Is there any mathematics to describe neutrinos with mass?

1. Nov 11, 2015

MacRudi

beneath all problems with gravitons to describe mathematically (simple said our idea of a graviton is a gluon with spin 2 which is only predicted through CFT in 5 dimensional AdS) we have another problem mathematically to describe.
We found 3 generations of neutrinos with mass through experiments. But where is the mathematic for it, that we can predict why and how the 3 generations of neutrinos can be described?

Is there any theory embedded in our standard theory, which can describe it?

2. Nov 11, 2015

Staff: Mentor

There are multiple theories that describe massive neutrinos. They are usually not considered parts of the Standard Model but that is a matter of semantics.
Those theories do not predict the neutrino masses, in the same way the Standard Model doesn't predict the other particle masses. They are free parameters in the models.

3. Nov 11, 2015

MacRudi

thanks. Yes I know, that there are some theorys but I ask for a mathematic embedded into standard model. It is interesting, that we can have an idea of a graviton, what it should be in particle physics and habe a QT mathematic for this. Also we have the same method for a Higgs Boson as it is mathematically only a castrated Tachyon through symmetry breaking. Before symmetry breaking it is only an ordinary Tachyon mathematically and will be castrated mathematically. mathematically it is a Tachyon with sombrero head which keeps him from flying away. lol It is all the same thinking behind. But for neutrinos we have no idea in the same method way. This is why I ask, if there is now any mathematics which can be embedded in the same thinking as we do with gravitons and Higgs bosons through QT thinking.

4. Nov 11, 2015

Staff: Mentor

As I said, usually neutrino masses are not considered as part of the standard model. This is an arbitrary definition of "standard model", but it means the question cannot have an answer.

There is nothing tachyonic about the Higgs, and I have no idea where you got that impression.
The extensions of the SM that include neutrino masses are much better understood than the attempts to add gravity. We don't know which theory is true (if any) for the neutrino masses, but all those models are well understood.

5. Nov 11, 2015

MacRudi

Seems you are not skilled in scalarfield mathematics. My Texmaker Skills are not good enough to write it here. Maybe @fzero is doing me a favor to explain it mathematically why a higgs boson is a tachyon before its symmetry breaking.
To the extension of SM it is known as SO (10) I would guess you mean. This would be the only Lie group theory which could be embedded into the SM. But we have many ?????? because this has many other problems on the other side beside that SUSY is not really confirmed, but other problems in itself. Other Group theorys have the problem that we cannot embed it into the SM. And complete other theories are not particle physics as we know.

But I think in this case @fzero can tell it much better with mathematics and can tell why it is not really so well understood as you think.

6. Nov 11, 2015

fzero

I am fairly certain that mfb knows more particle physics than I do, so you shouldn't jump to such conclusions, which seem disrespectful in any case.

The Higgs boson looks like a tachyon if you expand the field around the false vacuum where $\langle H\rangle = 0$, because of the wrong sign of the mass term. Expanding around the true vacuum results in the correct, nontachyonic, mass term.

SO(10) is not the only extension of the SM. The simplest models of neutrino masses do not require any changes in the gauge group or adding SUSY. Typically these models involve adding a right-handed particle that can couple to the left-handed leptons of the SM through the Higgs field. Some basic equations are described at https://en.wikipedia.org/wiki/Seesaw_mechanism, while http://arxiv.org/abs/hep-ph/0603118 provides a comprehensive, but much more technical review of the subject. The the discussion of RH neutrinos begins in section II and continues in section IV. They go into far more detail than I could and the explanation to equation ratio seems rather good to me.

7. Nov 12, 2015

MacRudi

thanks so much for your help @fzero

and it would maybe help to show the dilemma of the false field and the hope to find compliment Higgspart to make the higgs mechanism as description complete. (we have then similar discussion here as in the special geometry thread)

to the Lie Group discussion. But without any higgs mechanism we only can hope that SO (10) is the right answer. Right?

8. Nov 14, 2015

serp777

Nice pun--matter of semantics.