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.