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Enhancement and Suppression of the Neutrino-Nucleon Total Cross Section at Ultra-High Energies

We argue that high gluon density effects at small $x$ are important for the calculation of ultra-high energy neutrino nucleon cross sections due to the phenomenon of geometric scaling. We calculate the cross section for $νN \to μX$, including high gluon density effects, using the all twist formalism of McLerran and Venugopalan and show that it can be related to the dipole nucleon cross section measured in DIS experiments. For neutrino energies of $E_ν\sim 10^{12}$ GeV, the geometric scaling region extends all the way up to $Q^2 \sim M^2_{W}$. We show that geometric scaling can lead to an {\it enhancement} of the neutrino nucleon total cross section by 1-2 orders of magnitude compared to the leading twist cross section and discuss the implications for neutrino observatories. At extremely high energies, gluon saturation effects suppress the neutrino nucleon total cross section and lead to its unitarization.