybe only 2, this is yet unknown), if you wait twice as long, the muon neutrino transforms back to an electron neutrino, in an oscillating way.
BTW, the fact that this transformation was observed indicated that we needed several different masses, which indicates that neutrinos HAVE to have a tiny mass.

cheers,
Patrick.

What I meant to say was that is there something like a conservation law so that
if superpositions change after two particles (which are not neutrinos) have interacted, should there have been some changing superpositions before the particles interacted.
For example could there be oscillating W particles which oscillate like neutrinos do?

Nereid
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Perhaps you could explain what you mean a bit more sol2; your post seems to have nothing to do with neutrinos - oscillations, mass, etc. To me, it seems like something which belongs in Theory Development - have you posted your ideas there?

selfAdjoint
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Solar neutrinos come from the core of the sun to the earth. They don't feel the electromagnetic force and interact only weakly. Mostly they pass through the earth without any sign of their presence. It takes huge mass of matter and ultra sensitive instruments to detect even a few.

Solar wind contains atoms and particles from the upper layers of the sun. They are mostly electrically charged and interact strongly with the earth's magnetic field. They produce huge displays of auroras and can interfere with broadcasts worldwide.

These two streams have different sources, different scales, and vastly different interactions. Pretty much they are totally independent of each other.

Last edited:
vanesch
Staff Emeritus
Science Advisor
Gold Member
kurious said:
What I meant to say was that is there something like a conservation law so that
if superpositions change after two particles (which are not neutrinos) have interacted, should there have been some changing superpositions before the particles interacted.
For example could there be oscillating W particles which oscillate like neutrinos do?

You seem to think that because there is "superposition" after the interaction, that there should be "superposition" before the interaction ; whether there's a law of "conservation of superposition" ; coming down to a linear time evolution operator. In a certain sense, yes. The needed superpositions BEFORE interaction are energy superpositions. So you need quarks and electrons with a certain energy spread which covers the mass difference of the different neutrino mass states. But the mass difference is tiny !
The thing that is special with neutrinos is the following:
|electron neutrino> = 1/sqrt(2) (|mass A neutrino> + |mass B neutrino>)
|muon neutrino> = 1/sqrt(2) (|mass A neutrino> - |mass B neutrino>)

So the "electron neutrino mass" is not defined ! It is a mixture of something that has mass A and something that has mass B.

For electrons, this is not the case: the mass eigenstate of an electron is also the "electroweak interaction eigenstate" (the one that enters into the feynman diagrams).

In electroweak interactions, it are "electron neutrinos" that interact in the first family (up and down quarks) and "muon neutrinos" that interact in the second family. Because in the sun, there are predominantly only quarks of the first family, only pure electron neutrinos are produced there.
But once they are produced, and allowed to freely evolve, they obey the schrodinger evolution equation, and we have that:
|electron neutrino after time t> = 1/sqrt(2) (exp(-i A t) |mass A neutrino> + exp(- i B t) | mass B neutrino> )

You can clearly see that, apart from a global phase factor which doesn't matter, for long enough t, |electron neutrino after time t> = |muon neutrino>. And still twice as long later, it is back an electron neutrino.

One thing is sure: just after the interaction, only a pure electron neutrino can be produced. Whether you consider this a "superposition" or not is your business, it depends on what basis you use. But if you use the mass basis, which is also the energy eigenstates, then you see that it is indeed a superposition ; this basis is helpfull to calculate the time evolution. Most particles don't have this: because the "interaction eigenstate" is equal to the mass eigenstate, the time evolution only adds an insignificant phase factor, and the particle remains itself in the interaction basis.

To come back to your question: if energy eigenstates are truely stationary states, and we end up with a superposition of stationary states, what gives ?
Well, this can in principle be described by a superposition of incoming particles with slightly different energies ; alternatively, you can absorb the energy uncertainty (mass difference) into the other product particle. But in practice this is ridiculous: the elementary particle interaction takes place on time scales which are SO small, that anyway the time-energy uncertainty gives us uncertainties much larger than this tiny mass difference.

cheers,
patrick.