# Tau energy loss and ultrahigh energy skimming tau neutrinos

## TL;DR

This paper analyzes the propagation and energy loss of ultrahigh energy tau neutrinos and taus, quantifying uncertainties in flux predictions relevant for astrophysical neutrino detection experiments.

## Contribution

It provides a comprehensive evaluation of tau energy loss models and their impact on tau flux predictions, including uncertainty analysis for various distances and energies.

## Key findings

- Uncertainty in tau energy loss and neutrino cross section partially cancel, reducing overall flux uncertainty.
- Theoretical uncertainty ranges from 30% to factors of 3.8 depending on energy and distance.
- Monte Carlo simulations agree with analytic calculations for tau propagation.

## Abstract

We consider propagation of high energy earth-skimming taus produced in interactions of astrophysical tau neutrinos. For astrophysical tau neutrinos we take generic power-law flux, $E^{-2}$ and the cosmogenic flux initiated by the protons. We calculate tau energy loss in several approaches, such as dipole models and the phenomenological approach in which parameterization of the $F_2$ is used. We evaluate the tau neutrino charged-current cross section using the same approaches for consistency. We find that uncertainty in the neutrino cross section and in the tau energy loss partially compensate giving very small theoretical uncertainty in the emerging tau flux for distances ranging from $2$ km to $100$ km and for the energy range between $10^6$ GeV and $10^{11}$ GeV, focusing on energies above $10^8$ GeV. When we consider uncertainties in the neutrino cross section, inelasticity in neutrino interactions and the tau energy loss, which are not correlated, i.e. they are not all calculated in the same approach, theoretical uncertainty ranges from about $30\%$ and $60 \%$ at $10^8$ GeV to about factors of 3.3 and 3.8 at $10^{11}$ GeV for the $E^{-2}$ flux and the cosmogenic flux, respectively, for the distance of 10 km rock. The spread in predictions significantly increases for much larger distances, e.g., $\sim 1,000$ km. Most of the uncertainty comes from the treatment of photonuclear interactions of the tau in transit through large distances. We also consider Monte Carlo calculation of the tau propagation and we find that the result for the emerging tau flux is in agreement with the result obtained using analytic approach. Our results are relevant to several experiments that are looking for skimming astrophysical taus, such as the Pierre Auger Observatory, HAWC and Ashra. We evaluate the aperture for the Auger and discuss briefly application to the the other two experiments.