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, sigma(nu N), at energies as high as 10(11) GeV 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 sigma(nu N). This contrasts with the rate of horizontal air showers (HAS) due to neutrino interactions in the atmosphere, which is proportional to sigma(nu N). 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 sigma(nu N).