Ambiguity in Source Flux of Cosmic/Astrophysical Neutrinos

For high energy cosmic neutrinos Athar, Jeźabek, and Yasuda (AJY) have recently shown that the existing data on neutrino oscillations suggest that cosmic neutrino flux at the AGN/GRB source, F(ν_e):F(ν_μ):F(ν_τ)~1:2:0, oscillates to F(ν_e):F(ν_μ):F(ν_τ)~1:1:1. These results can be confirmed at AMANDA, Baikal, ANTARES and NESTOR, and other neutrino detectors with a good flavor resolution. Here, we rederive the AJY result from quasi bi-maximal mixing, and show that observation of F(ν_e):F(ν_μ):F(ν_τ)~1:1:1 does not necessarily establish cosmic neutrino flux at the AGN/GRB source to be F(ν_e):F(ν_μ):F(ν_τ)~1:2:0. We also note that if the length scale for the quantum-gravity induced decoherence for astrophysical neutrinos is of the order of a Mpc, then independent of the MNS matrix, the Liu-Hu-Ge (LHG) mechanism would lead to flux equalization for the cosmic/astrophysical neutrinos.