We consider models where the scale of supersymmetry breaking lies between 5 x 10(6) and 5 x 10(8) GeV. In this class of theories, which includes models of mediated supersymmetry breaking, the lightest supersymmetric particle is the gravitino, and the next to lightest is typically a long-lived charged slepton with a lifetime between a microsecond and a second, depending on its mass. We investigate the production of these particles by the diffuse flux of high energy neutrinos colliding with nucleons in the Earth, and the potential for their observation in large ice or water Cerenkov detectors. The small production cross section is partially compensated by the very long range of sleptons. The signal, two well-separated parallel tracks, has very little background. Using the Waxman-Bahcall limit for the neutrino flux results in up to four events a year in km3 experiments.
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