# How to give left-handed neutrinos alone Majorana mass?

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On Wikipedia, it says https://en.wikipedia.org/wiki/Georgi–Glashow_model#Breaking_SU(5):

Fermions transforming as a 1 under SU(5) are now thought to be necessary because of the evidence for neutrino oscillations, unless a way is found to introduce a tiny Majorana coupling for the left-handed neutrinos.

This text tries to explain how the $$(1,2)_{-1/2}$$ of left-handed lepton (with a upper component of the doublet as left-handed neutrino) and $$(1,1)_{0}$$ as right-handed neutrino, can get a mass.

My question is that how many ways can $$(1,2)_{-1/2}$$ and $$(1,1)_{0}$$ can get a mass?

It seems to me

1). $$(1,1)_{0}$$ alone can get a Majorana mass.

2). $$(1,2)_{-1/2}$$ and $$(1,1)_{0}$$ together can get a Dirac mass.

3). Is there any difficulty for $$(1,2)_{-1/2}$$ alone (say a upper component of the doublet as left-handed neutrino) to get a Majorana mass? I do not see an immediate no go reason. But Wikipedia seems to say this is a big new discovery? See Wikipedia: "unless a way is found to introduce a tiny Majorana coupling for the left-handed neutrinos." Why?

The original text goes like:

This post imported from StackExchange Physics at 2020-12-01 17:41 (UTC), posted by SE-user annie marie heart
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