# Right handed neutrinos

1. Dec 25, 2007

### Jim Kata

Does that fact that it has been shown that neutrinos have mass in any way imply that there must be right handed neutrinos?

2. Dec 25, 2007

### Jim Kata

Follow up question. If there are right handed neutrinos is there an explanation as to why they haven't been observed?

3. Dec 25, 2007

### mjsd

not necessarily, because you can have a majorana mass term consisting of only one type of neutrino field: $$(\nu_L)^c \nu_L \Delta$$ but to make this term (after spontaneous symmetry breaking) to be invariant under the unbroken gauge group (SU(3) color and U(1) electric charge), then you need $$\Delta$$ to be a triplet field under weak-SU(2). So you can do without the right handed neutrino $$\nu_R$$ but have to introduce a new scalar field $$\Delta$$ to the Standard Model instead to give neutrino a mass.

having said that there are reasons to favor the existence of the right-handed neutrino to explain neutrino mass (eg. see-saw mechanism)

One explanation (the typical one) is that they are too heavy to be seen at colliders at current operating energies. The see-saw mechanism where light neutrino masses are related to heavy right-handed neutrino masses via
$$M_\text{light} \simeq \frac{\langle\phi\rangle^2}{M_\text{heavy}}$$
where $$\langle\phi\rangle$$ is the electroweak breaking VEV which is about 174GeV, tells us that if $$M_\text{light} \sim 0.1 \,\text{eV}$$ then that implies a $$M_\text{heavy}$$ of the order of $$10^{14}\,\text{GeV}$$ which is 100,000,000,000 times higher in energy than the current colliders can reach.

Last edited: Dec 25, 2007
4. Dec 25, 2007

### blechman

Actually, if you allow for non-renormalizable operators in the SM (coming from a GUT theory, for example) then you immediately get a Majorana mass without adding anything (no new scalars)! In fact, the UNIQUE(!) dimension-5 operator will do it:

$$\mathcal{L}_5=\frac{c}{M}(HL)^2$$

where L is the lepton doublet and H is the Higgs doublet, and c is some dimensionless coupling, and M is the UV scale where the SM breaks down (GUT scale, for instance). When you set H equal to its vev, then this will become a Majorana mass for the left handed neutrino, whose value is the same as what you'd expect from the see-saw mechanism. No RH neutrinos necessary. No new scalars necessary.

5. Dec 26, 2007

### mjsd

yes, perhaps it would be a good idea to point this out to the OP as well.
hope I didn't confuse anyone.