  We present a new calculation of the cross sections for charged current (CC)
and neutral current (NC) $\nu N$ and $\bar{\nu} N$ interactions in the neutrino
energy range $10^{4}<E_{\nu}<10^{12}$ GeV using the most recent MSTW parton
distribution functions (PDFs), MSTW 2008. We also present the associated
uncertainties propagated from the PDFs, as well as parametrizations of the
cross section central values, their uncertainty bounds, and the inelasticity
distributions for ease of use in Monte Carlo simulations. For the latter we
only provide parametrizations for energies above $10^7$ GeV. Finally, we assess
the feasibility of future neutrino experiments to constrain the $\nu N$ cross
section in the ultra-high energy (UHE) regime using a technique that is
independent of the flux spectrum of incident neutrinos. A significant deviation
from the predicted Standard Model cross sections could be an indication of new
physics, such as extra space-time dimensions, and we present expected
constraints on such models as a function of the number of events observed in a
future subterranean neutrino detector.
