Flavor distribution of UHE cosmic neutrino oscillations at neutrino telescopes

If the ultrahigh-energy (UHE) cosmic neutrinos produced from a distant astrophysical source can be measured at a km 3 -size neutrino telescope such as the IceCube or KM3NeT, they will open a new window to understand the nature of flavor mixing and to probe possible new physics. Considering the conventional UHE cosmic neutrino source with the flavor ratio φ e : φ μ : φ τ = 1 : 2 : 0 , I point out two sets of conditions for the flavor democracy φ e T : φ μ T : φ τ T = 1 : 1 : 1 to show up at neutrino telescopes: either θ 13 = 0 and θ 23 = π / 4 (CP invariance) or δ = ± π / 2 and θ 23 = π / 4 (CP violation) in the standard parametrization of the 3 × 3 neutrino mixing matrix V. Allowing for slight μ – τ symmetry breaking effects characterized by Δ ∈ [ - 0.1 , + 0.1 ] , I find φ e T : φ μ T : φ τ T = ( 1 - 2 Δ ) : ( 1 + Δ ) : ( 1 + Δ ) as a good approximation. Another possibility to constrain Δ is to detect the ν ¯ e flux of E ν ¯ e ≈ 6.3 PeV via the Glashow resonance channel ν ¯ e e → W - → anything . I also give some brief comments on (1) possible non-unitarity of V in the seesaw framework and its effects on the flavor distribution at neutrino telescopes and (2) a generic description and determination of the cosmic neutrino flavor composition at distant astrophysical sources.