Shadowing of ultrahigh energy neutrinos

The rise with energy of the neutrino-nucleon cross section implies that at energies above few TeV the Earth is becoming opaque to cosmic neutrinos. The neutrinos interact with the nucleons through the weak charged current, resulting into absorption, and the weak neutral current, which provides a redistribution of the neutrino energy. We Mellin transform the neutrino transport equation and find its exact solution in the moment space. A simple analytical formula is provided, which describes accurately the neutrino spectrum, after the neutrinos have traversed the Earth. The effect of the weak neutral current is most prominent for an initial flat neutrino spectrum and we find that at low energies (around 1 TeV) the neutrino intensity is even enhanced.