# Neutrino Oscillation <-> Neutrino Mass

Doc Dienstag
Wikipedia says that the phenomenon of Neutrino Oscillation implies that the neutrino has a non-zero mass (http://en.wikipedia.org/wiki/Neutrino_oscillation" [Broken]).

Why is that? Why is it that Neutrino Oscillation can only exist, if neutrinos do have mass?

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Staff Emeritus
2021 Award
Because the rate of oscillation is proportional to the mass difference (squared, actually) between two states. If all three were massless, you wouldn't have oscillations.

Staff Emeritus
Wikipedia says that the phenomenon of Neutrino Oscillation implies that the neutrino has a non-zero mass (http://en.wikipedia.org/wiki/Neutrino_oscillation" [Broken]).

Why is that? Why is it that Neutrino Oscillation can only exist, if neutrinos do have mass?

The quick-and-dirty answer is that that is the way the neutrino physics has been formulated. The theoretical formulation for neutrinos predicted that, if there is some form of "mixing", then mass must be involved. So finding one implies the other based on current theoretical model.

A http://arxiv.org/abs/0712.1750" [Broken]. Note the physics shown in Fig. 2. Each of the neutrino state corresponds to a "mixing" of the neutrino mass states. So the current theory says that if you see a neutrino switching flavors, then the mechanism that describes this contains some value of masses for each of the neutrinos. So that's how we conclude that they have masses.

Zz.

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Mentor
The basic idea behind neutrino oscillations is that each neutrino "flavor" (e, mu, tau) is a QM superposition of three mass eigenstates (usually called nu_1, nu_2, nu_3) with different masses. The different masses have different wavelengths for the same energy, so as they propagate, they interfere with each other. This causes the probabilities of getting each flavor to oscillate with position.

Doc Dienstag
Masses of Neutrinos

Context:
Neutrino oscillation is an example for a phenomenon that led physicists to believe, that neutrinos do have masses and to refine the original Standard Modell, that did not account for neutrinos to have a mass other than zero.

Question:
Why though did people assume that neutrinos were massless in the first place? It seems to me, that there is no other difference between an electron-neutrino, a tauon-neutrino or a myon-neutrino other than their masses. How then did it make sense at the time to assume that there are three types (=generations?) of neutrinos without even knowing a difference between them? What would be the point of a Standard Model that has three different neutrinos with no difference between them?

Is the answer to my question perhaps that physicists only discovered that there are three types of neutrinos at the same time that they concluded that neutrinos must have a mass other than zero?

Thank you.

Doc Dienstag
Thank you very much for your help.

Would it be correct to say that, when Ray Davis Jr. started detecting the sun's neutrino flux in the late 60s, he was not only unaware of the fact that neutrinos do have masses, but he was also unaware of the fact that there are three types of neutrinos?

Staff Emeritus
Thank you very much for your help.

Would it be correct to say that, when Ray Davis Jr. started detecting the sun's neutrino flux in the late 60s, he was not only unaware of the fact that neutrinos do have masses, but he was also unaware of the fact that there are three types of neutrinos?

That's why for the longest time, there was a "solar neutrino mystery", which was the missing amount of electron neutrino from the sun reaching the earth from that predicted. It is only recently that that mystery has been solved.

Zz.

humanino

there is no other difference between an electron-neutrino, a tauon-neutrino or a myon-neutrino other than their masses
There is at least another difference : they carry leptonic charge. Technically, they are also color singlet but that is irrelevant. Anyway, for instance in TASI02 lectures on neutrino physics, you find some reasons why the SM does not include neutrino masses. I don't know of a short, neat, "big principle" answer to this question. There are several possible terms you may imagine, and why none of them is possible requires separate arguments.

Homework Helper
Gold Member
Thank you very much for your help.

Would it be correct to say that, when Ray Davis Jr. started detecting the sun's neutrino flux in the late 60s, he was not only unaware of the fact that neutrinos do have masses, but he was also unaware of the fact that there are three types of neutrinos?
"Unaware" is not quite appropriate. He probably knew that there were two types of neutrino that had been seen by then. When he found too few solar neutrinos, either errors (of which there were several at the time) in solar models or some loss of neutrino through oscillation or decay or absorption were all considered. Davis was aware of these possibilities.
I don't think he worried too much about why, but was more concerned with getting the measurement right, which he did.

Hi Doc, the history of that is a little long and convoluted. But to answer your second question, people analyzed the decay of things like the Z boson. So Z --> v vbar. In short, the more species of neutrinos there are, the shorter the decay width is. It was then inferred that there had to be exactly three light (possibly but not necessarily massless) neutrinos.

