Probing the LSND mass scale and four neutrino scenarios with a neutrino telescope

We show in this Letter that the observation of the angular distribution of upward-going muons and cascade events induced by atmospheric neutrinos at the TeV energy scale, which can be performed by a kilometer-scale neutrino telescope, such as the IceCube detector, can be used to probe a large neutrino mass splitting, |Δm2|∼(0.5–2.0) eV2, implied by the LSND experiment and discriminate among four neutrino mass schemes. This is due to the fact that such a large mass scale can promote non-negligible νμ→νe,ντ/ν̄μ→ν̄e,ν̄τ conversions at these energies by the MSW effect as well as vacuum oscillation, unlike what is expected if all the neutrino mass splittings are small.