Disentangling neutrino-nucleon cross section and high energy neutrino flux with a km3 neutrino telescope

The energy-zenith angular event distribution in a neutrino telescope provides a unique tool to determine at the same time the neutrino-nucleon cross section at extreme kinematical regions, and the high-energy neutrino flux. By using a simple parametrization for fluxes and cross sections, we present a sensitivity analysis for the case of a km3 neutrino telescope. In particular, we consider the specific case of an underwater Mediterranean telescope placed at the NEMO site, although most of our results also apply to an under-ice detector such as IceCube. We determine the sensitivity to departures from standard values of the cross sections above 1 PeV which can be probed independently from an a priori knowledge of the normalization and energy dependence of the flux. We also stress that the capability to tag downgoing neutrino showers in the PeV range against the cosmic-ray induced background of penetrating muons appears to be a crucial requirement to derive meaningful constraints on the cross section.