Neutrino Masses in Supersymmetric SU ( 3 ) C × SU ( 2 ) L × U ( 1 ) Y × U ( 1 ) ′ Models

We consider various possibilities for generating neutrino masses in supersymmetric models with an additional U(1)′ gauge symmetry. One class of models involves two extra U(1)′ ×U(1)′′ gauge symmetries, with U(1)′′ breaking at an intermediate scale and yielding small Dirac masses through high-dimensional operators. The right-handed neutrinos N c i can naturally decouple from the low energy U(1)′, avoiding cosmological constraints. A variant version can generate large Majorana masses for N c i and an ordinary see-saw. We secondly consider models with a pair of heavy triplets which couple to left-handed neutrinos. After integrating out the heavy triplets, a small neutrino Majorana mass matrix can be generated by the induced non-renormalizable terms. We also study models involving the double-see-saw mechanism, in which heavy Majorana masses for N c i are associated with the TeV-scale of U(1) ′ breaking. We give the conditions to avoid runaway directions in such models and discuss simple patterns for neutrino masses.