Ultrahigh-Energy Neutrino-Nucleon Cross Sections and Perturbative Unitarity
arXiv:hep-ph/0103207 · doi:10.1016/S0370-2693(01)00545-7
Abstract
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 {\em 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 $E_ν\simeq 10^8 {\rm GeV}$. 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.
11 pages, 3 figures, RevTeX, additional references