Neutrino Telescopes as a Probe of Broken $\mu$-$\tau$ Symmetry

Abstract

It is known that neutrino oscillations may map ${\varphi }_e:{\varphi }_{\mu }:{\varphi }_{\tau }=1:2:0$, the initial flavor ratios of ultrahigh-energy neutrino fluxes produced from a distant astrophysical source, into ${\varphi }_e^D:{\varphi }_{\mu }^D:{\varphi }_{\tau }^D=1:1:1$ at the detector of a neutrino telescope. We remark that this naive expectation is only valid in the $\mu$-$\tau$ symmetry limit, in which two neutrino mixing angles satisfy ${\theta }_{13}=0$ and ${\theta }_{23}=\pi /4$. Allowing for the slight breaking of $\mu$-$\tau$ symmetry, we find ${\varphi }_e^D:{\varphi }_{\mu }^D:{\varphi }_{\tau }^D=(1-2\Delta ):(1+\Delta ):(1+\Delta )$ with $\Delta$ characterizing the combined effect of ${\theta }_{13}\ne 0$ and ${\theta }_{23}\ne \pi /4$. Current neutrino oscillation data indicate $-0.1\lesssim \Delta \lesssim +0.1$. We also look at the possibility to probe $\Delta$ by detecting the ${\bar{\nu }}_e$ flux of $E_{{\bar{\nu }}_e}\approx 6.3\mathrm{PeV}$ via the Glashow resonance channel ${\bar{\nu }}_{e}e\to W^{-}\to anything$.

Comments: 10 pages, 1 figure. Slight changes made. Phys. Rev. D (in press)