Ultrahigh-Energy Neutrino-Nucleon Cross Sections and Perturbative Unitarity

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 $E_{\nu }\simeq 10^8\mathrm{GeV}$. 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.

arXiv comment11 pages, 3 figures, RevTeX, additional references

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