Small-x Growth of Nucleon Structure Functions and Its Manifestations in Ultrahigh-Energy Neutrino Astrophysics

Abstract

Rapid growth of neutrino-nucleon cross-sections at high energies due to hypothetical hard pomeron enhancement of $νN$-structure functions is discussed. Differential and integral hadron moments, which, together with cross-sections, define rates of hadron-electromagnetic cascades in a neutrino detector are calculated for different power-law decreasing neutrino spectra. For comparison two small-x extrapolation schemes are discussed. First includes Regge theory inspired hard pomeron enhancement of $νN$-structure functions. The second is obtained with the help of trivial extrapolation of perturbative QCD structure functions from the large x region to the small x one. Implications of hard pomeron effects for cross-sections and hadron moments are demonstrated. The most pronounced manifestations are found in integral hadron moments for the case of charged current electron (anti)neutrinos scattering off nucleons.