  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. 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.
