Tau Neutrino Appearance with a 1000 Megaparsec Baseline

Abstract

A high-energy neutrino telescope, such as the AMANDA detector, may detect neutrinos produced in sources, distant by a 1000 megaparsecs, which produce mostly ${\ensuremath{\nu}}_{e}$ or ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ neutrinos. Above 1 PeV, ${\ensuremath{\nu}}_{e}$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ are absorbed by charged-current interactions in the Earth, but the Earth never becomes opaque to ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ since the ${\ensuremath{\tau}}^{\ensuremath{-}}$ produced in a charged-current ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ interaction decays back into ${\ensuremath{\nu}}_{\ensuremath{\tau}}$. This provides an experimental signature for neutrino oscillations. The appearance of a ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ component would be evident as a flat zenith angle dependence of a source intensity at the highest neutrino energies, which would indicate ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing with a sensitivity to $\ensuremath{\Delta}{m}^{2}$ as low as ${10}^{\ensuremath{-}17}{\mathrm{eV}}^{2}$, 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 ${10}^{20}\mathrm{eV}$.