The role of ν_τ ultrahigh energy astrophysics in Km^3 detectors

TL;DR

This work assesses ultrahigh-energy ν_{τ} signals in km^3 detectors, showing that tau-induced tracks can dominate over muon signals over a broad energy range due to the energy-enhanced tau range, provided ν_{τ} flux is non-negligible either from flavor oscillations or hadronic charm production. The analysis combines tau radiative losses, tau lifetime, and electroweak interactions to compute the tau range, identifying a maximal range around R_{τ,max} ≈ 191 km at E_{τ,max} ≈ 3.8×10^9 GeV and two critical energies that delineate a ν_{τ}-dominant window (E_{τ1} ≈ 5.6×10^8 GeV to E_{τ2} ≈ 1.7×10^12 GeV). It also examines resonant  e  interactions at E_{ u}^{res} ≈ 6.3×10^{15} eV, which yield short tau ranges but measurable event rates (a few per year in small volumes) alongside potentially tens of ν_{τ}-driven events at lower energies depending on the flux models (AGN-SS, CR-2, CR-4). The results imply that ν_{τ} astrophysics could provide direct evidence of ν_{τ} and flavor oscillations with observable consequences for the design and interpretation of km^3 neutrino detectors.

Abstract

We show that the expected $ ν_τ $ signals, by their secondary tau tracks, in Km^3 detectors at highest cosmic ray energy window $ 1.7\cdot 10^{21} eV \gt E_τ \gt 1.6 x 10^{17} eV$, must overcome the corresponding $ ν_μ $ (or muonic) ones. Indeed, the Lorentz-boosted tau range length grows (linearly) above muon range, for $ E_τ \RAISE 1.6 x 10^8 GeV$ and reaches its maxima extension, $ R_{τ_{\max}} \simeq 191 km$, at energy $E_τ \simeq 3.8 x 10^9 GeV$. At this peak the tau range is nearly 20 times the corresponding muon range (at the same energy) implying a similar ratio in $ ν_τ $ over $ ν_μ $ detectability. This dominance, however may lead (at present most abundant $ ν_τ $ model fluxes) to just a rare spectacular event a year (if flavor mixing occurs). Lower energetic $ τ$ and $ ν_τ $ signals $ (\barν_e e\to \barν_τ τ, ν_τ N\to ...) $ at energy range ($ 10^5 ÷10^7 GeV$) may be more easily observed in km^3 detectors at a rate of a few $ (\barν_e e\to \barν_τ τ) $ to tens event $ (ν_τ N\to τ+ $ anything) a year.