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

Abstract

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 $\sim\ln{s}$ if $F_{2}^{\nu N}$ is scaled by the power $\ln(1/x)$. Therefore, the asymptotic behavior of $F_{2}^{\nu N}\propto\ln^{2}(1/x)$ for small $x$ often assumed in the literature already leads to violation of the Froissart bound for $\sigma^{\nu N}$.