  We study the Peccei-Quinn (PQ) symmetry of the sterile right-handed neutrino
sector and the gauge symmetries of the Standard Model. Due to four-fermion
interactions, spontaneous breaking of these symmetries at the electroweak scale
generates top-quark Dirac mass and sterile-neutrino Majorana mass. The top
quark channel yields massive Higgs, $W^\pm$ and $Z^0$ bosons. The sterile
neutrino channel yields the heaviest sterile neutrino Majorana mass, sterile
Nambu-Goldstone axion (or majoron) and massive scalar $\chi$boson. Four-fermion
operators effectively induce their tiny couplings to SM particles. We show that
a sterile QCD axion is the PQ solution to the strong CP problem. The lightest
and heaviest sterile neutrinos ($m_N^e\sim 10^2$ keV and $m_N^\tau\sim 10^2$
GeV), a sterile QCD axion ($m_a< 10^{-8}$ eV, $g_{a\gamma}< 10^{-13} {\rm
GeV}^{-1}$) and a Higgs-like $\chi$boson ($m_\chi\sim 10^2$ GeV) can be dark
matter particle candidates, for the constraints of their tiny couplings and
long lifetimes inferred from the $W$-boson decay width, Xenon1T and precision
fine-structure-constant experiments. The axion and $\chi$boson couplings to SM
particles are below the values reached by current laboratory experiments and
astrophysical observations for directly or indirectly detecting dark matter
particles.
