Consequences of an Abelian $Z^{\prime }$ 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 $U^{\prime }(1)$ and neutrino phenomenology. We consider gauging each of the symmetries above with a minimal extended matter content. This includes the $Z^{\prime }$, an order parameter to break the $U^{\prime }(1)$, 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 nonthermal dark matter production mechanism involving the decay of the $Z^{\prime }$. Finally, we present a parametric relation that implies that any sterile neutrino dark matter candidate should not be expected to contribute to neutrino masses beyond ten parts per million.

Figure 1

The process $N_s\to \nu +\gamma$ proceeding via a loop of W-bosons and leptons. The decay rate is proportional to ${\sin }^2\theta$.