Models featuring spontaneous CP-violation, an invisible axion and light neutrino masses

We study models with three Higgs doublets and a complex Higgs singlet which feature a Peccei-Quinn symmetry and an invisible axion. The models are classified according to which subgroups of Peccei-Quinn symmetry and abelian chiral lepton transformations are explicitly broken by the scalar potential. In particular those theories which feature spontaneous CP-violation are identified. Included among these are a model due to Zhitnitskii, together with a new model which has natural flavour conservation due to the surviving U(1) symmetry. We demonstrate that it is possible to relate the large vacuum expectation value for the singlet to small neutrino masses in both of those models via the see-saw mechanism. (orig.)