Limits on sterile neutrino mixing using atmospheric neutrinos in Super-Kamiokande

We present limits on sterile neutrinomixing using 4,438 live-days of atmospheric neutrinodata from the Super-Kamiokandeexperiment. We search for fast oscillations driven by an eV$^2$-scale mass splitting and for oscillations into sterile neutrinosinstead of tau neutrinosat the atmospheric mass splitting. When performing both these searches we assume that the sterilemass splitting is large, allowing $\sin^2(\Delta m^2 L/4E)$ to be approximated as $0.5$, and we assume that there is no mixing between electron neutrinosand sterile neutrinos($|U_{e4}|^2 = 0$). No evidence of sterileoscillations is seen and we limit $|U_{\mu4}|^2$ to less than 0.041 and $|U_{\tau4}|^2$ to less than 0.18 for $\Delta m^2 > 0.8$ eV$^2$ at the 90% C.L. in a 3+1 framework. The approximations that can be made with atmospheric neutrinosallow these limits to be easily applied to 3+N models, and we provide our results in a generic format to allow comparisons with other sterile neutrinomodels.