Ultra-High Energy Neutrino-Nucleon Cross Section and Radiative Corrections

Abstract

A cubic kilometer scale experiment has been proposed to detect cosmic neutrinos of energy from tens of GeV up to the highest energies observed for cosmic rays, around 10**20 eV, or possibly even beyond. Detection efficiencies depend crucially on the neutrino-nucleon cross section at these energies at which radiative corrections beyond the lowest order approximation could become non-negligible. The differential cross sections can be modified by more than 50% in some regions of phase space. Estimates of corrections to the quantities most relevant for neutrino detection at these energies give, however, less dramatic effects: The average inelasticity in the outgoing lepton is increased from about 0.19 to 0.24. The inclusive cross section is reduced by roughly half a percent. The dominant uncertainty of the standard model ultra-high energy neutrino-nucleon cross section therefore still comes from uncertainties of the parton distributions in the nucleon at very low momentum fractions.