Propagation of ultrahigh-energy neutrinos through the Earth

The dispersion relation in matter of ultrahigh-energy neutrinos above the pole of the $W$ resonance ($E_{\nu} \gsim {\rm 10}^{7} {\rm GeV} $), is studied. We perform our calculation using the real-time formulation of Thermal Field Theory in which the massless limit for the $W$ boson is taken. The range of active-to-sterile neutrino oscillation parameters for which there is significant mixing enhancement during propagation through the interior of the Earth, and therefore significant attenuation of neutrino beams in the Earth at high energies, is estimated. Finally, this range is considered in view of the cosmological and astrophysical constraints.