Spontaneously stabilised dark matter from a fermiophobic $U(1)'$ gauge symmetry

We consider the possibility that dark matter is stabilised by a discrete $Z_2$ symmetry which arises from a subgroup of a $U(1)'$ gauge symmetry, spontaneously broken by integer charged scalars, and under which the chiral quarks and leptons do not carry any charges. A chiral fermion $\chi$ with half-integer charge is odd under the preserved $Z_2$, and hence becomes a stable dark matter candidate, being produced through couplings to right-handed neutrinos with vector-like $U(1)'$ charges, as in the type Ib seesaw mechanism. We calculate the relic abundance in such a low energy effective seesaw model containing few parameters, then consider a high energy renormalisable model with a complete fourth family of vector-like fermions, where the chiral quark and lepton masses arise from a seesaw-like mechanism. With the inclusion of the fourth family, the lightest vector-like quark can contribute to the dark matter production, enlarging the allowed parameter space that we explore.