# I Neutrino flavour eigenstates and expansion of the universe

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1. Jun 16, 2017

### Carlos L. Janer

Neutrinos were flavor eigenstates at the time of their decoupling from baryonic matter. Since they were not pure mass eigenstates, how do you take this fact into account if you try to study how they evolved as the universe expanded?

Could we determine if the heaviest neutrino could be non relativistic at present times?

Can we even try?

2. Jun 16, 2017

### Staff: Mentor

The flavor eigenstates are superpositions of the mass eigenstates, and you can simply follow the mass eigenstates over time.
The heaviest neutrino has a mass of at least 50 meV (mixing) and of at most ~70 meV (cosmological constraints), at its present temperature of 2 K = 0.17 meV these neutrinos are moving at a few percent the speed of light.

3. Jun 16, 2017

### Carlos L. Janer

Thanks for the info.

There's something I don't get, though. Should the heavier neutrinos not be unstable and decay into the lightest one? If the're not flavour eigenstates I do not see what could prevent that from happening.

4. Jun 16, 2017

### Staff: Mentor

What would be the corresponding decay process?

5. Jun 16, 2017

### Carlos L. Janer

EM? Two low energy photons? Not saying I'm right, just asking why I'm wrong.

6. Jun 16, 2017

Staff Emeritus
The lifetime is so long that there may not have been enough time for a single neutrino in the universe to decay.

7. Jun 16, 2017

Staff Emeritus
Violates conservation of angular momentum.

8. Jun 16, 2017

### Carlos L. Janer

Does your assertion indicate that you have a decay process in mind? I'm asking, not pretending to know. What would the point in that be?

9. Jun 16, 2017

### Carlos L. Janer

Why do the two photons have to be exactly equal and propagate in opposite directions?

I keep telling you that if I'm asking is because I don't know.

10. Jun 16, 2017

Staff Emeritus
At what point did I say that? It's bad enough that you come here pushing fringe theories, but don't put words in my mouth.

11. Jun 16, 2017

### Carlos L. Janer

I honestly don't have any idea what you are talking about.

Whenever I have something to say I just say it straight away. Life is already complicated enough to try to double guess what other people may have in their minds and are, allegedly, not willing to tell.

I think straight, I walk straight and I talk straight. Do not try to find any hidden message because there is none.

12. Jun 16, 2017

### Staff: Mentor

Here's what you said:

@Vanadium 50 did not say the two photons had to be exactly equal and propagate in opposite directions. Your question, just quoted, implies that he did say that. That's why he objected to it.

13. Jun 16, 2017

### kimbyd

Photons only interact with charged particles. Neutrinos aren't charged.

Such a decay process, if it were to exist, would require either W or Z boson intermediaries, and would thus be suppressed dramatically by the very small mass differences between neutrino flavors.

Btw, I found this paper on neutrino decay:
https://arxiv.org/abs/1208.4600

14. Jun 16, 2017

### Carlos L. Janer

Well, this reference considers posible neutrino electromagnetic interactions. I's beyond me, at the moment, but I will post the reference in case you can tackle it (of course, provided that you're interested in the subject):
https://arxiv.org/abs/1403.6344

15. Jun 16, 2017

### Staff: Mentor

None of which have been observed; as the introduction to the paper says, we have no evidence for the existence of neutrino electromagnetic interactions. So we also have no evidence that heavier neutrinos could decay into lighter ones by such a process.

16. Jun 16, 2017

### Carlos L. Janer

I am not even sure that I should be answering your remarks.

If there are neutrino electromagnetic decays, the outgoing photons would be of very low energy and, therefore, extremely dificult to detect.

So, what are your implying? Do you think that both authors, Carlos Giunti and Alexander. I Studenikin are a couple of incompetent researchers? Is it an heresy to question the validity of the Standard Model of Particle Physics and look for Physics beyond it? Should their paper citations be banned from this forum? Have you asked your colleague Orodruin, who works in neutrino physics, if all his papers conform to the scientific consensus on Fundamental Physics?

