2.30 pm Monday October 30
We propose a novel approach for studying $\nu_\mu \rightarrow \nu_\tau$ oscillations with extragalactic neutrinos. Active Galactic Nuclei and Gamma Ray Bursts are believed to be sources of ultrahigh energy muon neutrinos. With distances of 100 Mpc or more, they provide an unusually long baseline for possible detection of $\nu_\mu \rightarrow \nu_\tau$ with mixing parameters $\Delta m^2$ down to $10^{-17}$eV$^2$, many orders of magnitude below the current accelerator experiments. By solving the coupled transport equations, we show that high-energy $\nu_\tau$'s, as they propagate through the earth, cascade down in energy, producing the enhancement of the incoming $\nu_\tau$ flux in the low energy region, in contrast to the high-energy $\nu_\mu$'s, which get absorbed. For an AGN quasar model we find the $\nu_\tau$ flux to be a factor of $2$ to $2.5$ larger than the incoming flux in the energy range between $10^2$~GeV and $10^4$~GeV, while for a GRB fireball model, the enhancement is $10\%$-$27\%$ in the same energy range and for zero nadir angle. We demonstrate that a kilometer-size neutrino telescope has a very good chance of detecting the appearance of tau neutrinos when both muon and hadronic/electromagnetic showers are detected. We find significant signal to background ratios for the hadronic/electromagnetic showers with energies above 10 TeV to 100 TeV initiated by the extragalactic neutrinos. We also show that the tau neutrinos from point sources have the potential for discovery above a 1 TeV threshold.