Towards Determination of the Initial Flavor Composition of Ultrahigh-energy Neutrino Fluxes with Neutrino Telescopes

We propose a simple but useful parametrization of the flavor composition of ultrahigh-energy neutrino fluxes produced from distant astrophysical sources: $\phi^{}_e : \phi^{}_\mu : \phi^{}_\tau = \sin^2 \xi \cos^2 \zeta : \cos^2 \xi \cos^2 \zeta : \sin^2 \zeta$. We show that it is possible to determine or constrain $\xi$ and $\zeta$ by observing two independent neutrino flux ratios at the second-generation neutrino telescopes, provided three neutrino mixing angles and the Dirac CP-violating phase have been well measured in neutrino oscillations. Any deviation of $\zeta$ from zero will signify the existence of cosmic $\nu^{}_\tau$ and $\bar{\nu}^{}_\tau$ neutrinos at the source, and an accurate value of $\xi$ can be used to test both the conventional mechanism and the postulated scenarios for cosmic neutrino production.