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

Abstract

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, $g_{a\gamma }<10^{-13}{\mathrm{GeV}}^{-1}$) 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.

arXiv commentThe final version appears in Nuclear Physics B

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