# Electron and Muon Neutrinos difference

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1. Jun 6, 2015

### unscientific

1. The problem statement, all variables and given/known data

Neutrinos with energy of about $1 GeV$ are measured in an underground detector and compared with simulations of neutrinos produced in the atmosphere. Measured flux of upward going muon neutrinos $(\nu_\mu + \bar \nu_\mu)$ is half compared to simulations while measured flux of downward going muon neutrinos matches simulations. For electron type neutrinos, both upward and downward fluxes matches simulations. Why is this so?

2. Relevant equations

3. The attempt at a solution

I know that neutrinos are left-handed while anti-neutrinos are right-handed. Also, a muon is much heavier than an electron so any relativistic electrons produced are left-handed, while a muon can be both.

2. Jun 6, 2015

### Orodruin

Staff Emeritus
The fact that the muon is heavier is irrelevant. I suggest you look up neutrino oscillations.

3. Jun 6, 2015

### unscientific

I found a very good explanation from the book "Beam Line: Fall 2001". The sun only produces electron-type neutrinos, so any muon neutrinos present must have been due to interactions.

So basically muon upward-going neutrinos originated from distant parts of the atmosphere, below the horizon and have been around for a long time. In contrast, downward moving neutrinos started much closer at the atmosphere. So upward moving muon neutrinos have had time to oscillate, while downward moving muon neutrinos don't. Atmospheric muon neutrinos oscillate into a tau neutrino, as the probability is related to the difference in masses. Thus it oscillates between a muon neutrino and a tau neutrino. Since the oscillation is $\sim \sin^2(ΔM(\frac{L}{E}))$., the average observed upward moving is $\frac{1}{2}$ of the downward moving.

For electron neutrinos, they are produced in the sun, and have had time to oscillate on their way to earth. So measured upward and downward fluxes are equal for electron neutrinos.

4. Jun 6, 2015

### Orodruin

Staff Emeritus
This is not correct, neutrino oscillations are not due to interactions.

The mechanism behind the flavour conversion of solar neutrinos is quite different than that for the atmospheric ones. It is mainly based on matter enhanced neutrino oscillations and MSW flavour conversion. It is not the same as vacuum oscillations.

Other than that, you are fairly well on target. Just pay attention to the fact that the mass squared difference appearing in the oscillation formula is the mass squared difference of the neutrino mass eigenstates - not of the charged leptons or the neutrino flavour eigenstates (flavour eigenstates do not have a definite mass).

5. Jun 6, 2015

### unscientific

So the electron neutrino does oscillate? Does this explain why the the measured upward/downward fluxes are equal?

6. Jun 6, 2015

### Orodruin

Staff Emeritus
Yes, but for atmospheric neutrino energies, the only mass difference which is important is that of the third mass eigenstate and the others (this mass squared difference is large). Can you use this fact to explain why electron neutrinos are not much involved in atmospheric neutrino oscillations?

7. Jun 6, 2015

### unscientific

So it oscillates between a tau neutrino and an electron neutrino? Since the mass difference is bigger than when it oscillates with a muon.

8. Jun 6, 2015

### Orodruin

Staff Emeritus
No. Again, this has nothing to do with the mass differences of the charged leptons. As I told you, the relevant mass eigenstate for atmospheric neutrino oscillations is the third one. How can you relate this to the fact that (atmospheric) electron neutrinos do not oscillate?

9. Jun 6, 2015

### unscientific

What do you mean by "third mass eigenstate"? Why don't atmospheric electron neutrinos oscillate? I feel like I'm completely missing the point here.

10. Jun 7, 2015

### Orodruin

Staff Emeritus
Neutrinos mix. This means that the interaction eigenstates are not equivalent to the mass eigenstate, i.e., the states with definite mass are not the electron, mu and tau neutrinos, but rather linear combinations of these. The amplitude of oscillations depend on the amount of the flavour states in each mass eigenstate, given by the mixing matrix.