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The flavor distribution of Cosmic Neutrinos

Simple approximate expressions for the relative flavor fluxes of energetic cosmic neutrinos detected on Earth, are presented in terms of their initial fluxes at the surface of the producing cosmic sites, assuming the neutrino mixing angles to lie in the experimentally favored region. These expressions highlight the main sensitivities to the initial production fluxes as well as to small variations of the mixing angles within the experimentally preferred region, thus providing simple methods to disentangle these physical quantities from cosmic neutrino data. This is more so, due to some striking mathematical properties of the relative neutrino flavors at $(s_{23}=1/\sqrt{2}, s_{13}=0)$, which somehow characterize the whole experimentally preferred region. We also assess the quality of our approximate expressions through a numerical comparison with the exact results.