Anomaly-free dark matter with harmless direct detection constraints

Dark matter (DM) interacting with the SM fields via a Z-boson (Z-portal') remains one of the most attractive WIMP scenarios, both from the theoretical and the phenomenological points of view. In order to avoid the strong constraints from direct detection and dilepton production, it is highly convenient that the Z has axial coupling to DM and leptophobic couplings to the SM particles, respectively. The latter implies that the associated U(1) coincides with baryon number in the SM sector. In this paper we completely classify the possible anomaly-free leptophobic Z with minimal dark sector, including the cases where the coupling to DM is axial. The resulting scenario is very predictive and perfectly viable from the present constraints from DM detection, EW observables and LHC data (di-lepton, di-jet and mono-jet production). We analyze all these constraints, obtaining the allowed areas in the parameter space, which generically prefer mZ less than or similar to 500 GeV, apart from resonant regions. The best chances to test these viable areas come from future LHC measurements.