Divergence in tracing the flavors of astrophysical neutrinos: can JUNO help IceCube?

TL;DR

This work addresses how to infer the original flavor fractions $\eta_e,\eta_\mu,\eta_\tau$ of ultrahigh-energy astrophysical neutrinos from the observed flavor ratios $f_e,f_\mu,f_\tau$ at Earth, accounting for the PMNS mixing via a linear relation. It derives general expressions for $\eta$ in terms of $f$ and the PMNS matrix elements, introducing determinants $D_0$ and coefficients $C_{\alpha\beta}$ built from $|U_{\alpha i}|^2$, and highlights that exact $\mu$-$\tau$ symmetry can drive $D_0=0$, causing divergent inferences for $\eta_\mu$ and $\eta_\tau$. In the special case of exact $\mu$-$\tau$ symmetry, the problem reduces to determining $\eta_e$ and $\eta_\mu+\eta_\tau$ from $f_e$ and $f_\mu=f_\tau$, with explicit formulas and numerical estimates showing how JUNO and Daya Bay inputs tighten the mapping. The study emphasizes the practical impact: precise measurements of $\mu$-$\tau$ symmetry breaking are essential for reliably tracing the astrophysical flavor composition, and JUNO/Daya Bay will play a crucial role in this precision era.

Abstract

We derive the flavor fractions $(η^{}_e , η^{}_μ, η^{}_τ)$ for ultrahigh-energy neutrinos originating from a remote astrophysical source by using their flavor ratios $(f^{}_e , f^{}_μ, f^{}_τ)$ observed at a neutrino telescope, and find that a potential divergence may appear in inferring the values of $η^{}_μ$ and $η^{}_τ$ as an unavoidable consequence of the approximate $μ$-$τ$ interchange symmetry of lepton flavor mixing. We illustrate such an effect by applying our formula to the IceCube all-sky neutrino flux data ranging from 5 TeV to 10 PeV in the naive assumption that the relevant sources have a common flavor composition. We show that only $η^{}_e$ and $η^{}_μ+ η^{}_τ$ can be extracted from the measurements of $f^{}_e$, $f^{}_μ$ and $f^{}_τ$ if the $μ$-$τ$ flavor symmetry is exact, and the JUNO and Daya Bay precision antineutrino oscillation data will help a lot in this connection.