geek update

Ok had to look at some work in U(1) abelian gauge models.  Specifically in connection to right handed neutrinos and see saw models.  Forgetting Supersymmetric models for a moment, which by the way I still need to read up on, you could have the ordinary tree-level seesaw models or the radiative see-saw.  It seems a lot of papers go for the radiative see-saw.  It gives you the leeway to introduce extra fields that allow for extra candidates for dark matter.  However in the ordinary Type seesaw model, the right handed neutrinos acquires a Majorana mass through the scalar field that mediates the extra gauge symmetry, after this symmetry is broken at a high scale.  You arrange the symmetry assignments such that you can can Dirac mass terms either through the Standard Model Higgs field or perhaps another SU(2) doublet.  And normal Seesaw commences.

However my only complication is knowing if in this case, you can have active-sterile neutrino oscillations in this case.  Obviously the mass matrix looks different in the mass basis than from the weak basis.  But it is quite possible, say, for one right neutrino to have U(1) assignment +1 and the ordinary neutrino to have -1.  Then you have symmetry breaking oscillations.  Which at the first thought of it, sounds wrong to me.  So I must be missing something.



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