Tau energy losses at ultra-high energy: continuous versus stochastic treatment

TL;DR

This paper compares stochastic and continuous models for tau lepton energy losses at ultra-high energies, assessing their accuracy in predicting tau fluxes after propagation through matter.

Contribution

It introduces a comparative analysis of stochastic versus continuous energy loss treatments for tau leptons at ultra-high energies.

Findings

Stochastic and continuous models yield similar tau flux predictions under certain conditions.

Continuous approximation is reasonably accurate for specific energy ranges and spectra.

Differences between models become significant at very high energies or for particular injection spectra.

Abstract

We study the energy losses of the tau lepton in matter through electromagnetic processes at ultra-high energy (UHE). We use both a stochastic and a continuous framework to treat these interactions and compare the flux of tau leptons propagated after some amount of matter. We discuss the accuracy of the approximation of continuous energy losses by studying the propagation in standard rock of taus with both mono-energetic and power law injection spectra.