Invisible Z' and dark matter: LHC vs LUX constraints

We consider a simple, yet generic scenario in which a new heavy $Z'$ gauge boson couples both to SM fermions and to dark matter. In this framework we confront the best LHC limits on an extra gauge boson $Z'$ to the constraints on couplings to dark matter from direct detection experiments. In particular we show that the LHC searches for resonant production of dileptons and the recent exclusion limits obtained by the LUX collaboration give complementary constraints. Together, they impose strong bounds on the invisible branching ratio and exclude a large part of the parameter space for generic $Z'$ models. Our study encompasses many possible $Z'$ models, including SSM, $E_6$-inspired or B-L scenario.