We study oscillations of the high energy atmospheric neutrinos in the Earth into sterile neutrinos with the eV-scale mass. The MSW resonance and parametric enhancement of the $\bar{ \nu}_\mu\to\bar{ \nu}_s$ oscillations lead to distortion of the zenith angle distribution of the muon-track events which can be observed by IceCube. Due to matter effect, the IceCube signal depends not only on the mixing element $U_{ \mu 4}$ relevant for LSND and MiniBooNE but also on $U_{ \tau 4}$ and the CP-violating phase $\delta_{ 24}$. We show that the case with $U_{ \tau 4} = \delta_{ 24} = 0$ leads to the weakest IceCube signal and therefore should be used to bound $U_{ \mu 4}$. We compute the zenith angle distributions of the $\nu_\mu-$events for different energy intervals in the range (0.1 - 10) TeV and find that inclusion of the energy information (binning in energy) improves the sensitivity to $\nu_s$ drastically. We estimate that with already collected (during 3 - 4 years) IceCube statistics the bound $|U_{ \mu 4}|^2 < 0.01$ ($99\%$ C.L.) can be established and the mixing required by LSND and MiniBooNE can be excluded at $(4 - 6) \sigma$ confidence level.
Categories: hep-ph astro-ph.HE