Neutrino cross sections at high energies and the 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 at energies as high as 10^{11}GeV or higher. We find that the flux of up-going charged leptons per unit surface area produced by neutrino interactions below the surface is inversely proportional to the cross section. This contrasts with the rate of horizontal air showers (HAS) due to neutrino interactions in the atmosphere, which is proportional to the cross section. Thus, by comparing the HAS and up-going air shower (UAS) rates, the neutrino-nucleon cross section can be inferred. Taken together, up-going and horizontal rates ensure a healthy total event rate, regardless of the value of the cross section.