On Sterile neutrino explanation of LSND and MiniBooNE anomalies

We examine the compatibility between existing experimental data and a recently proposed explanation of the LSND and MiniBooNE anomalies, given in terms of a sterile neutrino $N$ whose decay is dominated by a radiative mode. We find that current experimental data on $\tau\rightarrow \mu\nu\nu\gamma$ decays are compatible with the sterile neutrino parameters required for the explanation of the anomalies, but $K\rightarrow \mu\nu\gamma$ shows a marginal tension with those parameters. We also propose experimental cuts on radiative $K$ decays that could test the sterile neutrino hypothesis better. Finally, we study the contribution of this sterile neutrino to $K\to\mu\nu e e$, and find that measurements of this process would provide powerful tests for the sterile neutrino explanation of the LSND and MiniBooNE anomalies, if the experimental cut on the invariant mass of the $e^{+}e^{-}$ pair could be reduced from its current value of 145 MeV to a value below 40 MeV.