Small-x Parton Densities from HERA and the Ultra-High Energy Neutrino-Nucleon Cross Sections

In light of recent measurements of the nucleon structure function in the small-$x$ deep-inelastic regime at HERA and the consequently improved theoretical understanding of the quark distributions in this range of parton fractional momentum, we present new results for the neutrino-nucleon cross section at ultra high energies, up to $ E_{\nu} \sim 10^{21}$ eV. The results are relevant to deep underground muon detectors looking for such neutrinos. For $\simeq 10^{20}$ eV neutrinos, our cross sections are about a factor of $4$ to $10$ times larger than the previously reported results by Reno, Quigg and Walker. We discuss implications of this new neutrino-nucleon cross section for a variety of current and future neutrino detectors.