Propagation of Muons and Taus at High Energies

The photonuclear contribution to charged lepton energy loss has been re-evaluated taking into account HERA results on real and virtual photon interactions with nucleons. With large $Q^2$ processes incorporated, the average muon range in rock for muon energies of $10^9$ GeV is reduced by only 5% as compared with the standard treatment. We have calculated the tau energy loss for energies up to $10^9$ GeV taking into consideration the decay of the tau. A Monte Carlo evaluation of tau survival probability and range show that at energies below $10^7-10^8$ GeV, depending on the material, only tau decays are important. At higher energies the tau energy losses are significant, reducing the survival probability of the tau. We show that the average range for tau is shorter than its decay length and reduce to 17 km in water for an incident tau energy of $10^9$ GeV, as compared with its decay length of 49 km at that energy. In iron, the average tau range is 4.7 km for the same incident energy.