Right-handed neutrino dark matter in the classically conformal U(1)' extended Standard Model

Abstract: We consider the dark matter (DM) scenario in the context of the classically conformal U(1)' extended standard model (SM), with three right-handed neutrinos (RHNs) and the U(1)' Higgs field. The model is free from all the U(1)' gauge and gravitational anomalies in the presence of the three RHNs. We introduce a $Z_2$-parity in the model, under which an odd-parity is assigned to one RHN, while all the other particles is assigned to be $Z_2$-even, and hence the $Z_2$-odd RHN serves as a DM candidate. In this model, the U(1)' gauge symmetry is radiatively broken through the Coleman-Weinberg mechanism, by which the electroweak symmetry breaking is triggered. There are three free parameters in our model, the U(1)' charge of the SM Higgs doublet ($x_H$), the new U(1)' gauge coupling ($g_X$), and the U(1)' gauge boson ($Z'$) mass ($m_{Z'}$), which are severely constrained in order to solve the electroweak vacuum instability problem, and satisfy the LHC Run-2 bounds from the search for $Z'$ boson resonance. In addition to these constraints, we investigate the RHN DM physics. Because of the nature of classical conformality, we find that a RHN DM pair mainly annihilates into the SM particles through the $Z'$ boson exchange. This is the so-called $Z'$-portal DM scenario. Combining the electroweak vacuum stability condition, the LHC Run-2 bounds, and the cosmological constraint from the observed DM relic density, we find that all constrains complementarily work to narrow down the allowed parameter regions, and, especially, exclude $m_{Z'} \lesssim 3.5$ TeV. For the obtained allowed regions, we calculate the spin-independent cross section of the RHN DM with nucleons. We find that the resultant cross section well below the current experimental upper bounds.