Consequences of an Abelian Z' for neutrino oscillations and dark matter

The Standard Model's accidental and anomaly-free currents: $B-L$, $L_e-L_\mu$, $L_e-L_\tau$, and $L_\mu-L_\tau$, could be indicative of a hidden gauge structure beyond the Standard Model. Additionally, neutrino masses can be generated by a dimension-5 operator that generically breaks all of these symmetries. It is therefore important to investigate the compatibility of a gauged $U'(1)$ and neutrino phenomenology. We consider gauging each of the symmetries above with a minimal extended matter content. This includes the $Z'$, an order parameter to break the $U'(1)$, and three right-handed neutrinos. We find all but $B-L$ require additional matter content to explain the measured neutrino oscillation parameters. We also discuss the compatibility of the measured neutrino textures with a non-thermal dark matter production mechanism involving the decay of the $Z'$. Finally, we present a parametric relation that implies that a sterile neutrino dark matter candidate should not be expected to contribute to neutrino masses beyond ten parts per million.