Neutrino Masses in Supersymmetric SU(3)_C x SU(2)_L x U(1)_Y x 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)' x 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.