Potential divergence in tracing $\mu$ and $\tau$ flavors of astrophysical neutrinos

TL;DR

This paper derives formulas relating astrophysical neutrino flavor ratios observed at detectors to their source ratios, highlighting potential divergences due to mu-tau symmetry and analyzing recent IceCube data.

Contribution

It provides analytical expressions for neutrino flavor fractions considering mu-tau symmetry breaking and applies them to IceCube observations.

Findings

Potential divergence in mu and tau flavor fractions due to mu-tau symmetry.

Analytical formulas linking source and observed flavor ratios.

Application to IceCube data from 5 TeV to 10 PeV.

Abstract

We derive general formulas for three flavor fractions $(\eta^{}_e , \eta^{}_\mu , \eta^{}_\tau)$ of the high-energy neutrinos originating from a remote astrophysical source by using their flavor ratios $(f^{}_e , f^{}_\mu , f^{}_\tau)$ observed at a neutrino telescope, and diagnose a potential divergence associated with $\eta^{}_\mu$ and $\eta^{}_\tau$ as an unavoidable consequence of the $\mu$-$\tau$ interchange symmetry exhibiting in the $3\times 3$ lepton flavor mixing matrix $U$. We present a complete set of analytical expressions for $(\eta^{}_e , \eta^{}_\mu , \eta^{}_\tau)$ as functions of two typical $\mu$-$\tau$ symmetry breaking parameters in the standard parametrization of $U$, and apply it to the recent IceCube all-sky neutrino flux data ranging from 5 TeV to 10 PeV in the assumption that the relevant sources have a common flavor composition. We also explain why only $\eta^{}_e$ and $\eta^{}_\mu + \eta^{}_\tau$ can be extracted from a precision measurement of $f^{}_e$ and $f^{}_\mu = f^{}_\tau$ in the exact $\mu$-$\tau$ flavor symmetry limit.