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

Abstract

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 (l) symmetry. We demonstrate that it is possible to relate the large vacuum expectation value for the singlet to small neutrino masses in both of these models via the see-saw..