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We discuss flavor-mixing probabilities and flavor ratios of high energy astrophysical neutrinos. In the first part of this paper, we expand the neutrino flavor-fluxes in terms of the small parameters U_{e3} and pi/4 - theta_{23}, and show that there are universal first and second order corrections. The second order term can exceed the first order term, and so should be included in any analytic study. We also investigate the probabilities and ratios after a further expansion around the tribimaximal value of sin^2 theta_{12} = 1/3. In the second part of the paper, we discuss implications of deviations of initial flavor ratios from the usually assumed, idealized flavor compositions for pion, muon-damped, and neutron beam sources, viz., (1 : 2 : 0), (0 : 1 : 0), and (1 : 0 : 0), respectively. We show that even small deviations have significant consequences for the observed flavor ratios at Earth. If initial flavor deviations are not taken into account in analyses, then false inferences for the values in the PMNS matrix elements (angles and phase) may result.
The flavor composition of astrophysical neutrinos observed in neutrino telescopes is a powerful discriminator between different astrophysical neutrino production mechanisms and can also teach us about the particle physics properties of neutrinos. In
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One of the important goals for future neutrino telescopes is to identify the flavors of astrophysical neutrinos and therefore determine the flavor ratio. The flavor ratio of astrophysical neutrinos observed on the Earth depends on both the initial fl