Ultra-High Energy Neutrino-Nucleon Scattering and Parton Distributions at Small x

The cross section for ultra-high energy neutrino-nucleon scattering is very sensitive to the parton distributions at very small values of Bjorken x ($x \leq 10^{-4})$. We numerically investigate the effects of modifying the behavior of the gluon distribution function at very small $x$ in the DGLAP evolution equation. We then use the Color Glass Condensate formalism to calculate the neutrino-nucleon cross section at ultra-high energies and compare the result with those based on modification of DGLAP evolution equation.