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 _i^c can naturally decouple from the low energy U(1)′, avoiding cosmological constraints. A variant version can generate large Majorana masses for N_i^c and an ordinary seesaw. 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 nonrenormalizable terms. We also study models involving the double-seesaw mechanism, in which heavy Majorana masses for N_i^c 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.