Anomaly-free chiral $U(1)_{D}$ and its scotogenic implication

We assume a dark $U_{D}$ symmetric hidden sector and explore its possible content such that neutrino mass and Dark Matter are generated through the scotogenic mechanism. The hidden sector is considered analogue to the Standard Model, namely the charge assignment of hidden fermions is chiral and anomaly-free. Moreover, $U_{D}$ is assumed broken by an only Higgs singlet that also generates masses to all hidden fermions, therefore the charge assignment is subjected to additional restriction. We search by computer program for charge assignments satisfying all these conditions, and identify the resulting minimal scotogenic models for Majorana neutrinos and Dirac neutrinos respectively in the sense of minimal number of messenger scalar involved. Particle spectrum, couplings, and phenomenologies of these minimal models are briefly discussed. DM is found multicomponent and always contains Dirac fermionic species.