Propagation of tau neutrinos and tau leptons through the Earth and their detection in underwater/ice neutrino telescopes

If muon neutrinos produced in cosmological sources oscillate, neutrino telescopes can have a chance to detect tau-neutrinos. In contrast to muon neutrinos the Earth is completely transparent for tau neutrinos thanks to the short life time of tau-leptons produced in charged current interactions. Tau-lepton decaysin flight producing another tau neutrino (regeneration chain). Thus, tau neutrinos cross the Earth without being absorbed, though loosing energy both in regeneration processes and in neutral current interactions. Neutrinos of all flavors can be detected in deep underwater/ice detectors by means of Cherenkov light emitted by charged leptons produced in neutrino interactions. Muon and tau-leptons have different energy loss features, which provide opportunities to identify tau-events among the multitude of muons. Some signatures of tau-leptons that can be firmly established and are background free have been proposed in literature, such as 'double bang' events. In this paper we present results of Monte Carlo simulations of tau-neutrino propagation through the Earth accounting for neutrino interactions, tau energy losses and tau decays. Parameterizations for hard part and corrections to the soft part of the photonuclear cross-section (which contributes a major part to tau energy losses) are presented. Different methods of tau-lepton identification in large underwater/ice neutrino telescopes are discussed. Finally, we present a calculation of tau neutrino double bang event rates in cubic km scale detectors.