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 $\eta =\{{\eta }_e^{},{\eta }_{\mu }^{},{\eta }_{\tau }^{}\}$ are correlated with the ones $f=\{f_e^{},f_{\mu }^{},f_{\tau }^{}\}$ measured at a neutrino telescope via $f=P\eta$, where the elements of $P$ consist of four lepton flavor mixing parameters. But realistic {\it inverse} flavor mapping $\eta =P^{-1}f$ 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 $\mu$-$\tau$ reflection symmetry case, formulate the corresponding constraints on $f_e^{}$ and $f_{\mu }^{}$ versus ${\eta }_e^{}$ and ${\eta }_{\mu }^{}$, 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.

12 pages, 3 figures