Neutrino Masses and the Gluino Axion Model

We extend the recently proposed gluino axion model to include neutrino masses. We discuss how the canonical seesaw model and the Higgs triplet model may be realized in this framework. In the former case, the heavy singlet neutrinos are contained in superfields which do not have any vacuum expectation value, whereas the gluino axion is contained in one which does. We also construct a specific renormalizable model which realizes the mass scale relationship $M_{SUSY} \sim f_a^2/M_U$, where $f_a$ is the axion decay constant and $M_U$ is a large effective mass parameter.