Search for Sterile Neutrinos Mixing with Muon Neutrinos in MINOS

We report results of a search for oscillations involving a light sterile neutrino over distances of 1.04 and $735\mathrm{k}\mathrm{m}$ in a ${\nu }_{\mu }$-dominated beam with a peak energy of $3\mathrm{G}\mathrm{e}\mathrm{V}$. The data, from an exposure of $10.56\times {10}^{20}\text{protons on target}$, are analyzed using a phenomenological model with one sterile neutrino. We constrain the mixing parameters ${\theta }_{24}$ and $\mathrm{\Delta }{m}_{41}^2$ and set limits on parameters of the four-dimensional Pontecorvo-Maki-Nakagawa-Sakata matrix, $\mathrm{\mid }{U}_{\mu 4}{\mathrm{\mid }}^2$ and $\mathrm{\mid }{U}_{\tau 4}{\mathrm{\mid }}^2$, under the assumption that mixing between ${\nu }_e$ and ${\nu }_s$ is negligible ($\mathrm{\mid }{U}_{e4}{\mathrm{\mid }}^2=0$). No evidence for ${\nu }_{\mu }\to {\nu }_s$ transitions is found and we set a world-leading limit on ${\theta }_{24}$ for values of $\Delta m^{2}_{41} \lesssim 1,$\mathrm{e}\mathrm{V}$^{2}$.