An Analysis of Cosmic Neutrinos: Flavor Composition at Source and Neutrino Mixing Parameters

Abstract: We examine the feasibility of deriving neutrino mixing parameters $\delta$ and $\theta_{13}$ from the cosmic neutrino flavor composition under the assumption that the flavor ratios of the cosmic neutrinos at the source were $F_{\nu_e}+F_{\bar{\nu}e}:F{\nu_\mu}+F_{\bar{\nu}\mu}: F{\nu_\tau}+F_{\bar{\nu}\tau}=1:2:0$. We analyze various uncertainties that enter the derivation of $\delta$ and $\theta{13}$ from the ratio of the shower-like to $\mu$-tracks events which is the only realistic source of information on the flavor composition at neutrino telescopes such as ICECUBE. We then examine to what extent the deviation of the initial flavor ratio from $1:2:0$ can be tested by measurement of this ratio at neutrino telescopes taking into account various sources of uncertainty.