Complementarity of DM Searches in a Consistent Simplified Model: the Case of Z'

We analyze the constraints from direct and indirect detection on fermionic Majorana Dark Matter (DM). Because the interaction with the Standard Model (SM) particles is spin-dependent, a priori the constraints that one gets from neutrino telescopes, the LHC and direct detection experiments are comparable. We study the complementarity of these searches in a particular example, in which a heavy $Z'$ mediates the interactions between the SM and the DM. We find that in most cases IceCube provides the strongest bounds on this scenario, while the LHC constraints are only meaningful for smaller dark matter masses. These light masses are less motivated by thermal relic abundance considerations. We show that the dominant annihilation channels of the light DM in the Sun are either $b \bar b$ or $t \bar t$, while the heavy DM annihilation is completely dominated by $Zh$ channel. The latter produces a hard neutrino spectrum which has not been previously analyzed. We study the neutrino spectrum yielded by DM and recast IceCube constraints to allow proper comparison with constraints from direct detection experiments and LHC exclusions.