# Neutrino-to-neutrinos interaction possible?

1. Oct 13, 2014

### Davephaelon

Could an energetic neutrino (of any flavor), on passing near an electron, nucleon, or nucleus, be stimulated to emit a neutrino pair (of any flavor)? An example might be an energetic electron-neutrino, passing close to a nucleus, and emitting a muon-neutrino/muon-antineutrino pair., with the original electron-neutrino losing the necessary amount of kinetic energy to create the additional neutrino pair. This reaction wouldn't violate any conservation laws that I know of, as the two new neutrinos would have opposite spin, so that would cancel, opposite lepton number, so that would cancel, and opposite lepton type, so that would cancel. I assume such an interaction would be mediated by a Z-zero, as no charge is involved, assuming it's possible.

The inspiration for this idea was that neutrino oscillation is known to be greatly enhanced when neutrinos pass through matter, whether the interior of the sun or solid rock. So, it seemed reasonable that other transformations were possible when neutrinos pass close to massive particles. Additionally, pair production occurs when an energetic gamma ray passes near a nucleus, though, in that case the gamma ray is transmuted into an electron-positron pair. A closer analogy to the hypothetical interaction above is when an energetic electron passes near a nucleus and spits out an electron-positron pair, while the original electron loses the appropriate energy to create the electron-positron pair.

2. Oct 13, 2014

Staff Emeritus
Such an interaction would be at third-order weak. That's shorthand for saying "it can occur - but doesn't."

3. Oct 13, 2014

### Davephaelon

Is there a specific reason why it would be a 3rd order weak interaction?

Unfortunately, that fact basically negates an idea that I'd been thinking about for the last week. The idea was that such an interaction might masquerade as neutrino oscillation, but unlike neutrino oscillation this (I now know, non-occurring interaction) would conserve lepton family type, so it seemed appealing. I was thinking that by dividing up the energy of the incident neutrino among three neutrinos, the average energy of all three would fall below the detection threshold of the various detectors, and thus be interpreted as missing neutrinos. In turn, the appearance of other flavors, among the pairs, would be interpreted as neutrino oscillation, such as the pure muon-neutrino beam in MINOS yielding a small percent of electron-neutrinos in the Far Detector.

Well, no sense thinking about it anymore, as it was a flash in the pan idea.

Thank you for responding.

4. Oct 14, 2014

### Orodruin

Staff Emeritus
What you describe is similar to pair production of electron-positron pairs by a high energy electron. This would require the exchange of two photons. However, neutrinos do not interact electromagnetically and you would instead require the exchange of two Z bosons.

There are also other problems with your idea, the most apparent one being that we have observed both appearance and disappearance in oscillation experiments whereas your model could only explain disappearance. We have also seen the oscillatory behaviour of the probabilities as well as observed that the neutrinos are still present, just in different flavours.

Furthermore, neutrino oscillations occur also in vacuum and, unlike neutrino interactions, get suppressed at higher energies.

Historically, many mechanisms have been proposed as a possible reason for flavour conversion (examples include neutrino decay and decoherence), but only oscillations have survived the last decade of scrutiny in oscillation experiments.

Last edited: Oct 14, 2014
5. Oct 14, 2014

Staff Emeritus
It's worse than I thought. It's fourth-order weak. And the specific reason is because there are four weak vertices in the diagram.

6. Oct 14, 2014

### Davephaelon

Orodruin:

Thank you for explaining the reasons why my idea isn't plausible. That the proposed interaction requires two Z bosons I surmise explains why it has a low probability of occurring, as weak interactions requiring a single Z (or W) boson would be much easier for nature to implement. Are there plans to test vacuum oscillation by running neutrinos through long lengths of straight vacuum pipe? I understand that neutrino oscillation is evident through solid rock, or soil, over distances of a few hundred yards. So maybe an evacuated beam pipe of several miles, or tens of miles, (assuming real estate could be found to construct such a facility), could be used to test the much reduced cross-section of neutrino oscillation in vacuum.

[Personal theory oustide of the PF guidelines deleted by moderator]

Last edited by a moderator: Oct 14, 2014
7. Oct 14, 2014

### Orodruin

Staff Emeritus
The point is that for the neutrinos we have access to (of energies at which we have access to apart from ultra-high energy neutrinos observed by IceCube) and have measured oscillations for, the density of the Earth is sufficiently small to essentially count as a vacuum. Based on the observed neutrino cross sections (and electroweak theory) the probability for a neutrino to scatter on its way to the detector is extremely small. The typical scatter would involve charged current or neutral current interaction with a nucleus - similar to the processes used to detect neutrinos. Since such scatters involve the exchange of one W or Z, they are still significantly more probable than a process involving more Zs and Ws, but are still exceedingly rare.

Now, for energies around the GeV scale, matter effects on neutrino oscillations do start to affect the oscillation pattern. However, this is through so-called coherent forward scattering, which is essentially an interference effect on the neutrino propagator and therefore proportional to the Fermi constant (unlike the scattering, which is proportional to the Fermi constant squared). For reactor neutrino experiments, such as KamLAND or Daya Bay, we have neutrinos with energies in the MeV range and not even coherent forward scattering plays any role whatsoever.

