Neutrino mixing and neutrino telescopes

Abstract

Measuring flux ratios of high energy neutrinos is an alternative method to determine the neutrino mixing anglesand the CP phase. We conduct a systematic analysis of the neutrino mixing probabilities and of variousflux ratios measurable at neutrino telescopes. The considered cases are neutrinos from pion,neutron and muon-damped sources. The flux ratios involve measurements with andwithout taking advantage of the Glashow resonance. Explicit formulae in the case ofμ–τ symmetry(θ13 = 0 andθ23 = π/4) and its special casetri-bimaximal mixing (sin2 θ12 = 1/3) are obtained, and the leading corrections due to non-zeroθ13 andnon-maximal θ23 are given. The first-order correction is universal as it appearsin basically all ratios. We study in detail its dependence onθ13,θ23 and theCP phaseδ, finding that thedependence on θ23 is strongest. The flavour compositions for the considered neutrino sourcesare evaluated in terms of this correction. A measurement of a flux ratiois a clean measurement of the universal correction (and therefore ofθ13,θ23 and δ) if the zeroth-order ratio does not depend onθ12. This favours pion sources over the other cases, which in turn are good candidates to probeθ12. The only situations in which the universal correction does not appear are certainratios in the case of a neutron and muon-damped source, which depend mainly onθ12 and receive only quadratic corrections from the other parameters. We furthershow that there are only two independent neutrino mixing probabilities, give theallowed ranges of the considered flux ratios and of all probabilities, and show thatnone of the latter can be zero or one. Finally, we analyse situations in whichθ13 is sizableand θ23 is closeto π/4, and inwhich θ13 is closeto zero and θ23−π/4 is sizable.