The Wikipedia page on Georgi–Glashow model says
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
How many ways can $(1,2)_{-1/2}$ and $(1,1)_{0}$ can get a mass?
It seems to me that
$(1,1)_{0}$ alone can get a Majorana mass.
$(1,2)_{-1/2}$ and $(1,1)_{0}$ together can get a Dirac mass.
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:
