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, \Deltam(2)\ similar to (0.5-2.0) eV(2), 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 nu(mu) --> nu(e), nu(tau)/(nu(mu)) over bar --> (nu(e)) over bar,(nu(tau)) over bar 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. (C) 2003 Elsevier Science B.V. All rights reserved.