The High-Energy Behavior of Photon, Neutrino and Proton Cross Sections

TL;DR

This paper models high-energy photon, neutrino, and proton interactions with protons using a color dipole approach, successfully describing data across all energies and predicting asymptotic $ ext{ln}^2(s)$ behavior relevant for neutrino telescopes.

Contribution

It introduces a novel combination of the color dipole model with asymptotic $ ext{ln}^2(s)$ behavior to accurately describe and extrapolate high-energy cross sections.

Findings

Data consistent with $ ext{ln}^2(s)$ asymptotic behavior

Predictions for high-energy neutrino and charm production cross sections

Implications for neutrino telescope background estimation

Abstract

By combining the color dipole model of the nucleon with the assumption that cross sections behave asymptotically as $\ln^2(s)$, we are able to describe the data for photon, neutrino and hadron interactions with protons at all energies, $s$ is the center-of-mass energy of the interacting particles. Specifically, we extrapolate the perturbative QCD calculations into the regime of small fractional parton momenta $x$ using a color dipole description of the proton target that guarantees an asymptotic $\ln^2(s)$ behavior of all cross sections. The ambiguity of introducing a parametrization associated with the dipole approximation is mitigated by the requirement that the saturation of the small-$x$ structure functions produces $\ln^2(s)$-behaved asymptotic cross sections, in agreement with the data. The same formalism allows us to calculate the cross section for the hadronic pair production of charm particles. The results, in particular those for the high-energy neutrino and charm cross sections, are relevant for evaluating the sensitivity as well as the background in neutrino telescopes.