Cross Sections and Inelasticity Distributions of High-Energy Neutrino Deep Inelastic Scattering

Abstract

This study presents a comprehensive model for neutrino deep inelastic scattering (DIS) cross sections spanning energies from 50 GeV to 5$\times10^{12}$ GeV with an emphasis on applications to neutrino telescopes. We provide calculations of the total charged-current DIS cross sections and inelasticity distributions up to NNLO for isoscalar nucleon targets and up to NLO order for nuclear targets. Several modifications to the structure functions are applied to improve the modeling of the cross sections at low energies where perturbative QCD is less accurate and at high energies where there is non-negligible top quark production, and small-$x$ logarithms need to be resumed. Using the FONLL general-mass variable-flavor number scheme, we account for heavy quark mass effects and separate the heavy flavor components of the structure functions, obtaining predictions of their relative contributions to the cross sections and the uncertainties arising from the parton distribution functions. Additionally, the effects of final state radiation are implemented in the calculation of the double-differential cross section and discussed in terms of their impact on measurements at neutrino telescopes.