Comprehensive approach to tau-lepton production by high-energy tau neutrinos propagating through the Earth

There has been a recent surge in interest in the detection of τ -lepton-induced air showers from detectors at altitude. When a τ neutrino (ν_τ) enters the Earth, it produces τ leptons as a result of nuclear charged-current interactions. In some cases, this process results in a τ lepton exiting the surface of the Earth, which can subsequently decay in the atmosphere and produce an extensive air shower. These upward-going air showers can be detected via fluorescence, optical Cherenkov, or geomagnetic radio emission. Several experiments have been proposed to detect these signals. We present a comprehensive simulation of the production of τ leptons by ν_τ's propagating through Earth to aid the design of future experiments. These simulations for ν_τ's and leptons in the energy range from 1 0¹⁵ eV to 1 0²¹ eV treat the full range of incidence angles from Earth-skimming to diametrically traversing. Propagation of ν_τ's and leptons includes the effects of rock and an ocean or ice layer of various thicknesses. The interaction models include ν_τ regeneration and account for uncertainties in the Standard Model neutrino cross section and in the photonuclear contribution to the τ energy-loss rate.