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 $1{\mathrm{km}}^3$ 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 ${\mathrm{km}}^2$ detection area would be placed at $E^{2}dF/dE\simeq 3.7\times {10}^{-8}\mathrm{GeV}/{\mathrm{cm}}^2\sec \mathrm{sr}$ for ${\nu }_{\mu }$ and $4.6\times {10}^{-8}$ for ${\nu }_{\tau }$ with energies of ${10}^9\mathrm{GeV}$ in the absence of signals with an energy loss in a detection volume of 10 PeV or greater.