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In this paper, we derive simple and general perturbative formulas for theflavor flux ratios $R_{\alpha\beta}=\phi_{\nu_\alpha}/\phi_{\nu_\beta}$ thatcould be measured at neutrino telescopes. We discuss in detail the role of theuncertainties of the neutrino mixing parameters showing that they have to beseriously taken into account in any realistic discussion about flavormeasurements at neutrino telescopes. In addition, we analyze the impact of suchuncertainties in telling the standard neutrino oscillation framework fromscenarios involving, e.g., neutrino decay and we find that the ratio $R_{e\mu}$is the most sensitive one to "new physics" effects beyond the Standard Model.We also compute the more realistic muon-to-shower ratio for a particularconfiguration of the IceCube experiment, observing that using this experimentalquantity a clear separation between standard and non-standard neutrino physicscannot be obtained.Comment: 21 pages, 7 figures, LaTeX. Final version published in Phys. Rev.

Neutrino flux ratios at neutrino telescopes: The role of uncertainties of neutrino mixing parameters and applications to neutrino decay