LAUSR

Neutrino mass and dark matter are the two leading questions in science, which require the new physics beyond the conventional standard model [1]. Additionally, the muon anomalous magnetic moment recently measured also reveals a significant deviation at 4.2σ from the standard model prediction [2]. Within the attempts to solve simultaneously the first two issues, the scotogenic setup [3] is the most compelling. Indeed, it introduces an inert scalar doublet and three sterile neutrinos, which couple to the usual lepton doublets, producing the relevant neutrino masses through the one-loop contribution of these new fields, while the lightest of which, either a neutral inert scalar or a sterile neutrino, is viably to be a dark matter candidate. However, an exact Z2 parity, that necessarily makes all the new fields odd, plays the crucial role for the model properly working as well as stabilizing the dark matter. The origin of the Z2 was left as an open question. Further, it is found that the minimal scotogenic contributes insignificantly (and negative) to the muon g − 2 [4]. We suggest that if a new vector doublet is proposed instead of the inert scalar doublet, it cannot develop a vacuum expectation value due to the Lorentz invariance, in opposition to the inert scalar case that potentially breaks the Z2, inducing an unwanted tree-level neutrino mass. Additionally, the standard model symmetry demands that the vector doublet couples to normal matter only through new fermions; for such reason, the sterile neutrinos are presented. Furthermore, the Lagrangian of the vector doublet realizes a matter parity, instead of the Z2, which commonly arises as a residual gauge symmetry in the theories that let the vector doublet be a part of the extended gauge field.