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. In this paper we first explore the conditions for an anomaly-free leptophobic $Z'$, which (if flavour-blind) has to coincide with that from gauged baryon-number in the SM sector. Then there are very few possibilities where, besides leptophobia, the coupling to DM is axial; namely four (quite similar) cases if the content of the dark sector is minimal. 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 $m_{Z'}\lesssim 500$ GeV, apart from resonant regions. The best chances to test these viable areas come from future LHC measurements.