Testing freeze-in with axial and vector $Z'$ bosons

The freeze-in production of Feebly Interacting Massive Particle (FIMP) dark matter in the early universe is an appealing alternative to the well-known - and constrained - Weakly Interacting Massive Particle (WIMP) paradigm. Although challenging, the phenomenology of FIMP dark matter has been receiving growing attention and is possible in a few scenarios. In this work, we contribute to this endeavor by considering a $Z^\prime$ portal to fermionic dark matter, with the $Z^\prime$ having both vector and axial couplings and a mass ranging from MeV up to PeV. We evaluate the bounds on both freeze-in and freeze-out from direct detection, atomic parity violation, leptonic anomalous magnetic moments, neutrino-electron scattering, collider, and beam dump experiments. We show that FIMPs can already be tested by most of these experiments in a complementary way, whereas WIMPs are especially viable in the $Z^\prime$ low mass regime, in addition to the $Z^\prime$ resonance region. We also discuss the role of the axial couplings of $Z^\prime$ in our results. We therefore hope to motivate specific realizations of this model in the context of FIMPs, as well as searches for these elusive dark matter candidates.
Comment: v2: Minor corrections, discussion expanded, updated figures, references added. Matches journal version