Naturalness of the invisible axion model

We discuss the choice of parameters that is necessary to establish the enormous hierarchy between the doublet and singlet Higgs vacuum expectation values in the invisible axion model. We show that this choice is associated with an approximate symmetry of the theory, thus demonstrating that the hierarchy in this model is natural in the sense of 't Hooft. It is then shown that this choice also leads to the existence of Higgs particles with masses ∝MW, which is particularly relevant for invisible axion models featuring spontaneous CP-violation. We comment on how our conclusions are affected by the introduction of right-handed neutrinos with large Majorana masses within the context of the see-saw mechanism. (orig.)