# Neutrino symbol

## Main Question or Discussion Point

Do anyone know why in some article or books, they write the neutrino without distinguish the type among them.

e.g.

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

does it have speacial meaning to write like this?

## Answers and Replies

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fss
It's a general form of the muon decay. I guess the author doesn't distinguish the type of neutrino because they don't distinguish the charge of the muon that's decaying.

There are two reasons to not label the neutrinos. The first is the fact that we must conserve each lepton number in this reaction at tree level, so the nubar must be an electron-neutrino and the nu must be a mu neutrino.

The other reason is that neutrinos oscillate, so even if you produced a mu neutrino, it won't stay that way.

There are two reasons to not label the neutrinos. The first is the fact that we must conserve each lepton number in this reaction at tree level, so the nubar must be an electron-neutrino and the nu must be a mu neutrino.

The other reason is that neutrinos oscillate, so even if you produced a mu neutrino, it won't stay that way.
the second reason is more acceptable...since neutrino oscillation is happening...

jtbell
Mentor
At the moment the neutrino is created, it has probability 1 of being in whatever flavor state it's supposed to be in by conservation of lepton number, and probability 0 of being in some other flavor state. As time passes, the probabilities evolve in an oscillatory fashion. So at the moment of creation, we can label its flavor definitely.

At the moment the neutrino is created, it has probability 1 of being in whatever flavor state it's supposed to be in by conservation of lepton number, and probability 0 of being in some other flavor state. As time passes, the probabilities evolve in an oscillatory fashion. So at the moment of creation, we can label its flavor definitely.
so you mean that during the creation of neutrino, lepton number is conserved. After the creation they oscillate and lepton number do not conserved?

jtbell
Mentor
Correct.

so you mean that during the creation of neutrino, lepton number is conserved. After the creation they oscillate and lepton number do not conserved?
Just to clarify, the total lepton number IS conserved, but the lepton "family" numbers are not.

That is, before neutrino oscillation, it was thought there were three conserved lepton numbers, the electronic number $L_e$, the muonic number $L_\mu$, etc. Neutrino oscillation mixes these families, so those three numbers are not conserved. However the total number of leptons still is conserved, $L = L_e + L_\mu + L_\tau$.

so you mean that during the creation of neutrino, lepton number is conserved. After the creation they oscillate and lepton number do not conserved?
Correct.
I'm going to dispute that this is correct on the level of an individual event. The problem is that the neutrino flavor states are not physical states. Since these are superpositions of the neutrino mass eigenstates, the flavor states has indefinite mass. The means that the kinematics of the reaction are also not well defined. The sense in which it is correct to talk about neutrinos being created in flavor states is strictly that that leads to the correct mathematics in the limit that the neutrino mass states can't be distinguished by any process available either at production or detection.

Just to clarify, the total lepton number IS conserved, but the lepton "family" numbers are not.

That is, before neutrino oscillation, it was thought there were three conserved lepton numbers, the electronic number $L_e$, the muonic number $L_\mu$, etc. Neutrino oscillation mixes these families, so those three numbers are not conserved. However the total number of leptons still is conserved, $L = L_e + L_\mu + L_\tau$.
Total lepton number also may not be conserved. It depends on the nature of the mechanism generating the neutrino masses.

Total lepton number also may not be conserved. It depends on the nature of the mechanism generating the neutrino masses.
I thought neutrino oscillation just changes flavor, not the total number of leptons. So I don't understand what you mean here. Can you give more details?

While this is a bit off topic, are there any experimental constraints on the possible lagrangian terms for the neutrino masses? For instance, can we rule out the simplest possibility:
$$m\bar{\psi}\psi$$

I thought neutrino oscillation just changes flavor, not the total number of leptons. So I don't understand what you mean here. Can you give more details?

While this is a bit off topic, are there any experimental constraints on the possible lagrangian terms for the neutrino masses? For instance, can we rule out the simplest possibility:
$$m\bar{\psi}\psi$$
Neutrino oscillation does only change flavor. However, with certain mass-generating mechanism, neutrinos turn out to be their own anti-particles, meaning that there are non-zero lepton number-violating neutrino propagators.

As yet, there is no particular experiment reason to believe either way.

Oh, okay. The whole majorana vs dirac mass term issue.

Regarding comparing to experiment, I read some of a particle data group summary that was a pretty good intro:
http://pdg.lbl.gov/2006/reviews/numixrpp.pdf

However I'm still not fully understanding why there aren't more constraints on the mass term. If we can see flavor mixing, why can't we see "chirality mixing" due to the dirac mass term?

Oh, okay. The whole majorana vs dirac mass term issue.

Regarding comparing to experiment, I read some of a particle data group summary that was a pretty good intro:
http://pdg.lbl.gov/2006/reviews/numixrpp.pdf

However I'm still not fully understanding why there aren't more constraints on the mass term. If we can see flavor mixing, why can't we see "chirality mixing" due to the dirac mass term?
There are, in principle, effects that should be detectable; but, they tend to be suppressed by the smallness of the neutrino masses. For example, neutrinoless double beta decay would be incontrovertible evidence that neutrinos are Majorana in nature; but, the Feynman diagram for it has a neutrino mass insertion that suppresses the whole process, making it quite rare.

As for ordinary weak processes, in those cases the chirality of the neutrino is fixed by the interaction vertex (or nothing detectable is produced). And, then, a chirality flip is suppressed by a neutrino mass insertion.

so......what do the neutrino symbol mean in
$$\begin{array}{c}\mu^-\rightarrow e^-+\nu+\bar{\nu} \\ \pi^-\rightarrow \mu^-+\overline{\nu}\end{array}$$

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I think it is just for simplicity.