SimplestZ′model

The differences in family-lepton numbers are anomaly-free in the minimal standard model (MSM), and can therefore be gauged. For three generations of quarks and leptons, three models emerge depending on whether (i) $L_e-L_{\mu }$, (ii) $L_e-L_{\tau }$, or (iii) $L_{\mu }-L_{\tau }$ are gauged. These are the simplest models to feature a $Z^{\prime }$ boson because no fermions beyond those already present in the MSM are required to cancel gauge anomalies. We analyze the phenomenology of models (i) and (ii) in detail, and present constraints derived from low-energy neutral-current data and CERN LEP data. We find that these $Z^{\prime }$ bosons may have a relatively low mass yet still evade present experimental bounds, while remaining detectable in current accelerators. The introduction of neutrino masses into the models is then considered. We discuss how one may incorporate both the reported 17-keV neutrino, and the Mikheyev-Smirnov-Wolfenstein effect solution of the solar-neutrino problem. We then describe how to embed the extra U(1) gauge group into a horizontal SU(2)-symmetry group acting on leptons.