We report results of a search for oscillations involving a light sterile neutrino over distances of 1.04 and 735 km in a ${\nu }_{\mu }$-dominated beam with a peak energy of 3 GeV. The data, from an exposure of $10.56\times 10^{20}$ 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, $|U_{\mu 4}{|}^2$ 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 $\mathrm{\Delta }{m}_{41}^2\lesssim 1{\mathrm{eV}}^2$.

• Received 6 July 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.151803