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 $735\,\mathrm{km}$ in a $\nu_{\mu}$-dominated beam with a peak energy of $3\,\mathrm{GeV}$. The data, from an exposure of $10.56\times 10^{20}\,\textrm{protons on target}$, are analyzed using a phenomenological model with one sterile neutrino. We constrain the mixing parameters $\theta_{24}$ and $\Delta m^{2}_{41}$ and set limits on parameters of the four-dimensional Pontecorvo-Maki-Nakagawa-Sakata matrix, $|U_{\mu 4}|^{2}$ and $|U_{\tau 4}|^{2}$, under the assumption that mixing between $\nu_{e}$ and $\nu_{s}$ is negligible ($|U_{e4}|^{2}=0$). No evidence for $\nu_{\mu} \to \nu_{s}$ transitions is found and we set a world-leading limit on $\theta_{24}$ for values of $\Delta m^{2}_{41} \lesssim 1\,\mathrm{eV}^{2}$.