Neutrino Telescopes as a Probe of Broken $μ$-$τ$ Symmetry

Abstract

It is known that neutrino oscillations may map $ϕ_e : ϕ_μ: ϕ_τ= 1 : 2 : 0$, the initial flavor ratios of ultrahigh-energy neutrino fluxes produced from a distant astrophysical source, into $ϕ^D_e : ϕ^D_μ: ϕ^D_τ= 1 : 1 : 1$ at the detector of a neutrino telescope. We remark that this naive expectation is only valid in the $μ$-$τ$ symmetry limit, in which two neutrino mixing angles satisfy $θ_{13} = 0$ and $θ_{23} = π/4$. Allowing for the slight breaking of $μ$-$τ$ symmetry, we find $ϕ^D_e : ϕ^D_μ: ϕ^D_τ= (1 -2 Δ) : (1 +Δ) : (1 +Δ)$ with $Δ$ characterizing the combined effect of $θ_{13} \neq 0$ and $θ_{23} \neq π/4$. Current neutrino oscillation data indicate $-0.1 \lesssim Δ\lesssim +0.1$. We also look at the possibility to probe $Δ$ by detecting the $\barν_e$ flux of $E_{\barν_e} \approx 6.3 {\rm PeV}$ via the Glashow resonance channel $\barν_e e \to W^- \to anything$.