The LSND and MiniBooNE Oscillation Searches at High $\Delta m^2$

This paper reviews the results of the LSND and MiniBooNE experiments. The primary goal of each experiment was to effect sensitive searches for neutrino oscillations in the mass region with $\Delta m^2 \sim 1$ eV$^2$. The two experiments are complementary, and so the comparison of results can bring additional information with respect to models with sterile neutrinos. Both experiments obtained evidence for $\bar \nu_\mu \rightarrow \bar \nu_e$ oscillations, and MiniBooNE also observed a $\nu_\mu \rightarrow \nu_e$ excess. In this paper, we review the design, analysis, and results from these experiments. We then consider the results within the global context of sterile neutrino oscillation models. The final data sets require a more extended model than the simple single sterile neutrino model imagined at the time that LSND drew to a close and MiniBooNE began. We show that there are apparent incompatibilities between data sets in models with two sterile neutrinos. However, these incompatibilities may be explained with variations within the systematic error. Overall, models with two (or three) sterile neutrinos seem to succeed in fitting the global data, and they make interesting predictions for future experiments.