Why were they assumed to be massless as often read in intro texts? Well, giving them mass wasn't really that much of a theoretical problem, its just that they were so darn light that it almost didn't make much of a difference one way or the other for the sensitivity of the experiments of the time. It wasn't until people began to appreciate the implications of the theory of neutrino oscillations (which is actually very simple) and measured discrepancies in solar fluxes that it became a real possibility that there was indeed a small but nonzero mass.

Mentor
Until neutrino oscillations were observed during the last decade, there was simply no solid experimental evidence for neutrinos having mass. Analysis of various kinds of neutrino experiments (including earlier searches for neutrino oscillations) produced upper limits that became smaller and smaller as the years passed.

For example, the mass of the neutrino should affect the shape of the energy spectrum of the emitted electrons in beta decay, but for a long time, no such effects were visible. During the last couple of decades, some experimenters have claimed to observe features in the tritium beta-decay spectrum that are consistent with a neutrino mass of a few eV, but these are controversial because of experimental difficulties with such measurements. I think I remember reading that these results are inconsistent with the more recent results from neutrino oscillations.

I think that even when Pauli "invented" the neutrino in 1930, it was recognized that its mass would have to be much smaller than that of the electron, in order to fit within existing observations on beta decay.

humanino
For example, the mass of the neutrino should affect the shape of the energy spectrum of the emitted electrons in beta decay
The change would be, IIRC, at the high (electron-)energy end point of the spectrum, where there is no phase space available, huge statistical error bars, and therefore, poor experimental sensitivity. After writing this I found this LA paper where Figure 1 illustrates what I'm trying to describe. So my question is, at this point, this is unrelated to neutrinoless double-beta decay, right ? Would not that channel seem much easier for experimentalists ? But this requires Majorana neutrinos, right ? So, right now it seems certain that neutrinos have mass, but unlikely that it is Majorana ? Thanks for the feedback

Homework Helper
Gold Member

Question:
Why though did people assume that neutrinos were massless in the first place? It seems to me, that there is no other difference between an electron-neutrino, a tauon-neutrino or a myon-neutrino other than their masses. How then did it make sense at the time to assume that there are three types (=generations?) of neutrinos without even knowing a difference between them? What would be the point of a Standard Model that has three different neutrinos with no difference between them?

Is the answer to my question perhaps that physicists only discovered that there are three types of neutrinos at the same time that they concluded that neutrinos must have a mass other than zero?
I may be the only one here old enough to answer some of your questions.

1. There was no evidence in theory or experiment for a mass for the neutrino, and most theoretical formulations were much neater without a neutrino mass. Feynman made a convincing argument about a massless neutrino being the cornerstone of the V-A weak interaction. But a neutrino mass was always considered a possibility, and there were even conjectural papers about neutrino oscillation early on. The 1965 PDG tables (then a wallet card) listed 0(<0.2 keV) for the electron neutrino mass.

2. There are important differences between the three types of neutrino. Their Weak
Interactions are different, with conservation of neutrino flavor. When an electron neutrino strikes a nucleus, it can produce an electron, but a muon neutrino can only produce a muon.
It was originally believed the the mu neutrino might be the same as the electron neutrino.
The experimental discovery that they had mutually exclusive weak interactions won the Nobel prize for Lederman, Schwartz, and Steinberger.
Incidentally, there are 8 massless gluons, all different, and all needed, but experimental determination of this is still in the future if ever.

3. One of the beauties of the SM is that there are three families of leptons, in consistency and collaboration with three families of quarks.

genneth
One minor note: if neutrinos are massless, then they would necessarily move at the speed of light. In that limit, there is no advancement of proper time, so they couldn't oscillate. Thus, if they oscillate (as experimentally observed), they must have mass.

And to answer one of the other points: weak flavour is certainly something observably different between the neutrinos...

Incidentally, there are theoretical reasons (which are admittedly not perfectly understood on the "why?" level) for there being the same number of lepton families as quark families.

dustinthewind
This is an old post but I just had to fix this. Here is the reason they assumed they had zero mass. It is in this paper here, http://hitoshi.berkeley.edu/neutrino/PhysicsWorld.pdf . "Since right-handed neutrinos have never been detected, particle physicists concluded that neutrinos had to be massless."

I.E. because if you can go faster than them they would appear left handed. Their relative momentum would reverse their handed ness.

Read the 1st part of page 36. It should explain it fairly well.

However reciently they have been detected to be going faster than the speed of light by Cern. And the fact that they had mass was a problem. Because of their handed ness. However this new speed would lable them as possibly a tachion particle. Which may solve the problem of their mass and their handedness. Nothing can go faster than light either.