An extension of the SM based on effective Peccei–Quinn Symmetry

Peccei–Quinn (PQ) mechanism based on a chiral global U(1) symmetry is considered to be a simple and elegant solution for strong CP problem. The fact that the mechanism could be experimentally examined through the axion search makes it much more interesting and recently it causes a lot of attention again. However, it is also known that the mechanism is annoyed by two serious problems, that is, a domain wall problem and goodness of global symmetry. Any global symmetry is considered not to be exact due to the quantum effect of gravity. In this paper, we consider a solution to these problems, in which quark mass hierarchy and mixing, neutrino mass generation and existence of dark matter are closely related. In our solution, PQ symmetry is assumed to be induced through symmetry breaking at an intermediate scale of a local U(1) symmetry, and a global U(1) symmetry which plays a role of Froggatt–Nielsen symmetry . In the lepton sector, a remnant of the PQ symmetry controls neutrino mass generation and dark matter existence.