# Is neutrino oscillation a violation of a conservation law?

1. Aug 16, 2011

### alemsalem

Neutrinos are emitted with corresponding leptons (e, mu ,tau) and thats a conservations law(?)
what about when neutrinos oscillate into each other is that a violation of that law? also is there a corresponding oscillation in the other leptons and other particles??

Thanks

2. Aug 17, 2011

### kurros

Well, if there were no neutrino oscillations then yes, there would be a conserved quantum number, call it 'generation' or something. No interactions except for neutrino oscillations can change leptons of one generation into another. Weak interactions can change electrons into electron neutrinos though, muons into muon neutrinos etc, and vice versa.

There is sort of a corresponding 'oscillation' in the quarks, through the CKM matrix. Quarks of one generation can change into quarks of another generation through weak interations. This isn't generally considered an oscillation though, because the coherence length is very short, due to the big mass differences between the quarks.

Neutrinos only oscillate back and forth from one generation to another because the masses differences are very small, i.e. all the neutrinos propagate pretty much at exactly the same speed, or perhaps more importantly the phase of their wavefunction changes at basically the same speed. So the superposition of all neutrino mass eigenstates can be maintained over long distances. Quarks do not have this property; the generation changes during the interaction but then you definitely have one mass eigenstate of a quark or another very soon afterwards (and bound into a hadron at that), not some superposition of them, which would imply some superposition of hadrons.

This is a bit out of my comfort zone though so I guarantee nothing :p.

edit: I realised I should clarify a bit. Muons obviously can decay to electrons, so sure generation has changed, but you also produce a muon neutrino and an ANTI-electron neutrino in the process. The anti-electronness of the anti-electron neutrino "cancels" the electronness of the electron, so overall there is 0 "electronness" and +1 "muonness", even though you end up with an electron but no muon.

Last edited: Aug 17, 2011
3. Aug 18, 2011

### rkrsnan

Charged leptons do not undergo oscillations simply because their definition does not allow oscillations. In standard model, charged leptons are defined as the eigenstates of weak interaction having definite mass. A neutrino is also a weak eigenstate, but it is superposition of states having different masses which causes oscillations when they propagate. Techically you can even do the other way around by redefining charged leptons and neutrinos so that charged leptons oscillate and neutrinos do not. But nobody does that simply because it is a stupid thing to do practically.

For quarks we have another quantum number called color corresponding to strong interaction. If we take eigenstates of color, in general they will not be eigenstates of weak interaction. So we will have oscillation like phenomena when you involve both strong and weak interaction, ie a particle produced through strong interaction can change to any of the weak eigen states.