Charged current neutrino cross section and tau energy loss at ultrahigh energies

Abstract

We evaluate both the tau-lepton energy loss produced by photonuclear interactions and the neutrino charged current cross section at ultrahigh energies, relevant to neutrino bounds with Earth-skimming tau neutrinos, using different theoretical and phenomenological models for nucleon and nucleus structure functions. The theoretical uncertainty is estimated by taking different extrapolations of the structure function ${F}_{2}$ to very low values of $x$, in the low and moderate ${Q}^{2}$ range for the tau-lepton interaction and at high ${Q}^{2}$ for the neutrino-nucleus inelastic cross section. It is at these extremely low values of $x$ where nuclear shadowing and parton saturation effects are unknown and could be stronger than usually considered. For tau and neutrino energies $E={10}^{9}\text{ }\text{ }\mathrm{GeV}$ we find uncertainties of a factor 4 for the tau energy loss and of a factor 2 for the charged current neutrino-nucleus cross section.