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

We study the Peccei-Quinn (PQ) symmetry of sterile right-handed neutrino sector and the gauge symmetries of the Standard Model (SM). 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 channels 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 ($m_chisim 10^2$ GeV). Their tiny couplings to SM particles are effectively induced by four-fermion operators. We show that such sterile axion is the PQ solution to the strong CP problem. The lightest sterile neutrino ($m_N^esim 10^2$ keV), sterile QCD axion ($m_a< 10^{-6}$ eV, $g_{agamma}< 10^{-13} {rm GeV}^{-1}$) and $chi$boson can be dark matter particle candidates, for their tiny couplings and long lifetimes inferred from the Xenon1T experiment. 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.