Ultrahigh-energy neutrino–nucleon cross sections and perturbative unitarity

Unitarity relates the total cross section for neutrino–nucleon scattering to the neutrino–nucleon forward scattering amplitude. Assuming the validity of the perturbative expansion of the forward amplitude in the weak coupling constant, we derive a unitarity bound on the inelastic cross section. The inelastic cross section saturates this bound at a typical neutrino energy Eν≃108 GeV. This implies that calculations of the inelastic cross section that use current parton distribution functions and lowest order weak perturbation theory are unreliable above this energy.