The Electroweak Higgs and The Doublet-triplet Splitting Problem
The electroweak Higgs doublets come from an SO(10) 10H. Unfortunately, this same 10 also contains triplets. The masses of the doublets have to be stabilized at the electroweak scale, which is many orders of magnitude smaller than the GUT scale whereas the triplets have to be really heavy in order to prevent triplet-mediated proton decays. See doublet-triplet splitting problem.
Among the solutions for it is the Dimopoulos-Wilczek mechanism, or the choice of diag(0,0,0,1,1,0,0,0,-1,-1) of <45>. Unfortunately, this is not stable once the 16/ or 126/ sector interacts with the 45 sector.
Read more about this topic: SO(10) (physics)
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