# Mechanisms of mass generation for Dirac neutrinos

If neutrinos are Majorana particles, one way of explaining their small masses is the seesaw mechanism.

Now say I'd like my neutrinos to be Dirac, for symmetry to the quark sector. What mechanisms exist to explain Dirac neutrinos' mass?

Also, maybe interesting in this context: Why is the neutrino mass considered more in need on an explanation than the electron mass? Could the masses of the Fermions (I mean their terms in the Lagrangian, as well as their values) maybe all of the same origin?

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See, for instance, this link: ufn.ru/en/articles/1977/10/b –  Murod Abdukhakimov Dec 4 '12 at 8:21
Sorry, the previous article is in Russian. Here is a link to English version: sciencedirect.com/science/article/pii/0370157378900959 –  Murod Abdukhakimov Dec 4 '12 at 8:25
The Sterile Neutrino Wikipedia page (en.wikipedia.org/wiki/Sterile_neutrino) addresses possible neutrino mass sources. There doesn't seem to be any known mechanism to give Dirac neutrinos mass and if they are Dirac fermions beyond-the-standard-model physics is involved. –  Brandon Enright Apr 29 '13 at 22:23
By the way, I wonder why physicists speak about rest masses of neutrinos with such certainty. Experiments suggest that neutrinos do not propagate at c all their way, but we do not understand well how and with what can they interact. Where this belief, that deviations from c are caused by a tiny mass term, goes from? –  Incnis Mrsi Aug 22 '14 at 12:00

## 1 Answer

You can generate Dirac neutrino masses through the Higgs mechanism by introducing right handed neutrinos (in the same way you generate masses for the upper quarks). Since neutrino masses are at the sub-$eV$ scale, this means that the Yukawa couplings have to be unnaturally small, of order $10^{-12}$.

People prefer to keep $\mathcal{O}(1)$ Yukawa's and blame the unusual smallness of neutrino masses on the fact that these are neutral particles. If neutrinos happen to coincide with anti-neutrinos, then lepton number is violated by two units (global symmetries are not sacred). In this case it is natural to introduce a large Majorana mass scale $\Lambda$ which ends up suppressing the neutrino masses via See-saw mechanism as $\langle\phi\rangle^2/\Lambda$. People like this because this large scale turns out be quite close to the Grand Unification scale.

An alternative way to generate small masses for neutrinos without introducing a large Majorana scale or Right handed neutrinos is through radiative corrections. You can assume that neutrino masses are zero at the tree level (as in the SM) and generate small non-zero masses at 1 or 2-loop level by introducing new heavy scalar fields.

One nice example is the Zee model, where the SM scalar sector is extended to include a second Higgs doublet $\phi_2$ and a Higgs singlet $\omega$. The Loop producing neutrino masses is given by

These models also break lepton number, but generally at a much lower scale. (e.g. at TeV scale).

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