Why are you such an adamant defender of the SM of Particle Physics and de LambdaCDM-model, what do you like about fine tuning so much? They are, undoubtedly, the best theories we have. But they're not good enough.

17. Jun 16, 2017

### Staff: Mentor

They only discuss experimental lower bounds on the lifetime, but don't discuss new physics models that could lead to these decays.
meV, above to the cosmic microwave background. A large source of meV photons would be notable.

We cannot rule out neutrino/photon interactions, and at loop-level we have them even in the SM, but they have to be extremely weak. And that is elastic scattering - I still don't see how you would get a decay.

18. Jun 16, 2017

### Staff: Mentor

If such a decay took place now, yes, this is correct. But if, as you hypothesize, a heavier neutrino decayed into a lighter neutrino by such a mechanism, we wouldn't have to detect the photons to know it took place; we could just detect the change in the neutrino itself.

Also, as @mfb points out, if such decays had taken place in the early universe we would see the EM radiation from them, because it would have a significantly different spectrum from the CMBR and would be more intense. So if we can detect the CMBR, we would be able to detect the radiation from a significant number of such decays.

That, as the paper you linked to explicitly says, we have no evidence of neutrino electromagnetic interactions. And that, as noted above, if such interactions had taken place to a significant extent in the early universe, we would expect to have evidence of them.

As for the rest of your post, I have not made any of the claims you attribute to me.

Last edited: Jun 16, 2017
19. Jun 16, 2017

### Carlos L. Janer

I am not aware of any calculation of heavy neutrinos lifetime in that paper. But anyhow I am pretty sure that the relic neutrino bakgroud emission will never be detected.

Wrong! The EM radiation temperature would have been tiny because it depends on the neutrinos mass differenes and I hope that I do not have to remind you that the photon-matter decoupling happened at z=1100 (T=3000K). That radiation wavelength at present times (caused by the hypothetical heavy neutrinos decay) might even be larger that the size of our observable universe.

What on Earth do you think it gives you the right to insult me!

20. Jun 16, 2017

### Staff: Mentor

PTOLEMY tries to see the cosmic neutrino background.
Be careful with statements like that. You are wrong here.

The absolute mass difference might be small, but relative to the neutrino masses it is large (O(1)). No matter when the process happens, the photons would carry a significant fraction of the neutrino energy. Their energy goes down at the same rate as the neutrino energy (as long as they are relativistic). The photons today would have meV energies (~0.1 meV to few meV depending on the timescale), similar to the neutrinos, at roughly the same temperature as the CMB or hotter.
If the process happens faster than recombination, the photons might get buried in the CMB, but that case would need a more careful analysis.

21. Jun 16, 2017

### Carlos L. Janer

OK, I get it. You're right.

22. Jun 16, 2017

### Carlos L. Janer

It's getting late and I'm tired. I'm going to bed. It was nice talking to you.

23. Jun 16, 2017

### kimbyd

To examine this a little bit, you can contrast it against the decay of the muon, which typically looks like:

$$\mu \rightarrow \nu_\mu + \nu_\bar{e} + e$$

This is because lepton flavor is conserved in the standard model. In order to get a neutrino to decay into a lighter neutrino, you'd need, at the very least, for this decay to be possible:

$$\mu \rightarrow e + \gamma$$

It might be heavily suppressed, but it should at least happen with some frequency. I don't think any such decay has ever been observed.

24. Jun 16, 2017

### Staff: Mentor

On consideration, you're right, some of what I said that you quoted was uncalled for. I have edited the post of mine from which you quoted to remove that part. But I have let stand the plain statement that I did not make the claims you attributed to me, since it is true.

25. Jun 16, 2017

### Staff: Mentor

MEG searched for it, and set an upper limit of 4*10-13. One of the best branching fraction limits ever set for any particle, possibly the best after an obscure neutron decay*.

* 10-26 for a charge changing decay mode. The trick here is the huge number of neutrons in nuclei in the detector, where such an obscure decay would be possible, but the dominant decay of free neutrons is not available.