On Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound

A brief review of the results for the total cross section sigma(nu N) of ultrahigh-energy neutrino deep inelastic scattering on isoscalar nuclear targets is presented. These results are based on simple approximations for sigma(nu N) and are compared with the experimental data of the IceCube Collaboration. The total cross section sigma(nu N) is proportional to the structure function F-2(nu N) (M-V(2)/s, M-V(2)), where M-V is the intermediate boson mass and s is square of the energy of the center of mass. The coefficient in the front of F-2(nu N) (M-V(2)/s, M-V(2)) depends on the asymptotic behavior of F-2(nu N) at low values of x. It contains an additional term similar to ln s if F-2(nu N) is scaled by the power ln(1/x). Therefore, the asymptotic behavior of F-2(nu N) proportional to ln(2) (1/x) for small x often assumed in the literature already leads to violation of the Froissart bound for sigma(nu N).