Tau depolarization from electromagnetic interactions at very high energies*

The neutrino interaction length scales with energy, and becomes comparable to Earth's diameter above PeV energies. At such high energies, the tau's short lifetime leads to energetic regenerated tau neutrino flux, $\nu_\tau\to\tau\to \nu_\tau$, within the Earth. The next generation of neutrino experiments aim to detect ultra-high energy neutrinos, and many of them rely on detecting either the regenerated tau neutrino, or a tau decay shower. Both of these signatures are affected by polarization of the tau through the energy distribution of the secondary particles produced from the tau's decay. While $\tau$'s produced in weak interactions at such high energies are nearly 100\% polarized, it is expected that $\tau$'s experience some depolarization due to electromagnetic energy loss in the Earth. In this talk, we quantify the depolarization of $\tau$'s in electromagnetic interactions and its impact on the energy of the regenerated tau-neutrino. Taus with higher energy have more electromagnetic interactions than lower energy tau leptons, which causes more depolarization. The regenerated tau-neutrinos produced from depolarized taus have lower energies. We also show the effect of tau depolarization on the tau survival probability using Monte Carlo simulations such as nuPyProp and TauRunner.