Measuring the 13 Neutrino Mixing Angle and the CP Phase with Neutrino Telescopes

The observed excess of high-energy cosmic rays from the Galactic plane in the energy range around 10¹⁸  eV may be explained by neutron primaries generated in the photodissociation of heavy nuclei. In this scenario, lower-energy neutrons decay before reaching the Earth and produce a detectable flux in a 1  km³ neutrino telescope. The initial flavor composition of the neutrino flux, ϕ(ν̅ _e)∶ϕ(ν̅ _μ)∶ϕ(ν̅ _τ)=1∶0∶0, permits a combined ν̅ _μ/ν̅ _τ appearance and ν̅ _e disappearance experiment. The observable flux ratio ϕ(ν̅ _μ)/ϕ(ν̅ _e+ν̅ _τ) at Earth depends on the 13 mixing angle θ₁₃ and the leptonic CP phase δ_CP, thus opening a new way to measure these two quantities.