Effect of possible stronger neutrino interaction at $E_{\nu_\mu}\sim   10^{11}$ GeV upon the extraction of $\sin^2 \theta_W$ from the   neutral-current cross section at NuTeV
  The possibility exists that cosmic-ray neutrinos with energies of $\sim 10^{20}$ eV interact in the atmosphere with a cross section at the millibarn level, giving rise to some of the highest-energy air showers. In a specific dynamical model which can give rise to such a cross section, we show that there can be a small effect upon the extraction of the effective value of $\sin^2 \theta_W$ from $\nu_\mu$-hadron, neutral-current cross section data at NuTeV. 
Saul Barshay and Georg Kreyerhoff