Tau Neutrino Appearance with a 1000 Megaparsec Baseline

A high-energy neutrino telescope, such as the AMANDA detector, may detect neutrinos produced in sources, distant by a 1000 megaparsecs, which produce mostly ν_e or ν_μ neutrinos. Above 1 PeV, ν_e and ν_μ are absorbed by charged-current interactions in the Earth, but the Earth never becomes opaque to ν_τ since the τ^- produced in a charged-current ν_τ interaction decays back into ν_τ. This provides an experimental signature for neutrino oscillations. The appearance of a ν_τ component would be evident as a flat zenith angle dependence of a source intensity at the highest neutrino energies, which would indicate ν_τ mixing with a sensitivity to Δm² as low as 10^-17eV², for the farthest sources. In addition, the presence of tau neutrino mixing would allow neutrino astronomy well beyond the PeV cutoff, possibly out to the energies of protons observed above 10²⁰eV.