  We consider the Singlet Majorana fermion dark matter model, in which the
standard model particles interact with the dark sector through the mixing of a
singlet scalar and the Higgs boson. In this model both the dark matter and the
singlet scalar carry lepton number, the latter being a bilepton. We suppose the
existence of a $Z_2$ symmetry, remnant of some high energy local symmetry
breaking, that stabilizes the Majorana fermion. We analyzed the parameter space
of this model and found that the lepton number symmetry breaking scale, drove
by the singlet scalar, is constrained to be within hundreds to thousands of
GeV, so as to conform with the observed dark matter relic density. Finally, we
address the direct detection and invisible Higgs decay complementarity,
confronting our model with recent LUX and LHC constraints, as well as XENON1T
prospects.
