Ultrahigh-energy neutrino-nucleon deep-inelastic scattering and the Froissart bound

TL;DR

This paper derives a simple formula for ultrahigh-energy neutrino-nucleon scattering cross sections, showing that common assumptions about structure function behavior violate the Froissart bound at high energies.

Contribution

It provides a new formula linking the cross section to the structure function and demonstrates that certain asymptotic behaviors lead to Froissart bound violations.

Findings

The cross section is proportional to the structure function F_2^{nu N} evaluated at specific kinematic points.

Assuming F_2^{nu N} scales as ln^2(1/x) results in a violation of the Froissart bound.

The formula clarifies how low-x behavior influences high-energy scattering limits.

Abstract

We present a simple formula for the total cross section sigma^{nu N} of neutral- and charged-current deep-inelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which 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 the square of the center-of-mass energy. The coefficient in the front of F_2^{nu N}(x, Q^2) depends on the asymptotic low-x behavior of F_2^{nu N}. It contains an additional ln(s) term if F_2^{nu N} scales with a power of ln(1/x). Hence, an asymptotic low-x behavior F_2^{nu N} propto ln^2(1/x), which is frequently assumed in the literature, already leads to a violation of the Froissart bound on sigma^{nu N}.