Parameter degeneracy and information loss in inverse flavor mapping for high-energy astrophysical neutrinos

Abstract

Given a high-energy astrophysical neutrino flux, its source flavor ratios $η= \{η^{}_e, η^{}_μ, η^{}_τ\}$ are correlated with the ones $f = \{f^{}_e, f^{}_μ, f^{}_τ\}$ measured at a neutrino telescope via $f = P η$, where the elements of $P$ consist of four lepton flavor mixing parameters. But realistic {\it inverse} flavor mapping $η= P^{-1} f$ encounters unavoidable parameter degeneracy and information loss, especially in or near the $\det P = 0$ limit allowed by current neutrino oscillation data. In this work we explore the parameter correlation condition for $\det P = 0$ including the $μ$-$τ$ reflection symmetry case, formulate the corresponding constraints on $f^{}_e$ and $f^{}_μ$ versus $η^{}_e$ and $η^{}_μ$, and illustrate to what extent the source flavor distribution can be mapped by using the recent IceCube all-sky neutrino flux data ranging from 5 TeV to 10 PeV under the assumption that the relevant sources have a common flavor composition.