A previous calculation of electroweak $\mathcal{O}(\alpha )$ corrections to deep-inelastic neutrino scattering, as e.g. measured by NuTeV and NOMAD, is supplemented by higher-order effects. In detail, we take into account universal two-loop effects from $\Delta \alpha$ and $\Delta \rho$ as well as higher-order final-state photon radiation off muons in the structure function approach. Moreover, we make use of the recently released $\mathcal{O}(\alpha )$-improved parton distributions MRST2004QED and identify the relevant QED factorization scheme, which is DIS-like. As a technical by-product, we describe slicing and subtraction techniques for an efficient calculation of a new type of real corrections that are induced by the generated photon distribution. A numerical discussion of the higher-order effects suggests that the remaining theoretical uncertainty from unknown electroweak corrections is dominated by nonuniversal two-loop effects and is of the order 0.0003 when translated into a shift in ${sin}^2{\theta }_{\mathrm{W}}=1-M_{\mathrm{W}}^2/M_{\mathrm{Z}}^2$. The $\mathcal{O}(\alpha )$ corrections implicitly included in the parton distributions lead to a shift of about 0.0004.

• Received 12 September 2005

DOI:https://doi.org/10.1103/PhysRevD.72.093002