Estimating non-linear QCD effects in ultrahigh energy neutrino events at IceCube

The number of ultrahigh energy events at IceCube is estimated, for the first time, taking into account non-linear QCD effects in the neutrino - hadron cross section. We assume that the extragalactic neutrino flux is given by ${\mathrm{\Phi }}_{\nu }(E_{\nu })={\mathrm{\Phi }}_0{E}_{\nu }^{-2}$ and estimate the neutrino - hadron cross section using the dipole approach and a phenomenological model for the dipole - hadron cross section based on non-linear QCD dynamics. We demonstrate that the non-linear prediction is able to describe the current IceCube data and that the magnitude of the non-linear effects is larger than 20 % for visible energies of order of 2 PeV and increases with the neutrino energy. Our main conclusion is that the non-linear QCD effects are non-negligible and should be taken into account in the analysis of the number of ultrahigh energy events.