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We study the Peccei-Quinn (PQ) symmetry of the sterile right-handed neutrinosector and the gauge symmetries of the Standard Model. Due to four-fermioninteractions, spontaneous breaking of these symmetries at the electroweak scalegenerates top-quark Dirac mass and sterile-neutrino Majorana mass. The topquark channel yields massive Higgs, $W^\pm$ and $Z^0$ bosons. The sterileneutrino channel yields the heaviest sterile neutrino Majorana mass, sterileNambu-Goldstone axion (or majoron) and massive scalar $\chi$boson. Four-fermionoperators effectively induce their tiny couplings to SM particles. We show thata sterile QCD axion is the PQ solution to the strong CP problem. The lightestand 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, $g_{a\gamma}< 10^{-13} {\rmGeV}^{-1}$) and a Higgs-like $\chi$boson ($m_\chi\sim 10^2$ GeV) can be darkmatter particle candidates, for the constraints of their tiny couplings andlong lifetimes inferred from the $W$-boson decay width, Xenon1T and precisionfine-structure-constant experiments. The axion and $\chi$boson couplings to SMparticles are below the values reached by current laboratory experiments andastrophysical observations for directly or indirectly detecting dark matterparticles.

Spontaneous Peccei-Quinn symmetry breaking renders sterile neutrino, axion and $\chi$boson to be candidates for dark matter particles