Propagation of extremely high energy leptons in Earth: Implications for their detection by the IceCube neutrino telescope

We present the results of numerical calculations on the propagation of extremely high energy (EHE) neutrinos and charged leptons in Earth for trajectories in the whole phase space of nadir angles. Our comprehensive calculation has shown that not only the secondary produced muons but also taus survive without decaying in the energy range of 10–100 PeV with an intensity approximately three orders of magnitude lower than the neutrino flux regardless of the EHE neutrino production model. They form detectable horizontal or downgoing events in a 1km³ underground neutrino telescope such as the IceCube detector. The event rate and the resulting detectability of EHE signals in comparison with the atmospheric muon background are also evaluated. The 90% C.L. upper limit of EHE neutrino fluxes by a km² detection area would be placed at E²dF/dE≃3.7×10^-8GeV/cm²secsr for ν_μ and 4.6×10^-8 for ν_τ with energies of 10⁹GeV in the absence of signals with an energy loss in a detection volume of 10 PeV or greater.