A further study of μ-τ symmetry breaking at neutrino telescopes after the Daya Bay and RENO measurements of θ13

Current neutrino oscillation data indicate that θ13 is not strongly suppressed and θ23 might have an appreciable deviation from π/4, implying that the 3×3 neutrino mixing matrix V does not have an exact μ-τ permutation symmetry. We make a further study of the effect of μ-τ symmetry breaking on the democratic flavor distribution of ultrahigh-energy (UHE) cosmic neutrinos at a neutrino telescope, and find that it is characterized by |Vμi|2−|Vτi|2 which would vanish if either θ23=π/4 and θ13=0 or θ23=π/4 and δ=±π/2 held. We observe that the second-order μ-τ symmetry breaking term Δ¯ may be numerically comparable with or even larger than the first-order term Δ in the flux ratios ϕeT:ϕμT:ϕτT≃(1−2Δ):(1+Δ+Δ¯):(1+Δ−Δ¯), if sin(θ23−π/4) and cos δ have the same sign. The detection of the UHE ν¯e flux via the Glashow-resonance channel ν¯ee→W−→anything is also discussed by taking account of the first- and second-order μ-τ symmetry breaking effects.