Measuring flavor ratios of high-energy astrophysical neutrinos

We discuss the prospects for next generation neutrino telescopes, such as IceCube, to measure the flavor ratios of high-energy astrophysical neutrinos. The expected flavor ratios at the sources are $\phi_{\nu_e}:\phi_{\nu_{\mu}}:\phi_{\nu_{\tau}} = 1:2:0$, and neutrino oscillations quickly transform these to $1:1:1$. The flavor ratios can be deduced from the relative rates of showers ($\nu_e$ charged-current, most $\nu_\tau$ charged-current, and all flavors neutral-current), muon tracks ($\nu_\mu$ charged-current only), and tau lepton lollipops and double-bangs ($\nu_\tau$ charged-current only). The peak sensitivities for these interactions are at different neutrino energies, but the flavor ratios can be reliably connected by a reasonable measurement of the spectrum shape. Measurement of the astrophysical neutrino flavor ratios tests the assumed production mechanism and also provides a very long baseline test of a number of exotic scenarios, including neutrino decay, CPT violation, and small-$\delta m^2$ oscillations to sterile neutrinos.