Heavy Sterile Neutrinos in Tau Decays and the MiniBooNE Anomaly

Current results of the MiniBooNE experiment show excess events that indicate neutrino oscillations, but only if one goes beyond the standard 3 family scenario. Recently a different explanation of the events has been given, not in terms of oscillations but by the production and decay of a massive sterile neutrino with large transition magnetic moment. We study the effect of such a sterile neutrino in the rare decays $\tau^- \rightarrow \mu^- \mu^+ \pi^- \nu$ and $\tau^{-}\rightarrow \mu^{-} \mu^{+} e^{-} \nu \nu$. We find that searches for these decays featuring displaced vertices between the $\mu^-$ and the other charged particles, constitute good tests for the existence of the sterile neutrino proposed to explain the MiniBooNE anomaly. These searches could be done with already existing experimental data.