Estimating nonlinear 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 nonlinear 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 nonlinear QCD dynamics. We demonstrate that the nonlinear prediction is able to describe the current IceCube data and that the magnitude of the nonlinear 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 nonlinear QCD effects are non-negligible and should be taken into account in the analysis of the number of ultrahigh energy events.

Figure 1

Comparison between the energy dependence of the number of UHE neutrinos events at IceCube predicted by the phenomenological nonlinear GBW model (solid blue line) and that obtained using the QCD improved parton model for the structure functions and the CT10 parametrization for the parton distribution functions (dashed orange line). For comparison we also present the $E^{-2}$ result and the expected background reported by the IceCube Observatory. IceCube data are from Ref. [3].

Figure 2

Comparison between the energy dependence of the number of UHE neutrinos events at IceCube predicted by the phenomenological nonlinear GBW model (solid blue line) and those obtained disregarding the nonlinear QCD effects, denoted GBW lin (dashed red line) and Color Transp (dotted green line) in the figure. The green region is the expected background reported by the IceCube Observatory. IceCube data are from Ref. [3].

Figure 3

Energy dependence of the ratio between the linear and nonlinear predictions for the number of neutrino events at IceCube.