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

In this paper, we derive simple and general perturbative formulas for the flavor flux ratios $R_{\alpha\beta}=\phi_{\nu_\alpha}/\phi_{\nu_\beta}$ that could be measured at neutrino telescopes. We discuss in detail the role of the uncertainties of the neutrino mixing parameters showing that they have to be seriously taken into account in any realistic discussion about flavor measurements at neutrino telescopes. In addition, we analyze the impact of such uncertainties in telling the standard neutrino oscillation framework from scenarios 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 particular configuration of the IceCube experiment, observing that using this experimental quantity a clear separation between standard and non-standard neutrino physics cannot be obtained.