The bottom line is: Neutrinos interact very very very seldom. This is the reason we need such big detectors.

For the rest of the post, I would have to agree with Scientific America, Nuovo Ciemento, and Matt Strassler. The weak force simply has a different structure and the existence of magnetic monopoles (or GUTs in general) are still without experimental evidence. This line of discussion is also going towards speculation of personal theories, which is outside of the scope of PF according to the terms and guidelines.

8. Oct 14, 2014

### Davephaelon

Orodruin:

I've heard of the Fermi constant and coherent forward scattering, but really didn't know exactly what they were, so I have a big learning curve ahead of me. I was aware of the energy dependence of neutrino interactions from various literature and the extremely low likelyhood of interaction with matter. I read once that a light-year of solid lead would be needed for a single neutrino to interact, or something to that effect. One new thing I learned from the posts here was that the order of probability of an interaction is a function of the number of vertices in the Feynman diagram for that interaction.

I'm currently reading "The MINOS Experiment: results and prospects" by J.J Evans, but the technical detail is such that I need to learn more of the physics to properly understand and appreciate it. This also applies to other highly technical papers that I've been looking at. I have the 3rd edition of "Introduction to High Energy Physics" by Donald H. Perkins. It's a bit dated (1987), but I assume most of the content is still relevant to current physics theory, with the exception of the confirmation of neutrino oscillation in the experiments that you mentioned, and possibly a few other thing.

Thanks for the detailed response.

9. Oct 14, 2014

### Davephaelon

Is it possible for you to draw a Feynman diagram of the interaction with the tools on this site? I would be interested to see what it looks like.

10. Oct 14, 2014

### Orodruin

Staff Emeritus
To be quite honest, Perkins' book from '87 is seriously outdated. A short selection of things we have discovered since:
- Neutrino oscillations
- The top quark
- The tau neutrino
- The Higgs(!)
The last item on this list really implies that any textbook not revised since summer 2012 is outdated.

11. Oct 14, 2014

Staff Emeritus
I don't think so. You have an incoming nu and a nucleus - a Z is exchanged (2 vertices) between them and scatters the nu. The nu then emits a virtual Z (one more vertex) which then couples to a nu nubar pair (one more vertex), There are other diagrams at the same order.

12. Oct 15, 2014

### Davephaelon

Since such an interaction is greatly suppressed by the usual rules of physics, might the same interaction be possible, but occur via the oscillation mechanism? Hopefully, I don't sound too naive, as a layperson with a broad general knowledge of physics.

13. Oct 15, 2014

### Staff: Mentor

The oscillation does not produce more neutrinos or change their energy.

Muon-neutrino + electron -> Muon + electron-neutrino with a subsequent decay of the muon involves two W bosons, but the muon has enough time to decay so this process is more frequent. The conversion of muon-neutrinos to muons is one of the processes used in neutrino detectors (although nuclei are more likely interaction partners than electrons), so it does happen with a reasonable, well-known probability.

14. Oct 17, 2014

### Davephaelon

mfb,

In the interaction: νμ + e- → μ- + νe wouldn't there be just one W on the left side of the equation? (I couldn't make the nu symbol Italic, but hopefully it will look OK).

15. Oct 17, 2014

### Staff: Mentor

mfb's comment about two W's was for the total process: $\nu_\mu + e^- \rightarrow \mu^- + \nu_e$ followed by decay of the muon: $\mu^- \rightarrow e^- + \nu_\mu + \bar \nu_e$.

16. Oct 17, 2014

### Davephaelon

jtbell,

I was assuming that, but I just wanted to make sure. I should have rephrased the question. When I saw his post, my first thought was that would be 4 weak vertices, so the reaction couldn't happen, even though I was well aware that it was one of the neutrino detection interactions used in detectors. Then I realized it had to be two separate interactions, one on each side that he was referring to.

By the way how did you manage to make the Greek letters go Italic?

17. Oct 17, 2014

### Staff: Mentor

18. Oct 17, 2014

### Davephaelon

jtbell,

Thank you for referring me to that. I'll print it out so I'll have it as a handy reference. I assume it must also show how to put the bar over particle symbols, as well, to indicate the anti-particle (haven't completely read it yet).

19. Oct 17, 2014

### Davephaelon

Now in weak interactions mediated by the W's and Z bosons, since each such interaction is shown as a wiggly line with 2 end points (2 vertices), such interactions, I assume, can only have an even number of vertices - 2, 4, 6, etc. But, for a single interaction since a 4 vertice weak interaction has too low a probability to occur, only 2 vertice weak interactions can occur with the W or Z. Would these assumptions be true, or am I generalizing too much? Also, is there any reaction that could produce a 3 vertice weak interaction?

20. Oct 17, 2014

### Staff: Mentor

You can always see the LaTeX code for an equation that someone else has posted here, by using the "Reply" option on the post, and examining the quoted post (you don't actually have to post the reply, of course!). Or you can hover the mouse over the equation and click on it the right way. On my Mac with a single-button mouse, I do a control-click and get a popup menu. (On a PC I think it's right-click.) Then I choose "Show Math As" followed by "TeX Commands".

The overbar is in the list of "Frequently Used Symbols" in that FAQ, but probably not where you might think to look for it... it's listed as an option for "complex conjugate."