Neutrino Cross Sections and Future Observations of Ultrahigh-Energy Cosmic Rays

We show that future detectors of ultrahigh-energy cosmic-ray neutrinos will be able to measure neutrino-nucleon cross section, σ_νN, at energies as high as 10¹¹GeV or higher. We find that the flux of upgoing charged leptons per unit surface area produced by neutrino interactions below the surface is inversely proportional to σ_νN. This contrasts with the rate of horizontal air showers (HAS) due to neutrino interactions in the atmosphere, which is proportional to σ_νN. Thus, by comparing the HAS and upgoing air shower rates, the neutrino-nucleon cross section can be inferred. Taken together, upgoing and horizontal rates ensure a healthy total event rate, regardless of the value of σ_νN.