Investigating the effects of the QCD dynamics in the neutrino absorption by the Earth’s interior at ultrahigh energies

Abstract

The opacity of the Earth to incident ultra high energy neutrinos is directly connected with the behaviour of the neutrino - nucleon ($\sigma^{\nu N}$) cross sections in a kinematic range utterly unexplored. In this work we investigate how the uncertainties in $\sigma^{\nu N}$ due the different QCD dynamic models modify the neutrino absorption while they travel across the Earth. In particular, we compare the predictions of two extreme scenarios for the high energy behaviour of the cross section, which are consistent with the current experimental data. The first scenario considered is based on the solution of the linear DGLAP equations at small-$x$ and large-$Q^2$, while the second one take into account the unitarity effects in the neutrino - nucleon cross section by the imposition of the Froissart bound behaviour in the nucleon structure functions at large energies. Our results indicate that probability of absorption and the angular distribution of neutrino events are sensitive to the the QCD dynamics at ultra high energies.