Effective aligned 2HDM with a DFSZ-like invisible axion

We discuss the possibility of having a non-minimal scalar sector at the weak scale within the framework of invisible axion models. To frame our discussion we consider an extension of the Dine–Fischler–Srednicki–Zhitnitsky invisible axion model with two additional Higgs doublets blind under the Peccei–Quinn symmetry. Due to mixing effects among the scalar fields, it is possible to obtain a rich scalar sector at the weak scale in certain decoupling limits of the theory. In particular, this framework provides an ultraviolet completion of the so-called aligned two-Higgs-doublet model and solves the strong CP problem. The axion properties and the smallness of active neutrino masses are also discussed.