On ultrahigh-energy neutrino-nucleon deep-inelastic scattering and the Froissart bound

TL;DR

This paper reviews ultrahigh-energy neutrino-nucleon scattering cross sections, highlighting how certain assumptions about structure functions can violate the Froissart bound at high energies.

Contribution

It demonstrates that common assumptions about the structure function F_2^{ u N} lead to violations of the Froissart bound in ultrahigh-energy neutrino interactions.

Findings

The cross section is proportional to the structure function F_2^{ u N}.

Assuming F_2^{ u N} \\propto \\ln^2(1/x) leads to Froissart bound violation.

The behavior of F_2^{ u N} at low x critically affects high-energy cross section limits.

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}.