Precise measurement of neutrino and antineutrino differential cross sections

The NuTeV experiment at Fermilab has obtained a unique high-statistics sample of neutrino and antineutrino interactions using its high-energy sign-selected beam. We present a measurement of the differential cross section for charged-current neutrino and antineutrino scattering from iron. We determine the relative $\overline{\ensuremath{\nu}}$ to $\ensuremath{\nu}$ cross section, $r={\ensuremath{\sigma}}^{\overline{\ensuremath{\nu}}}/{\ensuremath{\sigma}}^{\ensuremath{\nu}}$, at high energy with errors a factor of 2 smaller than the previous world average. Structure functions, ${F}_{2}(x,{Q}^{2})$ and $x{F}_{3}(x,{Q}^{2})$, are determined by fitting the inelasticity, $y$, dependence of the cross sections. This measurement has significantly improved systematic precision as a consequence of more precise understanding of hadron and muon energy scales.